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A spatial optimization algorithm for geodesign
Landscape and Urban Planning 144 (2015) 10–21
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Landscape and Urban Planning journal homepage: www.elsevier.com/locate/landurbplan
Research paper
A spatial optimization algorithm for geodesign Tessa Eikelboom a,∗ , Ron Janssen a , Theodor J. Stewart b,c a
Department of Spatial Economics, Faculty of Economics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands Department of Statistical Sciences, University of Cape Town, Rondebosch 7701, South Africa c Manchester Business School, The University of Manchester, Manchester M15 6PB, UK b
a r t i c l e
i n f o
Article history: Received 3 February 2015 Received in revised form 3 August 2015 Accepted 15 August 2015
1. Introduction Combining expert knowledge with local knowledge in collaborative workshops is becoming common in land use planning. In the past, planners presented their information on large hard copies of maps and used sheets of tracing paper to add stakeholder information to the map (Burrough, McDonnell, Burrough, & McDonnell, 1998). The arrival of Geographical Information Systems (GIS) replaced the transparent maps by map layers presented within a GIS on a computer screen (Longley, Goodchild, Maguire, & Rhind, 2005). The next step was the development of a large number of spatial decision support systems to assist decision makers in the field of resource allocation and, in particular, spatial planning issues (Geertman & Stillwell, 2009). In recent years involvement of stakeholders has increased. In the early years, the emphasis was on communication; in later years this shifted to participation where active involvement of stakeholders was required (Sieber, 2006). At present, the focus is on collaboration: stakeholders actively working together to reach the best result. Support systems evolved along ´ ´ & Meredith, 2004; c, with this development (Balram, Dragicevi Dragicevic & Balram, 2006). This typically involved map-based tools to support group work and collaborative tasks (Carver, 2003; Jankowski, 2009; Zellner, Lyons, Hoch, & Weizeorick, 2012). These tools could be used in face-to-face meetings on location but could also be used online (Kingston, Carver, Evans, & Turton, 2000). Parallel to this process has been a movement to combine the sketching approach, common in landscape architecture, with numerical analysis available in GIS (Bishop, 2013). This combination has recently been labelled “Geodesign” and is defined as follows:
∗ Corresponding author. Tel.: +31 30 5985170; fax: +31 20 5989 553. E-mail address: [email protected] (T. Eikelboom). http://dx.doi.org/10.1016/j.landurbplan.2015.08.011 0169-2046/© 2015 Elsevier B.V. All rights reserved.
Geodesign is a design and planning method which tightly couples the creation of design proposals with impact simulations informed by geographic contexts, systems thinking and digital technology (Steinitz, 2012, p.12). Combining the creation of design proposals with numerical analysis requires interactive approaches and opens the way to quantitative decision support techniques such as multi-criteria analysis and optimization. This may well lead to a revival of the use of optimization in the planning process as optimization systematically searches through the space of management options (Seppelt, Lautenbach, & Volk, 2013; Stewart & Janssen, 2014). This study presents a genetic algorithm for spatial optimization to be used in collaborative planning workshops. A current planning process to develop a long-term adaptation strategy for the peat meadow area of the province of Friesland is used as an illustration of the potential use of the algorithm. Results of the optimization are compared with the results achieved by stakeholders in collaborative workshops (see also Janssen, Eikelboom, Brouns, & Verhoeven, 2014). The utility of optimization models to generate planning alternatives and to facilitate their evaluation and elaboration was already recognized in 1979 by Brill et al. and is still considered a promising method for generating alternative land-use designs, for further consideration in spatial decision-making (Duke, Dundas, & Messer, 2013; Ligmann-Zielinska, Church, & Jankowski, 2008). Change to attribute values is needed to be able to maximize the objectives. Using these algorithms creates analytical and computational problems. GIS makes use of two types of data: attribute data and topology (Longley et al., 2005). An attribute table includes both the decision variables, e.g. types of land use, together with any attribute values which need to be included in the objective functions. Topologies are typically arranged using one of two models: vector or raster. Entities in vector format are represented by strings of coordinates (points). Two points can be connected to form a line segment, while sequences of lines can be connected end to end, returning to the starting point to form a polygon (parcel or area).
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Attribute data are stored for each polygon (which can be of varying sizes). Data in a raster model are stored in a two-dimensional matrix of uniformly sized cells on a regular grid. Depending on the model used, each grid cell is assumed to have homogeneous properties. By their nature raster data are substantially easier to include in mathematical representations for purposes of optimization. As a result most GIS-based applications of multi objective optimization use raster-based data as their input (Cao et al., 2011; Karakostas & Economou, 2013; Klein, Holzkamper, Calanca, Seppelt, & Fuhrer, 2013; Ko & Chang, 2012; Porta et al., 2013). Using a rasterbased representation of a planning region Janssen, van Herwijnen, Stewart, and Aerts (2008) showed that it was possible to formulate a spatial planning problem in mathematical terms and apply multi objective optimization to generate optimal solutions interactively. Unfortunately, they also had to conclude that using a grid size which would realistically describe the planning region leads to unrealistically long computation times, as a result of the large number of decision variables. This prevented use in a fully interactive setting where short response times are essential. Although it is clear that a vector representation leads to a more efficient representation of the problem, it is also clear that the switch from raster to vector creates new complications. In a raster each grid cell has the same shape and size, borders on exactly four other grid cells and has four borders of equal length. In a vector format each polygon can have any shape and size, and have any number of borders of various lengths. Janssen et al. (2008) differentiate between two types of objectives, namely: simple additive objectives, which associate costs and/or benefits with the allocation of any particular land use to a specific cell, then sum these cost and/or benefits across all cells; and spatial objectives which indicate the extent to which the different land uses are contiguous (i.e., the extent to which activities are or are not fragmented across the region). The shift from a grid to vector-based representation does not create great difficulties for the additive objectives. The differences in area size of the decision units can easily be accommodated using area size as a weighting factor in calculating overall performance. The shift from raster to vector is not so easily implemented for the spatial objectives, as we shall discuss in the next section. The main goal of this study is to solve a reference point (generalized goal programming) representation that can be used to generate land use plans which maximize both additive and spatial objectives in a vector-based GIS environment. The conceptual basis of the reference point approach is described by Miettinen, Ruiz, and Wierzbicki (2008). In essence it finds the nearest Pareto optimal solution (i.e. in which no objective can be improved without loss to at least one other objective) to a set of aspirations (goals) defined by the user (as described later). By experimenting with different aspiration levels, a sequence of alternative Pareto optimal solutions can be generated by the algorithm. The approachis a follow up to a similar algorithm developed for raster environments (Janssen et al., 2008; Stewart, Janssen, & van Herwijnen, 2004). A full mathematical description and numerical testing of the vector-based version can be found in Stewart and Janssen (Stewart & Janssen, 2014). The present study focuses on application of the algorithm. To test its usefulness it was integrated in a geodesign tool and applied to a planning process in a peat meadow area in the Netherlands (see also Janssen et al., 2014). The objective of this study is to demonstrate the potential and limitations of a genetic optimization algorithm to support collaborative land use planning workshops. The following questions will be addressed:
• Can the algorithm be used to generate a relevant set of alternatives to be used to start the decision process? This could be alternatives linked to objectives of specific groups of
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stakeholders, but could also be intermediate alternatives or even the full set of non-dominated alternatives. • What are the similarities and differences between collaborative planning results and the results achieved by the algorithm and can these differences be explained? • How can stakeholder input be combined with results from the algorithm in an interactive design process to get the best of both worlds? Section 2 provides a brief outline of the model developed in Stewart and Janssen (2014), describing the formal problem formulation in mathematical terms, the (generalized goal programming model and the numerical solution to this model by means of a genetic algorithm approach. Section 3 addresses the integration of the algorithm within the decision support system and describes the graphical interface between algorithm and user. Sections 4–6 present results. Section 4 shows how the algorithm can be used to generate a set of non-dominated alternatives and to start the collaborative workshop. Section 5 focusses on the differences between interactive and computational design, where plans generated by the stakeholders in collaborative workshops are compared with plans generated by the algorithm. Section 6 combines stakeholder input with model results and describes the use of the algorithm in an iterative design process. Finally, Section 7 provides conclusions.
2. The optimization model This section describes the structure of the Proximity Optimized Land Use Model. To suit interactive decision making, the optimization model has to permit land use changes, changes in restriction on total area for each land use, changes in objective weights, and the possibility to influence the importance of additive and spatial objectives. The primary decision problem is that of selecting a land use (out of a list of K possibilities) for each of N parcels of land defined in a GIS. It is convenient to represent the problem in terms of NK binary variables ıpk where ıpk = 1 if and only if land use k is allocated to parcel p (otherwise ıpk = 0). Each parcel is allocated one and only one land use. This implies the algebraic constraint: K
ıpk = 1 for
p = 1, 2, . . ., N
(1)
k=1
Two further sets of constraints may be imposed to limit the choice of ıpk : • Bounds on total area allocated to a given land use: Let ap be the area of parcel p. The total area allocated to land use k is thus given N by a ı . It is possible that lower and upper bounds on the p=1 p pk area allocated to land use k, say ALk and AU respectively, may need k to be imposed, requiring then that choice of decision variables need to be subject to constraints of the form:
ALk ≤
N
ap ıpk ≤ AU k
for
k = 1, 2, . . ., K
(2)
p=1
• Restrictions on specific combinations: In some cases, a parcel p may be unsuited to land use k, in which case the restriction ıpk = 0 is imposed for this combination. Alternatively, the user may wish to fix the land use allocated to parcel p to choice ; this may be achieved by specifying this parcel to be unsuitable for all land uses k = / .
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each parcel p, all other parcels were ranked in order of increasing distance from p, and the nearest n parcels as proximate to parcel p were selected. Denote the set of parcels proximate to p by p , and define p as the maximum distance dpq for all q ∈ p . In effect, all parcels proximate to p have centroids within a circle of radius p around the centroid of parcel p. The aim is then, for each type of land use, to maximize the degree of proximity of those parcels which are allocated this land use. See Stewart and Janssen (2014) for a formal definition of this measure of proximity. 2.3. Aggregation of multiple objectives
Fig. 1. Illustration of proximity relations between the polygon marked (A) and three others, where (B) is adjacent and proximate to (A) and (C) is not adjacent but within the radius defining proximity, and (D) is not proximate to (A) (Stewart & Janssen, 2014).
2.1. Additive objectives Any optimization study requires specification of the objectives to be optimized. In most cases of interest, there exist multiple objectives that need to be aggregated in some way. The easiest objective form is additive: for each of M concerns (often referred to as criteria), some form of value can be realized by the allocation of land use k to parcel p. Let vpjk be the value realized in terms of criterion j if land use k is allocated to parcel p. ‘Additive’ in this context, means that the overall value achieved in terms of criterion j is obtained as the area-weighted average of the values in each parcel, i.e. Vj defined by:
N K Vj =
p=1
v ı a k=1 pjk pk p
N
for
a p=1 p
j = 1, 2, . . ., M
(3)
which sums the values realized by the ıpk selections multiplied by the area of the parcel, divided by the total area. 2.2. Spatial objectives A less directly quantitative type of objective is to ensure that the spatial extent of each land use should be sufficiently compact to allow proper management. Various compactness measures have been suggested (e.g., Aerts, Eisinger, Heuvelink, & Stewart, 2003; Porta et al., 2013; Santé-Riveira, Boullón-Magán, Crecente-Maseda, & Miranda-Barrós, 2008; Vanegas, Cattrysse, & Van Orshoven, 2011). In Stewart et al. (2004) a series of cluster-based measures was derived from qualitative expressions of preference for different layout patterns, but these were based on a regular grid representation of the region. This cluster-based approach raised many implementation problems when extended to a more general vector-based GIS structure. With small adaptations, the model presented below is that of the proximity-based approach described initially in Stewart and Janssen (2014), in which it was demonstrated that the resulting land use clusters were more-orless indistinguishable from those obtained when optimizing the cluster-based measures directly. The proximity model however is much more rapidly and easily implemented than the clustering approach. The proximity spatial objective is based on the centroid-tocentroid distances between pairs of land parcels (Fig. 1). Let (xp , yp ) be the coordinates of the centroid of parcel p. The distance between any pair of parcels p and q was defined by the Euclidean distance between their centroids: dpq =
(xp − xq )2 + (yp − yq )2 . Then, for
In effect, there is a total of M + K objectives (where M is the number of criteria and K the number of land uses). For ease of further explanation, the relevant achievement measures to be maximized are defined by zi for i = 1, 2, . . ., M + K, where zj = Vj for j = 1, . . ., M and zM+k represents the proximity measure defined by Stewart and Janssen (2014) for land uses k = 1, . . ., K. In this study, the objectives are all comparably scaled between 0 and 1. Aggregation of the objectives by weighted summation, i.e. to optimize a function of the M+K form Z = wi zi , is a flawed approach in general, and can geni=1 erate highly misleading results (Miettinen, 2008, p11 and p40). In brief, there are two reasons for this assertion:In non-convex problems (the spatial objectives will not in general be expected to be convex), there may exist efficient (potentially optimal solutions) which are not reachable by any weighted summation. Even for convex problems, the weighted sum approach implies constant preference tradeoffs at all performance levels, a property which is seldom true in general (for example, decreasing marginal values are typical). This study followed the interactive reference point approach as described in Stewart and Janssen (2014), but with a modification to what they term the scalarizing function to produce a smoother function which was found numerically convenient. For each objective, first an estimated “ideal” level, Ii , was established. For the spatial objectives, a tight enough clustering will make the proximity objective close to 1, so that it suffices to set IM+k = 1. For the additive objectives, the constraints and individual parcel values may make Vj = 1 far from achievable. In order to obtain a more realistic estimate, the vpjk for the given objective j of all allowable combinations of p and k were sorted, and then a selection was made from the top (taking only the best suitable land use for each parcel), until all parcels are allocated. The resulting value of Vj for this allocation is an estimate of Ij . Then, for each objective, a “reference point” (or “aspiration level”) was selected less than the estimated ideal. These aspirations relate to the reference point methodology described earlier. They represent a desired level of achievement for each objective, and can be varied by the user experimentally (to see what may happen if higher levels of achievement are sought for some objectives, relative to others). Let Ai represent the aspiration level chosen in this way. An aggregated measure of goal achievement is then defined by the following scalarizing function to be minimized:
M+K
S=
i=1
Wi
I − z 4 i i Ii − Ai
(4)
Each of the bracketed terms in (4) has a functional form as illustrated in Fig. 2, which shows the relevant term for two possible values of the aspiration level when the underlying achievement level is scaled so that the ideal=1. Comparing the two curves it is clear how the term with a lower aspiration level is less than that for the higher aspiration at the same achievement level. However, when achievement for the objective with higher aspiration level
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Fig. 2. Scalarizing function terms for two possible values of the aspiration level relative to the ideal, namely 0.85 (corresponding to an objective with high aspiration) and 0.65 (moderate to low aspiration).
is high enough, further increases in achievement may contribute less to the improvement in S than increases in achievement for the objective with lesser aspiration but at a currently lower current level of achievement. More specifically, the following features may be observed: 1. When the value of zi exceeds the aspiration level Ai , further gains have very small marginal value, so that minimization of S avoids the problem which occurs with weighted summation in which extreme solutions often occur (very good on some objectives, while very poor on others). 2. On the other hand, the existence of positive marginal values, however small, ensures that the resulting solution is efficient (Pareto optimal). 3. As values of zi decrease below Ai , an increasingly severe penalty is placed on further reductions, tending to generate balanced solutions. Clearly, a shift in the aspiration level modifies the point at which the higher penalties come into play. It is possible also to affect the solutions by changing the weights Wi , which affect the magnitude of the penalties applied at the same relative underachievement of aspirations. Experience has however shown that the numerical results obtained are more sensitive to adaptation of the aspiration levels than to changes in the weights (Supplementary information). 3. Implementation in a geodesign tool The optimization routine was implemented in a geodesign tool. The model parameters were linked to interactive buttons. The tool was constructed with CommunityViz 4.3 Scenario 360, which is an extension to ArcGIS (Community VIZ, 2015). A previous version of the geodesign tool without optimization was successfully applied to support decision making in various planning activities (Janssen et al., 2014). Tool performance was studied in various evaluation studies (Eikelboom & Janssen, 2015). Hommerts, a small area in The Netherlands is used to demonstrate the use of the tool (Fig. 3). This area is part of a planning process to develop long term strategies for the peat meadow areas of the Dutch province of Friesland (Janssen et al., 2014). The size of the area is about 50 km2 and is mainly used for commercial dairy farming, but is also important for its high natural, cultural and historical values. Important problems in the region are soil subsidence
causing damage to buildings and infrastructure, deterioration of landscape values, and inefficient water management (Brouns et al., 2014). Options to change the area are land use changes, introduction of new crops and changes in water management. This study area is suitable for demonstrating the optimization algorithm as it concerns multiple objectives, land uses and spatial variations. The geodesign tool builds on the input of M × K value maps that represent the value of objective k for land use m. As an example, Fig. 4 shows the value maps for three objectives for land use intensive grassland. In the application the value maps are combined in the visualization of traffic light boxes that provide information on three stakeholder objectives simultaneously. The traffic light boxes show the status of three objectives where red means a low value and green a high value. When users apply changes that influence the values of the objectives, the colours of the boxes change accordingly. This visualization can be used to evaluate the impact of changes directly and the advantage of the boxes is that they can be placed on top of different maps and that they visualize three objectives simultaneously. The graphical user interface (Fig. 5) allows the decision makers to design spatial measures and receive real-time feedback on the effects. For this study, the tool was extended with buttons to change the optimization constraints. Users can interact with the interface in four ways: (A) change land use, (B) apply water management measures, (C) set optimization constraints, and (D) start optimization. After each change it takes only a few seconds to update the map dynamically. 4. Alternatives to start the decision process It is useful to start with a set of alternatives that provide an overview of the range of possible solutions. One possibility to do this is to generate a set of alternatives where each objective is maximized separately (single objective maxima) and combine this set with compromise alternatives. In this study the optimization algorithm was used to generate alternatives of single objective maxima for M objectives and one intermediate alternative based on equal weights. The objective weights Wi and additive objective aspiration levels Ai were varied to generate single objective maxima for agriculture, soil and nature, and an intermediate alternative (see also Section 2.3). The spatial aspiration level was set at its lowest value (0.4) because inclusion of spatial objectives decreases the importance of satisfying the additive objectives. Five different types
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Fig. 3. Dutch peat meadow area ‘Hommerts’.
of land uses were available: intensive and extensive grasslands, nature and wet crops hemp and algae. To provide an unrestricted decision space for the allocated amount of each land use no area constraints were applied. As expected, the generation of the single objective maxima with the optimization routine resulted in alternatives that each scored highest on the maximized objective. Fig. 6 shows that for each objective a different composition of land uses is preferred, also reflected in the allocated area for each land use (Table 1b). The intermediate alternative (Fig. 6d) results in intermediate values for all objectives. The alternative maximized for agriculture and the intermediate alternative have higher proximity scores compared with those alternatives maximized for soil and nature. This can also be observed from the maps (Fig. 6). The result is a set of non-dominated solutions to begin the planning process. A solution is non-dominated whether does not exist another feasible solution better than the current one in some
objective function without worsening other objective function (Belton & Stewart, 2002). The range of alternatives allows users to explore the decision space. In addition, these alternatives can support discussion as stakeholders often know exactly what they do not want instead of having a precise idea of their preferred solution. Proposals of other stakeholders can have a similar role, but the use of an optimization model can accelerate this negotiation process by providing the solution space systematically. 5. Interactive or computational design? This section summarizes the differences and similarities between interactive and computational designs. The optimization routine was used to generate alternatives similar to the strategies that were developed by stakeholders during a planning process in Friesland, the Netherlands. Aim of this process was to develop a long-term adaptation strategy for the peat meadow area of the
Fig. 4. Value maps for land use intensive grassland for objectives agriculture (a), soil (b) and nature (c). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 5. Graphical user interface of the geodesign tool that allows four types of interactions: (A) land use changes, (B) water management changes, (C) set optimization constraints, (D) start optimization.
province. Primary activities in this region are highly productive dairy farming, nature conservation, recreation and housing. The region is currently mainly used for commercial dairy farming but is also important for its high natural, cultural and historical values. Important problems in the region are soil subsidence causing damage to buildings and infrastructure, deterioration of landscape values, inefficient water management, poor water quality, and the changing perspectives for dairy farming (Janssen et al., 2014). For both approaches, the value maps representing the performance of the three objectives for each land use drove the decision making process. However, in addition to the value maps stakeholders also included local knowledge and information that was only indirectly related to the objectives such as land ownership, recent investments and water management infrastructure. To make the information manageable for the stakeholders the values of the three objectives were presented to the stakeholders as high (green) medium (yellow) or low (red), whereas the optimization routine used the quantitative values to allocate measures. In the workshop
stakeholders were asked to design a land use and water management plan for the following three policy strategies: 1. Business as usual: low impact technical measures only, no changes in land use; 2. Parallel tracks: create buffers to separate conflicting functions such as agriculture, housing and nature; 3. New Horizons: introduction of new crops, large changes in land use and water management. Each strategy implies different assumptions which were translated to qualitative objective weights. In the optimization constraints, these qualitative weights were translated to a numerical weight. The assignment for the first strategy ‘Business as usual’ was to apply low impact technical measures without changing land use. As a relatively simple measure the stakeholders decided to change the water level for intensive grasslands (Fig. 7a). To do
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Fig. 6. Optimization results of Maximized for agriculture (a), Maximized for soil (b), Maximized for nature (c), Intermediate (d).
Table 1 Non-dominated alternatives: (a) Objective weights, aspiration level and values, (b) land use, minimal and maximum area, allocated area, aspiration level, proximity score. (a) Additive objectives Alternatives Initial
Maximized for agriculture
Maximized for soil
Maximized for nature
Intermediate
Objectives
Weights
Aspiration level
Values
Agriculture Soil Nature Agriculture Soil Nature Agriculture Soil Nature Agriculture Soil Nature Agriculture Soil Nature
–
–
0.8 0.1 0.1 0.1 0.8 0.1 0.1 0.1 0.8 0.33 0.33 0.33
0.95 0.50 0.50 0.50 0.95 0.50 0.50 0.50 0.95 0.95 0.95 0.95
0.80 0.24 0.05 0.78 0.33 0.13 0.45 0.48 0.33 0.32 0.48 0.40 0.61 0.38 0.18
(b) Spatial objectives Alternatives
Land use
Alllocated area (ha)
Aspiration level
Proximity score
Initial Maximized for agriculture
Intensive grassland Extensive grassland Intensive grassland Nature Wet crop hemp Wet crop algae Extensive grassland Intensive grassland Nature Wet crop hemp Wet crop algae
2168 1146 1013 0 71 28 548 95 696 576 254 0 80 649 686 753 652 639 475 240 162
– 0.85 0.85 0.40 0.40 0.40 0.40 0.40 0.85 0.85 0.85 0.40 0.40 0.85 0.40 0.85 0.85 0.85 0.85 0.85 0.85
1.00 0.86 0.82 0 0.08 0 0.54 0.05 0.65 0.73 0.62 0 0.18 0.66 0.57 0.59 0.84 0.81 0.75 0.75 0.74
Maximized for soil
Maximized for nature
Extensive grassland Intensive grassland Nature Wet crop hemp Wet crop algae
Intermediate
Extensive grassland Intensive grassland Nature Wet crop hemp Wet crop algae
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Fig. 7. Strategy 1 ‘Business as usual’: stakeholder plan (a) and optimization result (b). Table 2 Strategy 1 ‘Business as usual’: (a) Objective weights, aspiration level and values, (b) land use, minimal and maximum area, allocated area, aspiration level, proximity score. (a) Additive objectives Business as usual
Objectives
Weights
Aspiration level
Values
Initial
Agriculture Soil Nature Agriculture Soil Nature Agriculture Soil Nature
–
–
+++ ++ + 0.5 0.4 0.1
–
0.80 0.24 0.05 0.78 0.35 0.12 0.76 0.37 0.14
Stakeholders
Optimization
0.95 0.85 0.65
(b) Spatial objectives Land use
Min area (ha)
Max area (ha)
Allocated Area (ha)
Aspiration level
Proximity score
Initial Intensive grassland
Intensive grassland 0
2168 2168
– 2168
1.00 –
No change Change in water level No change Change in water level
1500 0 1500 500
2168 2168 1650 650
1598 571 1515 654
– – 0.85 0.85
1 0.91 0.82 0.95 0.88 1
this they grouped parcels according to existing physical boundaries and selected parcels with one or more red traffic lights. In the optimization, stakeholder results were used to set the constraints. (Table 2b). As this strategy aims to improve agriculture, the weight and aspiration levels were set high for both the additive objectives (Table 2a) and the spatial objectives (Table 2b). Table 2 shows that both stakeholder and optimizer changed about 600 ha. Both did this in such a way that high proximity scores were achieved. Both approaches resulted in similar values for the objectives. However, Fig. 7 shows large differences in the spatial allocation of the measures: the stakeholders created four clusters of measures and the optimization routine grouped the changes in a single cluster (Fig. 7b).
Testing the sensitivity of this result by reducing the spatial aspiration level in the optimization resulted in higher values of the objectives but lower proximity scores. Furthermore, removing the area constraints led to 1500 ha with a change in water level and an increased in value for all three objectives. This alternative could serve as a reference to show stakeholders that allocating a larger area would increase the values. For the second strategy, ‘Parallel tracks’, stakeholders were asked to apply measures to separate different functions in the area. Houses in the area suffer from soil subsidence resulting from too low water levels and so stakeholders decided to allocate extensive grasslands with high water levels along the main road; this separates the houses from intensive grasslands with low water levels
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Fig. 8. Strategy 2 ‘Parallel tracks’: stakeholder plan (a) and optimization result (b).
Table 3 Strategy 2 ‘Parallel tracks’ (a) Objective weights, aspiration level and values, (b) land use, minimal and maximum area, allocated area, aspiration level, proximity score. (a) Additive objectives Parallel tracks
Objectives
Weights
Aspiration level
Values
Stakeholders
Agriculture Soil Nature Agriculture Soil Nature
++ ++ ++ 0.33 0.33 0.33
–
0.78 0.26 0.06 0.79 0.28 0.10
Optimization
0.50 0.50 0.50
(b) Spatial objectives Land use Extensive grassland Intensive grassland Extensive grassland Intensive grassland
Min area (ha)
Max area (ha)
–
–
227 1526
341 2289
(Fig. 8a). In the optimizer this was incorporated as a land use restriction such that only along the road extensive grasslands could be allocated. Contrary to the stakeholders the optimizer allocated the extensive grasslands to the south (Fig. 8b). These parcels were found to contribute to higher values for all three objectives (Table 3a). The stakeholders did not perform a comparative analysis and therefore were not aware of this variance. Other, unknown, reasons may have determined their decision to limit extensive grassland to the northern part of the area. The alternative generated by the optimizer could serve as a reference alternative for the stakeholders. For the strategy ‘New horizons’, stakeholders were asked to make radical changes to the area by allocating new crops by changing water management and land use. Stakeholders decided to allocate substantial areas of reed and wet crops. They tried to limit the changes to only a few landowners and did this in areas with a high number of red traffic lights for agriculture (Fig. 9a).
Allocated Area (ha)
Aspiration level
Proximity score
284 1908 354 1772
–
0.56 0.95 0.77 0.93
0.85 0.40
In the optimizer the areas allocated were included as area constraints. The optimization alternative resulted in similar objective values (Table 4a) and proximity scores (Table 4b) as the stakeholder plan. However, the maps show large differences (Fig. 9). It is clear that more than one solution exists. As the values of both plans are similar the result from the optimizer may serve as a point of reference for the stakeholders. 6. Iterative design This section demonstrates how the optimizer can be combined with user feedback to generate plans in an iterative way. In each step the optimizer presents a plan to the user. The user evaluates the plan and based on his/her preferences and local knowledge sets specifications and restrictions for the next round. The principle of this approach is shown in the example presented in Fig. 10. For practical reasons only three steps are shown. In the first step
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Fig. 9. Strategy 3 ‘New horizons’: stakeholder plan (a) and optimization result (b).
Table 4 Strategy 3 ‘New horizons’: (a) Objective weights, aspiration level and values, (b) land use, minimal and maximum area, allocated area, aspiration level, proximity value. (a) Additive objectives New horizons
Objectives
Weights
Stakeholders
Agriculture Soil Nature Agriculture Soil Nature
++ +++ + 0.3 0.6 0.1
Optimization
Aspiration level
Values
0.85 0.95 0.500
0.82 0.74 0.62 0.83 0.77 0.60
(b) Spatial objectives Land use
Min area (ha)
Max area (ha)
Allocated Area (ha)
Aspiration level
Proximity score
Intensive grassland Reed Wet crop hemp Wet crop algae Intensive grassland Reed Wet crop hemp Wet crop algae
0 0 0 0 0 0 0 0
1500 500 200 200 1500 500 200 200
1432 403 134 199 1432 403 134 199
0.40 0.85 0.85 0.854 0.40 0.85 0.85 0.854
0.88 0.84 0.75 0.72 0.90 0.89 0.70 0.68
the optimization algorithm generated an intermediate alternative with low spatial proximity aspiration. In the second step the spatial proximity scores were increased. In the third step both spatial aspiration and objective aspiration levels were raised. Step 1: In the first iteration, each land use was restricted to 1/5 of the total area and determined by dividing the total area by the number of land uses. In addition, equal objective weights and low spatial aspiration levels were set. This resulted in an intermediate alternative where land uses were scattered. Step 2: In response, the user selected parcels and restricted these for wet crop algae as allocated by the optimizer (shaded parcels). Also the users raised the spatial aspiration level of nature and wet
crops to cluster these land uses. This results in plan 2 with a cluster of wet crops around the restricted parcels and a cluster of nature in the north. This decision led to higher proximity scores and a slight decrease in objective values. Step 3: The users responded by restricting the parcels where farmers invested recently to remain intensive grassland (shaded area). The objective aspiration levels were raised to compensate for the decrease in values due to the second step. In addition, the users decrease the upper limit of nature area. The generated result (plan 3) is an alternative that has both higher objective values as well as higher proximity scores.
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Fig. 10. Iterative design with the use of optimization in three steps.
This example demonstrated how the optimization model can complement the interactive geodesign tool. Stakeholders can either accept, reject or adjust the results of the optimization model and thereby incorporate their preferences and local knowledge. 7. Conclusions This study addressed application of a genetic algorithm that can be used to generate land use plans that maximize both additive and spatial objectives in a vector-based GIS environment. To test the usefulness of the algorithm it was integrated in a geodesign tool and applied to a planning process in a peat meadow area in the Netherlands. The study showed how the algorithm can be used to (1) generate a set of alternatives to start a decision process, (2) to identify similarities and differences between collaborative planning results and results from optimization, and (3) as an interactive tool using feedback from stakeholders. It proved possible to generate a relevant set of non-dominated solutions to begin the planning process. The results showed that generating a set single objective maximum alternatives combined with compromise alternatives provides the stakeholder with a
set of alternatives that covers the range of possible solutions. Previous workshop experiences demonstrated that stakeholders first explore extreme situations to find out the influence of large changes. This exploration stage can be structured and accelerated using the optimization routine. When maximizing objectives, it has to be kept in mind that the spatial and additive objectives compete in achieving the best results for the area. Comparing results from the optimizer with stakeholder results demonstrated that both approaches generated plans with similar values for the objectives but with large differences in the maps that were produced. It is clear that there is no single optimal plan and that more than one solution exists. As the values of the objectives are similar to the stakeholder plans the result from the optimizer could be used as a point of reference for the stakeholders. One of the challenges in using an optimization for interactive design is to be able to explain the model assumptions such that the model results are accepted and found valid by the stakeholders. The model provides the user only with a result instead of the road to it. Integrating the optimizer in a geodesign tool demonstrated how the optimizer can complement stakeholder input if it is used as an interactive geodesign tool. Stakeholders can either accept, reject or
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adjust the results of the optimization model and thereby incorporate their preferences and local knowledge. The genetic algorithm has short response times which is a major prerequisite for interactive use. To conclude: collaborative planning is based on the assumption that the stakeholders have knowledge that is not, or even cannot be represented in a formal model. The challenge is to combine optimization with stakeholder input in such a way that both approaches complement each other to get the best of both worlds. References Aerts, J. C. J. H., Eisinger, E., Heuvelink, G. B. M., & Stewart, T. J. (2003). Using linear integer programming for multi-site land-use allocation. Geographical Analysis, 35, 148–169. ´ ´ T., & Meredith, T. (2004). A collaborative GIS method for Balram, S., Dragicevi c, integrating local and technical knowledge in establishing biodiversity conservation priorities. Biodiversity and Conservation, 13, 1195–1208. Belton, V., & Stewart, T. J. (2002). Multiple criteria decision analysis: An integrated approach. Dordrecht: Springer. Bishop, I. (2013). Optimization in geodesign. Landscape Architecture Frontiers, 1, 64–75. Brouns, K., Eikelboom, T., Jansen, P. C., Janssen, R., Kwakernaak, C., van den Akker, J. J. H., et al. (2015). Spatial analysis of soil subsidence in peat meadow areas in Friesland in relation to land and water management, climate change and adaptation. Journal of Environmental Management, 55. Burrough, P. A., McDonnell, R., Burrough, P. A., & McDonnell, R. (1998). Principles of geographical information systems (333 ed.). Oxford: Oxford University Press. Cao, K., Batty, M., Huang, B., Liu, Y., Yu, L., & Chen, J. (2011). Spatial multi-objective land use optimization: Extensions to the non-dominated sorting genetic algorithm-II. International Journal of Geographical Information Science, 25, 1949–1969. Carver, S. (2003). The future of participatory approaches using geographic information: Developing a research agenda for the 21st century. Urban and Regional Information Systems Association (URISA), 15(APA I), 61–72. Community VIZ, 2015. http://placeways.com/communityviz (last accessed 21-01-2015). Dragicevic, S., & Balram, S. (2006). Collaborative geographic information systems and science: A transdisciplinary evolution. In S. Balram, & S. Dragicevic (Eds.), Collaborative geographic information systems (pp. 341–350). Hershey, PA: Idea Group Publishers. Duke, J. M., Dundas, S. J., & Messer, K. D. (2013). Cost-effective conservation planning: Lessons from economics. Journal of Environmental Management, 125, 126–133. Eikelboom, T., & Janssen, R. (2015). Comparison of geodesign tools to communicate stakeholder values. Group Decision and Negotiation. Geertman, S., & Stillwell, J. (2009). Planning support systems: Best practices and new methods. Dordrecht: Springer. Jankowski, P. (2009). Towards participatory geographic information systems for community-based environmental decision making. Journal of Environmental Management, 90(6), 1966–1971. Janssen, R., Eikelboom, T., Brouns, K., & Verhoeven, J. T. A. (2014). Using geodesign to develop a spatial adaptation strategy for south east Friesland. In D. Lee, E.
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Dias, & H. J. Scholten (Eds.), Geodesign for land use planning. Dordrecht: Springer. Janssen, R., van Herwijnen, M., Stewart, T. J., & Aerts, J. C. J. H. (2008). Multiobjective decision support for land-use planning. Environment and Planning B—Planning & Design, 35, 740–756. Karakostas, S., & Economou, D. (2013). Enhanced multi-objective optimization algorithm for renewable energy sources: Optimal spatial development of wind farms. International Journal of Geographical Information Science, 28, 83–103. Kingston, R. P., Carver, S. J., Evans, A. J., & Turton, I. J. (2000). Web-based public participation geographical information systems: An aid to local environmental decision-making. Computers, Environment and Urban Systems, 24, 109–125. Klein, T., Holzkamper, A., Calanca, P., Seppelt, R., & Fuhrer, J. (2013). Adapting agricultural land management to climate change: A regional multi-objective optimization approach. Landscape Ecology, 28, 2029–2047. Ko, T. T., & Chang, Y. C. (2012). An integrated spatial planning model for climate change adaptation in coastal zones. Ocean & Coastal Management, 66, 36–45. Ligmann-Zielinska, A., Church, R. L., & Jankowski, P. (2008). Spatial optimization as a generative technique for sustainable multiobjective landuse allocation. International Journal of Geographical Information Science, 22, 601–622. Longley, P. A., Goodchild, M. F., Maguire, D. J., & Rhind, D. W. (2005). Geographic information systems and science. John Wiley & Sons (2nd Edition). Miettinen, K. (2008). Introduction to multiobjective optimization: Noninteractive approaches. In J. Branke, D. Kalyanmoy, K. Miettinen, & R. Slowinski (Eds.), Multiobjective optimization (pp. 1–26). Berlin, Heidelberg: Springer. Miettinen, K., Ruiz, F., & Wierzbicki, A. P. (2008). Introduction to multiobjective optimization: Interactive approaches. In J. Branke, D. Kalyanmoy, K. Miettinen, & R. Slowinski (Eds.), Multiobjective optimization (pp. 27–57). Berlin, Heidelberg: Springer. Porta, J., Parapar, J., Doallo, R., Rivera, F. F., Sante, I., & Crecente, R. (2013). High performance genetic algorithm for land use planning. Computers, Environment and Urban Systems, 37, 45–58. Santé-Riveira, I., Boullón-Magán, M., Crecente-Maseda, R., & Miranda-Barrós, D. (2008). Algorithm based on simulated annealing for land-use allocation. Computers & Geosciences, 34, 259–268. Seppelt, R., Lautenbach, S., & Volk, M. (2013). Identifying trade-offs between ecosystem services, land use, and biodiversity: A plea for combining scenario analysis and optimization on different spatial scales. Current Opinion in Environmental Sustainability, 5, 458–463. Sieber, R. (2006). Public participation geographic information systems: A literature review and framework. Annals of the Association of American Geographers, 96(3), 491–507. Steinitz, C. (2012). A framework for geodesign: Changing geography by design. Redlands, CA: ESRI Press. Stewart, T. J., & Janssen, R. (2014). A multiobjective GIS-based land use planning algorithm. Computers, Environment and Urban Systems, 46, 25–34. Stewart, T. J., Janssen, R., & van Herwijnen, M. (2004). A genetic algorithm approach to multiobjective land use planning. Computers & Operations Research, 31, 2293–2313. Vanegas, P., Cattrysse, D., & Van Orshoven, J. (2011). A multiple criteria heuristic solution method for locating near to optimal contiguous and compact sites in raster maps. In B. Murgante, G. Borruso, & A. Lapucci (Eds.), Geocomputation, sustainability and environmental planning (pp. 35–56). Berlin, Heidelberg: Springer. Zellner, M. L., Lyons, L. B., Hoch, C. J., & Weizeorick, J. (2012). Modeling, learning, and planning together: An application of participatory, agent-based modeling to environmental planning. URISA Journal, 24, 77–92.
Contents lists available at ScienceDirect
Landscape and Urban Planning journal homepage: www.elsevier.com/locate/landurbplan
Research paper
A spatial optimization algorithm for geodesign Tessa Eikelboom a,∗ , Ron Janssen a , Theodor J. Stewart b,c a
Department of Spatial Economics, Faculty of Economics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands Department of Statistical Sciences, University of Cape Town, Rondebosch 7701, South Africa c Manchester Business School, The University of Manchester, Manchester M15 6PB, UK b
a r t i c l e
i n f o
Article history: Received 3 February 2015 Received in revised form 3 August 2015 Accepted 15 August 2015
1. Introduction Combining expert knowledge with local knowledge in collaborative workshops is becoming common in land use planning. In the past, planners presented their information on large hard copies of maps and used sheets of tracing paper to add stakeholder information to the map (Burrough, McDonnell, Burrough, & McDonnell, 1998). The arrival of Geographical Information Systems (GIS) replaced the transparent maps by map layers presented within a GIS on a computer screen (Longley, Goodchild, Maguire, & Rhind, 2005). The next step was the development of a large number of spatial decision support systems to assist decision makers in the field of resource allocation and, in particular, spatial planning issues (Geertman & Stillwell, 2009). In recent years involvement of stakeholders has increased. In the early years, the emphasis was on communication; in later years this shifted to participation where active involvement of stakeholders was required (Sieber, 2006). At present, the focus is on collaboration: stakeholders actively working together to reach the best result. Support systems evolved along ´ ´ & Meredith, 2004; c, with this development (Balram, Dragicevi Dragicevic & Balram, 2006). This typically involved map-based tools to support group work and collaborative tasks (Carver, 2003; Jankowski, 2009; Zellner, Lyons, Hoch, & Weizeorick, 2012). These tools could be used in face-to-face meetings on location but could also be used online (Kingston, Carver, Evans, & Turton, 2000). Parallel to this process has been a movement to combine the sketching approach, common in landscape architecture, with numerical analysis available in GIS (Bishop, 2013). This combination has recently been labelled “Geodesign” and is defined as follows:
∗ Corresponding author. Tel.: +31 30 5985170; fax: +31 20 5989 553. E-mail address: [email protected] (T. Eikelboom). http://dx.doi.org/10.1016/j.landurbplan.2015.08.011 0169-2046/© 2015 Elsevier B.V. All rights reserved.
Geodesign is a design and planning method which tightly couples the creation of design proposals with impact simulations informed by geographic contexts, systems thinking and digital technology (Steinitz, 2012, p.12). Combining the creation of design proposals with numerical analysis requires interactive approaches and opens the way to quantitative decision support techniques such as multi-criteria analysis and optimization. This may well lead to a revival of the use of optimization in the planning process as optimization systematically searches through the space of management options (Seppelt, Lautenbach, & Volk, 2013; Stewart & Janssen, 2014). This study presents a genetic algorithm for spatial optimization to be used in collaborative planning workshops. A current planning process to develop a long-term adaptation strategy for the peat meadow area of the province of Friesland is used as an illustration of the potential use of the algorithm. Results of the optimization are compared with the results achieved by stakeholders in collaborative workshops (see also Janssen, Eikelboom, Brouns, & Verhoeven, 2014). The utility of optimization models to generate planning alternatives and to facilitate their evaluation and elaboration was already recognized in 1979 by Brill et al. and is still considered a promising method for generating alternative land-use designs, for further consideration in spatial decision-making (Duke, Dundas, & Messer, 2013; Ligmann-Zielinska, Church, & Jankowski, 2008). Change to attribute values is needed to be able to maximize the objectives. Using these algorithms creates analytical and computational problems. GIS makes use of two types of data: attribute data and topology (Longley et al., 2005). An attribute table includes both the decision variables, e.g. types of land use, together with any attribute values which need to be included in the objective functions. Topologies are typically arranged using one of two models: vector or raster. Entities in vector format are represented by strings of coordinates (points). Two points can be connected to form a line segment, while sequences of lines can be connected end to end, returning to the starting point to form a polygon (parcel or area).
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Attribute data are stored for each polygon (which can be of varying sizes). Data in a raster model are stored in a two-dimensional matrix of uniformly sized cells on a regular grid. Depending on the model used, each grid cell is assumed to have homogeneous properties. By their nature raster data are substantially easier to include in mathematical representations for purposes of optimization. As a result most GIS-based applications of multi objective optimization use raster-based data as their input (Cao et al., 2011; Karakostas & Economou, 2013; Klein, Holzkamper, Calanca, Seppelt, & Fuhrer, 2013; Ko & Chang, 2012; Porta et al., 2013). Using a rasterbased representation of a planning region Janssen, van Herwijnen, Stewart, and Aerts (2008) showed that it was possible to formulate a spatial planning problem in mathematical terms and apply multi objective optimization to generate optimal solutions interactively. Unfortunately, they also had to conclude that using a grid size which would realistically describe the planning region leads to unrealistically long computation times, as a result of the large number of decision variables. This prevented use in a fully interactive setting where short response times are essential. Although it is clear that a vector representation leads to a more efficient representation of the problem, it is also clear that the switch from raster to vector creates new complications. In a raster each grid cell has the same shape and size, borders on exactly four other grid cells and has four borders of equal length. In a vector format each polygon can have any shape and size, and have any number of borders of various lengths. Janssen et al. (2008) differentiate between two types of objectives, namely: simple additive objectives, which associate costs and/or benefits with the allocation of any particular land use to a specific cell, then sum these cost and/or benefits across all cells; and spatial objectives which indicate the extent to which the different land uses are contiguous (i.e., the extent to which activities are or are not fragmented across the region). The shift from a grid to vector-based representation does not create great difficulties for the additive objectives. The differences in area size of the decision units can easily be accommodated using area size as a weighting factor in calculating overall performance. The shift from raster to vector is not so easily implemented for the spatial objectives, as we shall discuss in the next section. The main goal of this study is to solve a reference point (generalized goal programming) representation that can be used to generate land use plans which maximize both additive and spatial objectives in a vector-based GIS environment. The conceptual basis of the reference point approach is described by Miettinen, Ruiz, and Wierzbicki (2008). In essence it finds the nearest Pareto optimal solution (i.e. in which no objective can be improved without loss to at least one other objective) to a set of aspirations (goals) defined by the user (as described later). By experimenting with different aspiration levels, a sequence of alternative Pareto optimal solutions can be generated by the algorithm. The approachis a follow up to a similar algorithm developed for raster environments (Janssen et al., 2008; Stewart, Janssen, & van Herwijnen, 2004). A full mathematical description and numerical testing of the vector-based version can be found in Stewart and Janssen (Stewart & Janssen, 2014). The present study focuses on application of the algorithm. To test its usefulness it was integrated in a geodesign tool and applied to a planning process in a peat meadow area in the Netherlands (see also Janssen et al., 2014). The objective of this study is to demonstrate the potential and limitations of a genetic optimization algorithm to support collaborative land use planning workshops. The following questions will be addressed:
• Can the algorithm be used to generate a relevant set of alternatives to be used to start the decision process? This could be alternatives linked to objectives of specific groups of
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stakeholders, but could also be intermediate alternatives or even the full set of non-dominated alternatives. • What are the similarities and differences between collaborative planning results and the results achieved by the algorithm and can these differences be explained? • How can stakeholder input be combined with results from the algorithm in an interactive design process to get the best of both worlds? Section 2 provides a brief outline of the model developed in Stewart and Janssen (2014), describing the formal problem formulation in mathematical terms, the (generalized goal programming model and the numerical solution to this model by means of a genetic algorithm approach. Section 3 addresses the integration of the algorithm within the decision support system and describes the graphical interface between algorithm and user. Sections 4–6 present results. Section 4 shows how the algorithm can be used to generate a set of non-dominated alternatives and to start the collaborative workshop. Section 5 focusses on the differences between interactive and computational design, where plans generated by the stakeholders in collaborative workshops are compared with plans generated by the algorithm. Section 6 combines stakeholder input with model results and describes the use of the algorithm in an iterative design process. Finally, Section 7 provides conclusions.
2. The optimization model This section describes the structure of the Proximity Optimized Land Use Model. To suit interactive decision making, the optimization model has to permit land use changes, changes in restriction on total area for each land use, changes in objective weights, and the possibility to influence the importance of additive and spatial objectives. The primary decision problem is that of selecting a land use (out of a list of K possibilities) for each of N parcels of land defined in a GIS. It is convenient to represent the problem in terms of NK binary variables ıpk where ıpk = 1 if and only if land use k is allocated to parcel p (otherwise ıpk = 0). Each parcel is allocated one and only one land use. This implies the algebraic constraint: K
ıpk = 1 for
p = 1, 2, . . ., N
(1)
k=1
Two further sets of constraints may be imposed to limit the choice of ıpk : • Bounds on total area allocated to a given land use: Let ap be the area of parcel p. The total area allocated to land use k is thus given N by a ı . It is possible that lower and upper bounds on the p=1 p pk area allocated to land use k, say ALk and AU respectively, may need k to be imposed, requiring then that choice of decision variables need to be subject to constraints of the form:
ALk ≤
N
ap ıpk ≤ AU k
for
k = 1, 2, . . ., K
(2)
p=1
• Restrictions on specific combinations: In some cases, a parcel p may be unsuited to land use k, in which case the restriction ıpk = 0 is imposed for this combination. Alternatively, the user may wish to fix the land use allocated to parcel p to choice ; this may be achieved by specifying this parcel to be unsuitable for all land uses k = / .
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each parcel p, all other parcels were ranked in order of increasing distance from p, and the nearest n parcels as proximate to parcel p were selected. Denote the set of parcels proximate to p by p , and define p as the maximum distance dpq for all q ∈ p . In effect, all parcels proximate to p have centroids within a circle of radius p around the centroid of parcel p. The aim is then, for each type of land use, to maximize the degree of proximity of those parcels which are allocated this land use. See Stewart and Janssen (2014) for a formal definition of this measure of proximity. 2.3. Aggregation of multiple objectives
Fig. 1. Illustration of proximity relations between the polygon marked (A) and three others, where (B) is adjacent and proximate to (A) and (C) is not adjacent but within the radius defining proximity, and (D) is not proximate to (A) (Stewart & Janssen, 2014).
2.1. Additive objectives Any optimization study requires specification of the objectives to be optimized. In most cases of interest, there exist multiple objectives that need to be aggregated in some way. The easiest objective form is additive: for each of M concerns (often referred to as criteria), some form of value can be realized by the allocation of land use k to parcel p. Let vpjk be the value realized in terms of criterion j if land use k is allocated to parcel p. ‘Additive’ in this context, means that the overall value achieved in terms of criterion j is obtained as the area-weighted average of the values in each parcel, i.e. Vj defined by:
N K Vj =
p=1
v ı a k=1 pjk pk p
N
for
a p=1 p
j = 1, 2, . . ., M
(3)
which sums the values realized by the ıpk selections multiplied by the area of the parcel, divided by the total area. 2.2. Spatial objectives A less directly quantitative type of objective is to ensure that the spatial extent of each land use should be sufficiently compact to allow proper management. Various compactness measures have been suggested (e.g., Aerts, Eisinger, Heuvelink, & Stewart, 2003; Porta et al., 2013; Santé-Riveira, Boullón-Magán, Crecente-Maseda, & Miranda-Barrós, 2008; Vanegas, Cattrysse, & Van Orshoven, 2011). In Stewart et al. (2004) a series of cluster-based measures was derived from qualitative expressions of preference for different layout patterns, but these were based on a regular grid representation of the region. This cluster-based approach raised many implementation problems when extended to a more general vector-based GIS structure. With small adaptations, the model presented below is that of the proximity-based approach described initially in Stewart and Janssen (2014), in which it was demonstrated that the resulting land use clusters were more-orless indistinguishable from those obtained when optimizing the cluster-based measures directly. The proximity model however is much more rapidly and easily implemented than the clustering approach. The proximity spatial objective is based on the centroid-tocentroid distances between pairs of land parcels (Fig. 1). Let (xp , yp ) be the coordinates of the centroid of parcel p. The distance between any pair of parcels p and q was defined by the Euclidean distance between their centroids: dpq =
(xp − xq )2 + (yp − yq )2 . Then, for
In effect, there is a total of M + K objectives (where M is the number of criteria and K the number of land uses). For ease of further explanation, the relevant achievement measures to be maximized are defined by zi for i = 1, 2, . . ., M + K, where zj = Vj for j = 1, . . ., M and zM+k represents the proximity measure defined by Stewart and Janssen (2014) for land uses k = 1, . . ., K. In this study, the objectives are all comparably scaled between 0 and 1. Aggregation of the objectives by weighted summation, i.e. to optimize a function of the M+K form Z = wi zi , is a flawed approach in general, and can geni=1 erate highly misleading results (Miettinen, 2008, p11 and p40). In brief, there are two reasons for this assertion:In non-convex problems (the spatial objectives will not in general be expected to be convex), there may exist efficient (potentially optimal solutions) which are not reachable by any weighted summation. Even for convex problems, the weighted sum approach implies constant preference tradeoffs at all performance levels, a property which is seldom true in general (for example, decreasing marginal values are typical). This study followed the interactive reference point approach as described in Stewart and Janssen (2014), but with a modification to what they term the scalarizing function to produce a smoother function which was found numerically convenient. For each objective, first an estimated “ideal” level, Ii , was established. For the spatial objectives, a tight enough clustering will make the proximity objective close to 1, so that it suffices to set IM+k = 1. For the additive objectives, the constraints and individual parcel values may make Vj = 1 far from achievable. In order to obtain a more realistic estimate, the vpjk for the given objective j of all allowable combinations of p and k were sorted, and then a selection was made from the top (taking only the best suitable land use for each parcel), until all parcels are allocated. The resulting value of Vj for this allocation is an estimate of Ij . Then, for each objective, a “reference point” (or “aspiration level”) was selected less than the estimated ideal. These aspirations relate to the reference point methodology described earlier. They represent a desired level of achievement for each objective, and can be varied by the user experimentally (to see what may happen if higher levels of achievement are sought for some objectives, relative to others). Let Ai represent the aspiration level chosen in this way. An aggregated measure of goal achievement is then defined by the following scalarizing function to be minimized:
M+K
S=
i=1
Wi
I − z 4 i i Ii − Ai
(4)
Each of the bracketed terms in (4) has a functional form as illustrated in Fig. 2, which shows the relevant term for two possible values of the aspiration level when the underlying achievement level is scaled so that the ideal=1. Comparing the two curves it is clear how the term with a lower aspiration level is less than that for the higher aspiration at the same achievement level. However, when achievement for the objective with higher aspiration level
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Fig. 2. Scalarizing function terms for two possible values of the aspiration level relative to the ideal, namely 0.85 (corresponding to an objective with high aspiration) and 0.65 (moderate to low aspiration).
is high enough, further increases in achievement may contribute less to the improvement in S than increases in achievement for the objective with lesser aspiration but at a currently lower current level of achievement. More specifically, the following features may be observed: 1. When the value of zi exceeds the aspiration level Ai , further gains have very small marginal value, so that minimization of S avoids the problem which occurs with weighted summation in which extreme solutions often occur (very good on some objectives, while very poor on others). 2. On the other hand, the existence of positive marginal values, however small, ensures that the resulting solution is efficient (Pareto optimal). 3. As values of zi decrease below Ai , an increasingly severe penalty is placed on further reductions, tending to generate balanced solutions. Clearly, a shift in the aspiration level modifies the point at which the higher penalties come into play. It is possible also to affect the solutions by changing the weights Wi , which affect the magnitude of the penalties applied at the same relative underachievement of aspirations. Experience has however shown that the numerical results obtained are more sensitive to adaptation of the aspiration levels than to changes in the weights (Supplementary information). 3. Implementation in a geodesign tool The optimization routine was implemented in a geodesign tool. The model parameters were linked to interactive buttons. The tool was constructed with CommunityViz 4.3 Scenario 360, which is an extension to ArcGIS (Community VIZ, 2015). A previous version of the geodesign tool without optimization was successfully applied to support decision making in various planning activities (Janssen et al., 2014). Tool performance was studied in various evaluation studies (Eikelboom & Janssen, 2015). Hommerts, a small area in The Netherlands is used to demonstrate the use of the tool (Fig. 3). This area is part of a planning process to develop long term strategies for the peat meadow areas of the Dutch province of Friesland (Janssen et al., 2014). The size of the area is about 50 km2 and is mainly used for commercial dairy farming, but is also important for its high natural, cultural and historical values. Important problems in the region are soil subsidence
causing damage to buildings and infrastructure, deterioration of landscape values, and inefficient water management (Brouns et al., 2014). Options to change the area are land use changes, introduction of new crops and changes in water management. This study area is suitable for demonstrating the optimization algorithm as it concerns multiple objectives, land uses and spatial variations. The geodesign tool builds on the input of M × K value maps that represent the value of objective k for land use m. As an example, Fig. 4 shows the value maps for three objectives for land use intensive grassland. In the application the value maps are combined in the visualization of traffic light boxes that provide information on three stakeholder objectives simultaneously. The traffic light boxes show the status of three objectives where red means a low value and green a high value. When users apply changes that influence the values of the objectives, the colours of the boxes change accordingly. This visualization can be used to evaluate the impact of changes directly and the advantage of the boxes is that they can be placed on top of different maps and that they visualize three objectives simultaneously. The graphical user interface (Fig. 5) allows the decision makers to design spatial measures and receive real-time feedback on the effects. For this study, the tool was extended with buttons to change the optimization constraints. Users can interact with the interface in four ways: (A) change land use, (B) apply water management measures, (C) set optimization constraints, and (D) start optimization. After each change it takes only a few seconds to update the map dynamically. 4. Alternatives to start the decision process It is useful to start with a set of alternatives that provide an overview of the range of possible solutions. One possibility to do this is to generate a set of alternatives where each objective is maximized separately (single objective maxima) and combine this set with compromise alternatives. In this study the optimization algorithm was used to generate alternatives of single objective maxima for M objectives and one intermediate alternative based on equal weights. The objective weights Wi and additive objective aspiration levels Ai were varied to generate single objective maxima for agriculture, soil and nature, and an intermediate alternative (see also Section 2.3). The spatial aspiration level was set at its lowest value (0.4) because inclusion of spatial objectives decreases the importance of satisfying the additive objectives. Five different types
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Fig. 3. Dutch peat meadow area ‘Hommerts’.
of land uses were available: intensive and extensive grasslands, nature and wet crops hemp and algae. To provide an unrestricted decision space for the allocated amount of each land use no area constraints were applied. As expected, the generation of the single objective maxima with the optimization routine resulted in alternatives that each scored highest on the maximized objective. Fig. 6 shows that for each objective a different composition of land uses is preferred, also reflected in the allocated area for each land use (Table 1b). The intermediate alternative (Fig. 6d) results in intermediate values for all objectives. The alternative maximized for agriculture and the intermediate alternative have higher proximity scores compared with those alternatives maximized for soil and nature. This can also be observed from the maps (Fig. 6). The result is a set of non-dominated solutions to begin the planning process. A solution is non-dominated whether does not exist another feasible solution better than the current one in some
objective function without worsening other objective function (Belton & Stewart, 2002). The range of alternatives allows users to explore the decision space. In addition, these alternatives can support discussion as stakeholders often know exactly what they do not want instead of having a precise idea of their preferred solution. Proposals of other stakeholders can have a similar role, but the use of an optimization model can accelerate this negotiation process by providing the solution space systematically. 5. Interactive or computational design? This section summarizes the differences and similarities between interactive and computational designs. The optimization routine was used to generate alternatives similar to the strategies that were developed by stakeholders during a planning process in Friesland, the Netherlands. Aim of this process was to develop a long-term adaptation strategy for the peat meadow area of the
Fig. 4. Value maps for land use intensive grassland for objectives agriculture (a), soil (b) and nature (c). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 5. Graphical user interface of the geodesign tool that allows four types of interactions: (A) land use changes, (B) water management changes, (C) set optimization constraints, (D) start optimization.
province. Primary activities in this region are highly productive dairy farming, nature conservation, recreation and housing. The region is currently mainly used for commercial dairy farming but is also important for its high natural, cultural and historical values. Important problems in the region are soil subsidence causing damage to buildings and infrastructure, deterioration of landscape values, inefficient water management, poor water quality, and the changing perspectives for dairy farming (Janssen et al., 2014). For both approaches, the value maps representing the performance of the three objectives for each land use drove the decision making process. However, in addition to the value maps stakeholders also included local knowledge and information that was only indirectly related to the objectives such as land ownership, recent investments and water management infrastructure. To make the information manageable for the stakeholders the values of the three objectives were presented to the stakeholders as high (green) medium (yellow) or low (red), whereas the optimization routine used the quantitative values to allocate measures. In the workshop
stakeholders were asked to design a land use and water management plan for the following three policy strategies: 1. Business as usual: low impact technical measures only, no changes in land use; 2. Parallel tracks: create buffers to separate conflicting functions such as agriculture, housing and nature; 3. New Horizons: introduction of new crops, large changes in land use and water management. Each strategy implies different assumptions which were translated to qualitative objective weights. In the optimization constraints, these qualitative weights were translated to a numerical weight. The assignment for the first strategy ‘Business as usual’ was to apply low impact technical measures without changing land use. As a relatively simple measure the stakeholders decided to change the water level for intensive grasslands (Fig. 7a). To do
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Fig. 6. Optimization results of Maximized for agriculture (a), Maximized for soil (b), Maximized for nature (c), Intermediate (d).
Table 1 Non-dominated alternatives: (a) Objective weights, aspiration level and values, (b) land use, minimal and maximum area, allocated area, aspiration level, proximity score. (a) Additive objectives Alternatives Initial
Maximized for agriculture
Maximized for soil
Maximized for nature
Intermediate
Objectives
Weights
Aspiration level
Values
Agriculture Soil Nature Agriculture Soil Nature Agriculture Soil Nature Agriculture Soil Nature Agriculture Soil Nature
–
–
0.8 0.1 0.1 0.1 0.8 0.1 0.1 0.1 0.8 0.33 0.33 0.33
0.95 0.50 0.50 0.50 0.95 0.50 0.50 0.50 0.95 0.95 0.95 0.95
0.80 0.24 0.05 0.78 0.33 0.13 0.45 0.48 0.33 0.32 0.48 0.40 0.61 0.38 0.18
(b) Spatial objectives Alternatives
Land use
Alllocated area (ha)
Aspiration level
Proximity score
Initial Maximized for agriculture
Intensive grassland Extensive grassland Intensive grassland Nature Wet crop hemp Wet crop algae Extensive grassland Intensive grassland Nature Wet crop hemp Wet crop algae
2168 1146 1013 0 71 28 548 95 696 576 254 0 80 649 686 753 652 639 475 240 162
– 0.85 0.85 0.40 0.40 0.40 0.40 0.40 0.85 0.85 0.85 0.40 0.40 0.85 0.40 0.85 0.85 0.85 0.85 0.85 0.85
1.00 0.86 0.82 0 0.08 0 0.54 0.05 0.65 0.73 0.62 0 0.18 0.66 0.57 0.59 0.84 0.81 0.75 0.75 0.74
Maximized for soil
Maximized for nature
Extensive grassland Intensive grassland Nature Wet crop hemp Wet crop algae
Intermediate
Extensive grassland Intensive grassland Nature Wet crop hemp Wet crop algae
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Fig. 7. Strategy 1 ‘Business as usual’: stakeholder plan (a) and optimization result (b). Table 2 Strategy 1 ‘Business as usual’: (a) Objective weights, aspiration level and values, (b) land use, minimal and maximum area, allocated area, aspiration level, proximity score. (a) Additive objectives Business as usual
Objectives
Weights
Aspiration level
Values
Initial
Agriculture Soil Nature Agriculture Soil Nature Agriculture Soil Nature
–
–
+++ ++ + 0.5 0.4 0.1
–
0.80 0.24 0.05 0.78 0.35 0.12 0.76 0.37 0.14
Stakeholders
Optimization
0.95 0.85 0.65
(b) Spatial objectives Land use
Min area (ha)
Max area (ha)
Allocated Area (ha)
Aspiration level
Proximity score
Initial Intensive grassland
Intensive grassland 0
2168 2168
– 2168
1.00 –
No change Change in water level No change Change in water level
1500 0 1500 500
2168 2168 1650 650
1598 571 1515 654
– – 0.85 0.85
1 0.91 0.82 0.95 0.88 1
this they grouped parcels according to existing physical boundaries and selected parcels with one or more red traffic lights. In the optimization, stakeholder results were used to set the constraints. (Table 2b). As this strategy aims to improve agriculture, the weight and aspiration levels were set high for both the additive objectives (Table 2a) and the spatial objectives (Table 2b). Table 2 shows that both stakeholder and optimizer changed about 600 ha. Both did this in such a way that high proximity scores were achieved. Both approaches resulted in similar values for the objectives. However, Fig. 7 shows large differences in the spatial allocation of the measures: the stakeholders created four clusters of measures and the optimization routine grouped the changes in a single cluster (Fig. 7b).
Testing the sensitivity of this result by reducing the spatial aspiration level in the optimization resulted in higher values of the objectives but lower proximity scores. Furthermore, removing the area constraints led to 1500 ha with a change in water level and an increased in value for all three objectives. This alternative could serve as a reference to show stakeholders that allocating a larger area would increase the values. For the second strategy, ‘Parallel tracks’, stakeholders were asked to apply measures to separate different functions in the area. Houses in the area suffer from soil subsidence resulting from too low water levels and so stakeholders decided to allocate extensive grasslands with high water levels along the main road; this separates the houses from intensive grasslands with low water levels
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Fig. 8. Strategy 2 ‘Parallel tracks’: stakeholder plan (a) and optimization result (b).
Table 3 Strategy 2 ‘Parallel tracks’ (a) Objective weights, aspiration level and values, (b) land use, minimal and maximum area, allocated area, aspiration level, proximity score. (a) Additive objectives Parallel tracks
Objectives
Weights
Aspiration level
Values
Stakeholders
Agriculture Soil Nature Agriculture Soil Nature
++ ++ ++ 0.33 0.33 0.33
–
0.78 0.26 0.06 0.79 0.28 0.10
Optimization
0.50 0.50 0.50
(b) Spatial objectives Land use Extensive grassland Intensive grassland Extensive grassland Intensive grassland
Min area (ha)
Max area (ha)
–
–
227 1526
341 2289
(Fig. 8a). In the optimizer this was incorporated as a land use restriction such that only along the road extensive grasslands could be allocated. Contrary to the stakeholders the optimizer allocated the extensive grasslands to the south (Fig. 8b). These parcels were found to contribute to higher values for all three objectives (Table 3a). The stakeholders did not perform a comparative analysis and therefore were not aware of this variance. Other, unknown, reasons may have determined their decision to limit extensive grassland to the northern part of the area. The alternative generated by the optimizer could serve as a reference alternative for the stakeholders. For the strategy ‘New horizons’, stakeholders were asked to make radical changes to the area by allocating new crops by changing water management and land use. Stakeholders decided to allocate substantial areas of reed and wet crops. They tried to limit the changes to only a few landowners and did this in areas with a high number of red traffic lights for agriculture (Fig. 9a).
Allocated Area (ha)
Aspiration level
Proximity score
284 1908 354 1772
–
0.56 0.95 0.77 0.93
0.85 0.40
In the optimizer the areas allocated were included as area constraints. The optimization alternative resulted in similar objective values (Table 4a) and proximity scores (Table 4b) as the stakeholder plan. However, the maps show large differences (Fig. 9). It is clear that more than one solution exists. As the values of both plans are similar the result from the optimizer may serve as a point of reference for the stakeholders. 6. Iterative design This section demonstrates how the optimizer can be combined with user feedback to generate plans in an iterative way. In each step the optimizer presents a plan to the user. The user evaluates the plan and based on his/her preferences and local knowledge sets specifications and restrictions for the next round. The principle of this approach is shown in the example presented in Fig. 10. For practical reasons only three steps are shown. In the first step
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Fig. 9. Strategy 3 ‘New horizons’: stakeholder plan (a) and optimization result (b).
Table 4 Strategy 3 ‘New horizons’: (a) Objective weights, aspiration level and values, (b) land use, minimal and maximum area, allocated area, aspiration level, proximity value. (a) Additive objectives New horizons
Objectives
Weights
Stakeholders
Agriculture Soil Nature Agriculture Soil Nature
++ +++ + 0.3 0.6 0.1
Optimization
Aspiration level
Values
0.85 0.95 0.500
0.82 0.74 0.62 0.83 0.77 0.60
(b) Spatial objectives Land use
Min area (ha)
Max area (ha)
Allocated Area (ha)
Aspiration level
Proximity score
Intensive grassland Reed Wet crop hemp Wet crop algae Intensive grassland Reed Wet crop hemp Wet crop algae
0 0 0 0 0 0 0 0
1500 500 200 200 1500 500 200 200
1432 403 134 199 1432 403 134 199
0.40 0.85 0.85 0.854 0.40 0.85 0.85 0.854
0.88 0.84 0.75 0.72 0.90 0.89 0.70 0.68
the optimization algorithm generated an intermediate alternative with low spatial proximity aspiration. In the second step the spatial proximity scores were increased. In the third step both spatial aspiration and objective aspiration levels were raised. Step 1: In the first iteration, each land use was restricted to 1/5 of the total area and determined by dividing the total area by the number of land uses. In addition, equal objective weights and low spatial aspiration levels were set. This resulted in an intermediate alternative where land uses were scattered. Step 2: In response, the user selected parcels and restricted these for wet crop algae as allocated by the optimizer (shaded parcels). Also the users raised the spatial aspiration level of nature and wet
crops to cluster these land uses. This results in plan 2 with a cluster of wet crops around the restricted parcels and a cluster of nature in the north. This decision led to higher proximity scores and a slight decrease in objective values. Step 3: The users responded by restricting the parcels where farmers invested recently to remain intensive grassland (shaded area). The objective aspiration levels were raised to compensate for the decrease in values due to the second step. In addition, the users decrease the upper limit of nature area. The generated result (plan 3) is an alternative that has both higher objective values as well as higher proximity scores.
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Fig. 10. Iterative design with the use of optimization in three steps.
This example demonstrated how the optimization model can complement the interactive geodesign tool. Stakeholders can either accept, reject or adjust the results of the optimization model and thereby incorporate their preferences and local knowledge. 7. Conclusions This study addressed application of a genetic algorithm that can be used to generate land use plans that maximize both additive and spatial objectives in a vector-based GIS environment. To test the usefulness of the algorithm it was integrated in a geodesign tool and applied to a planning process in a peat meadow area in the Netherlands. The study showed how the algorithm can be used to (1) generate a set of alternatives to start a decision process, (2) to identify similarities and differences between collaborative planning results and results from optimization, and (3) as an interactive tool using feedback from stakeholders. It proved possible to generate a relevant set of non-dominated solutions to begin the planning process. The results showed that generating a set single objective maximum alternatives combined with compromise alternatives provides the stakeholder with a
set of alternatives that covers the range of possible solutions. Previous workshop experiences demonstrated that stakeholders first explore extreme situations to find out the influence of large changes. This exploration stage can be structured and accelerated using the optimization routine. When maximizing objectives, it has to be kept in mind that the spatial and additive objectives compete in achieving the best results for the area. Comparing results from the optimizer with stakeholder results demonstrated that both approaches generated plans with similar values for the objectives but with large differences in the maps that were produced. It is clear that there is no single optimal plan and that more than one solution exists. As the values of the objectives are similar to the stakeholder plans the result from the optimizer could be used as a point of reference for the stakeholders. One of the challenges in using an optimization for interactive design is to be able to explain the model assumptions such that the model results are accepted and found valid by the stakeholders. The model provides the user only with a result instead of the road to it. Integrating the optimizer in a geodesign tool demonstrated how the optimizer can complement stakeholder input if it is used as an interactive geodesign tool. Stakeholders can either accept, reject or
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adjust the results of the optimization model and thereby incorporate their preferences and local knowledge. The genetic algorithm has short response times which is a major prerequisite for interactive use. To conclude: collaborative planning is based on the assumption that the stakeholders have knowledge that is not, or even cannot be represented in a formal model. The challenge is to combine optimization with stakeholder input in such a way that both approaches complement each other to get the best of both worlds. References Aerts, J. C. J. H., Eisinger, E., Heuvelink, G. B. M., & Stewart, T. J. (2003). Using linear integer programming for multi-site land-use allocation. Geographical Analysis, 35, 148–169. ´ ´ T., & Meredith, T. (2004). A collaborative GIS method for Balram, S., Dragicevi c, integrating local and technical knowledge in establishing biodiversity conservation priorities. Biodiversity and Conservation, 13, 1195–1208. Belton, V., & Stewart, T. J. (2002). Multiple criteria decision analysis: An integrated approach. Dordrecht: Springer. Bishop, I. (2013). Optimization in geodesign. Landscape Architecture Frontiers, 1, 64–75. Brouns, K., Eikelboom, T., Jansen, P. C., Janssen, R., Kwakernaak, C., van den Akker, J. J. H., et al. (2015). Spatial analysis of soil subsidence in peat meadow areas in Friesland in relation to land and water management, climate change and adaptation. Journal of Environmental Management, 55. Burrough, P. A., McDonnell, R., Burrough, P. A., & McDonnell, R. (1998). Principles of geographical information systems (333 ed.). Oxford: Oxford University Press. Cao, K., Batty, M., Huang, B., Liu, Y., Yu, L., & Chen, J. (2011). Spatial multi-objective land use optimization: Extensions to the non-dominated sorting genetic algorithm-II. International Journal of Geographical Information Science, 25, 1949–1969. Carver, S. (2003). The future of participatory approaches using geographic information: Developing a research agenda for the 21st century. Urban and Regional Information Systems Association (URISA), 15(APA I), 61–72. Community VIZ, 2015. http://placeways.com/communityviz (last accessed 21-01-2015). Dragicevic, S., & Balram, S. (2006). Collaborative geographic information systems and science: A transdisciplinary evolution. In S. Balram, & S. Dragicevic (Eds.), Collaborative geographic information systems (pp. 341–350). Hershey, PA: Idea Group Publishers. Duke, J. M., Dundas, S. J., & Messer, K. D. (2013). Cost-effective conservation planning: Lessons from economics. Journal of Environmental Management, 125, 126–133. Eikelboom, T., & Janssen, R. (2015). Comparison of geodesign tools to communicate stakeholder values. Group Decision and Negotiation. Geertman, S., & Stillwell, J. (2009). Planning support systems: Best practices and new methods. Dordrecht: Springer. Jankowski, P. (2009). Towards participatory geographic information systems for community-based environmental decision making. Journal of Environmental Management, 90(6), 1966–1971. Janssen, R., Eikelboom, T., Brouns, K., & Verhoeven, J. T. A. (2014). Using geodesign to develop a spatial adaptation strategy for south east Friesland. In D. Lee, E.
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