- Email: [email protected]
An economic-ecological model for regional land-use planning
Ecological Modelling, 31 (1986) 293-302
293
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
AN E C O N O M I C - E C O L O G I C A L M O D E L FOR REGIONAL LAND-USE PLANNING
ANTONIO S. C,~MARA, ANTON10 P. MANO, M. GRA~A MARTINHO, M. PAULA MARQUES
College of Sciences and Technology, New University of Lisbon, and Direc~o-Geral do Ordenamento, Lisbon (Portugal) JOAO F. NUNES, TERESA C. LOPES and ANTONIO CABELEIRA
Instituto Superior de Agronomia, Technical University of Lisbon, and Direcq~to-Geral do Ordenamento, Lisbon (Portugal)
ABSTRACT Camara, A.S., Mano, A.P., Martinho, M.G., Marques, M.P., Nunes, J.F., Lopes, T.C. and Cabeleira A., 1986. An economic-ecological model for regional land-use planning. Ecol. Modelling, 31: 293-302. A computer mathematical model developed to guide regional land-use planning in Portugal was introduced in this paper. The model determines the land-use mixes optimizing a pre-defined multi-objective function, including economic and ecologic variables, and defines control strategies necessary to achieve the optimal mixes at a given point in time. It is essentially based on heuristics, network theoretic concepts, dynamic simulation and multi-objective programming. The incorporation of logic programming is one of the major improvements currently being sought.
INTRODUCTION
The land-use planning process consists of defining and implementing, at given points in time, control strategies necessary to achieve a land-use mix optimizing a pre-defined multi-objective function, including economic and ecologic variables. Computer mathematical models have been developed in the past to guide land-use planning but, in general, they fail to include, simultaneously, spatial, dynamic and multi-objective considerations and do not define explicitly the plan implementation strategies. They are therefore unrealistic 0304-3800/86/$03.50
© 1986 Elsevier Science Publishers B.V.
294
and do not provide the planner with information on the means to achieve his ends. This paper introduces a model developed for Portugal's regional land-use planning that attempts to overcome these flaws. Its major features include: the consideration of economic and ecologic indicators to assess the different land-use mix alternatives, whose behavior in time is simulated by applying dynamic models; the definition of the control strategies required to implement the optimal land-use mix (or more generally the non-inferior set of land-use mixes); the possibility of accommodating dynamic input conditions; and, finally, its interactive nature. The structure, development and application of the model are discussed below. Possible improvements on the model regarding the application of artificial intelligence methods and stochastic control theory are also presented. M O D E L S T R U C T U R E A N D DEVELOPMENT
The model considers the region represented in a polygon map where each cell stands for a land use. Each cell may be visualized as a node in a network, each node having three types of multicommodity arcs: (a) arcs describing the internal economic, social, ecologic and aesthetic processes in cell i; (b) arcs describing the economic, social, ecologic and aesthetic impacts of i upon cells k; and (c) incoming arcs representing the impacts of cells j on cell i (Fig. la and b). Mass-balance type calculations including these processes enable one to define a vector including economic, social, ecologic and aesthetic valuations for each node at a given point in time. The knowledge of this vector and the definition of the objective function variables are the inputs to the model. Subsequent stages include (Fig. 2): (a) the generation of alternatives - - the enumeration of the alternative land uses for each cell i; (b) the elimination of alternatives - - a preliminary screening of the alternative land uses for cell i; (c) determination of non-inferior alternative mixes - - a search for non-inferior land-use mixes applying composition and screening processes, dynamic models and multiobjective programming formulations; and (d) definition of control strategies to implement the non-inferior alternatives by simple backtracking procedures. A detailed discussion of these modeling phases is presented below.
Inputs The first requirement of the model is the definition of cells i, i.e., the definition of land uses to be considered. Portugal's model considers, at this
295 arc d e s c r i b i n g the i n t e r n a l economic, s o c i a l , e c o l o g i c a l and a e s t h e t i c processes i n c e l l i J
• incoming arcs representing the impacts of c e l l s j upon c e l l i
~
the impacts o f i upon c e l l s k
Go \
\
\ _J
J
(b)
(a)
Fig. 1. (a) Network representation of a cell. (b) Network representation of a region.
point: agriculture, forests, conservation, recreation, urban and industrial land uses. Data inputs on the internal, incoming and departing multicommodity arcs from every cell i are also necessary. Special attention should be paid to the corresponding land uses-economic activities to provide a spatial dimension to subsequent economic analyses.
(I)
INPUTS D e f i n i t i o n of c e l l i Corresponding land uses - economic a t i v l t i e s Data On the i n t e r n a l , departing and incoming arcs i , j on p h y s i c a l , soeio-economic and ecological processes D e f i n i t i o n of the o b j e c t i v e f u n c t i o n v a r i a b l e s
I
(2) GENERATION OF ALTERNATIVES S u i t a b i l i t y analysis to generate a l t e r n a t i v e land uses for each c e l l i
I
(3) ELIMINATION OF ALTERNATIVES Screening f o r i n f e r i o r a l t e r n a t i v e land uses f o r c e l l i applying socio-economic, a e s t h e t i c , p o l i t i c a l and feasibility criteria
I (4)
DEFINITION OF NON-INFERIOR At.TERNATIVE LAND-USE MIXES D e f i n i t i o n of areas of i n f l u e n c e For each area of i n f l u e n c e : - enumeration and screening of a l t e r n a t i v e mixes analysis of economic, s o c i a l , ecological and a e s t h e t i c impacts - definition of n o n - i n f e r i o r a l t e r n a t i v e s o l u t i o n s for the area of influence D e f i n i t i o n of n o n - a l t e r n a t i v e land-Jse mixes f o r the region
I (5) OUTPUTS D e f i n i t i o n of control s t r a t e g i e s to implement the noninferior alternatives
Fig. 2. Portugal's model structure.
296
IV2 ~
---
BV4
"
~
IV3
IV4
/
-
"
~
DV2
DV3
DV4
Fig. 3. Graph model for the generation of alternative land uses for cell i. BV, base variables; IV, interaction variables; DV, determinant variables.
The other input to the model is the specification of the objective function variables which, at the moment, are in Portugal's model: economic variables - - income, employment and investment levels; ecologic variables - - water and air quality indexes; aesthetic variable - - aesthetic quality index; and social variables - - an index measuring housing, health and education levels and another index measuring leisure and cultural levels.
Generation of alternatives The generation of alternative land uses for each cell i is based on a graph model of the suitability analysis process, the nodes representing variables and the arcs relationships between variables (Fig. 3). These are divided into: base variables - - variables that characterize cell i physically (i.e. slopes, ridge lines, soil fertility); interaction variables - - variables that characterize cell i, but knowledge of which is only relevant if a given land use is going to be implemented in i, and that are related to the base variables (i.e., erosion potential, geotechnical factors, scenic sensitivity), and determinant variables variables determining the suitability levels of cell i to land use a, b, c . . . . . Z, and that are related to base and interaction variables. A systematic classification of the variables and relationships of the model, in terms of its measurement characteristics and types of mathematical functions, clarifies the nature of the suitability analysis model. Basically, the variables are of three types: (1) Nominal - - variables in which measurement is categorical in nature (i.e., land use, existence of ridge lines). Note that a number can be assigned to these variables (i.e., 1, industry; 2, .agriculture). (2) Ordinal - - variables in which measurement can be considered as the result of a ranking process (i.e., soil fertility). (3) Ratio - - variables having a given, fixed interval size and an absolute zero point (i.e., slopes, rainfall). -
-
297
On the other hand, the relationships can be divided into four categories: (1) y = f ( x ) : x = ai ~ y = Ki
(i.e., soil = a ~ geotechnical capacity = b)
(2) y = f ( x ) : x ~ [ ai, bi] =, y = K/ (3) y = f ( x ) : x = ai ~ y ~ [ Kl, Km] (4) y = Kx:
(i.e., slope ~ [ a, b] = construction suitability = c) (i.e.,soilfertitily=a=,land value ~ [ c, d] )
(i.e., slope = a ~ erosion = Ka)
Given data on the base variables and on the model relationships, the application of the graph model provides information on alternative land uses for each cell i. In the process, insights are also gained on the 'dominance' of variables and 'strength' of relationships. These will be helpful in designing more efficient, less redundant data bases for land-use planning. A final step in this phase consists of assigning to each alternative land use the control strategy required to implement it (i.e., zoning, incentives).
Elimination of alternatives In the previous stage, alternative land uses a, b, c , . . . , Z were generated for each cell i. The search for an optimal land-use mix could well become an almost unsolvable combinatorial optimization problem if the clearly inferior alternatives were not eliminated in a preliminary analysis. The elimination process involves two analytical steps: (a) analysis of the alternative land uses for each cell i per se by evaluating its internal arcs, providing a first screening; and (b) analysis of the incompatibility between adjacent land uses by evaluating incoming and departing arcs ji and ik, respectively, which provides a second preliminary selection. In both steps, the evaluations are based o n expert advice rather than on more detailed studies. A systematic selection of the experts' opinions provides elimination rules expressed in logical form (i.e., if ... then). These rules conform not only to economic, social, ecologic and aesthetic criteria, but also to political considerations and to the implementation feasibility. They are becoming more and more an important c o m p o n e n t of the model.
Definition of non-inferior alternative land-use mixes Definition of areas of influence The analysis of the network representing a region shows that 'strongly connected nodes' usually represent urban centers and that it is possible to
298 divide the region into 'sheds' around those centers by using as dividers the arcs that are loosely connected to the centers. This division facilitates the optimization search procedure. In regional planning terminology, these 'sheds' correspond to areas of influence, These may be found by applying to the regional network graph-theoretic concepts (strength of connection), Kirchoff laws, visualizing the network as an electric circuit where the centers are irradiators of electricity, or gravitational models. The multicommodity network (i.e., there are economic, social and ecologic flows) is converted into a single commodity graph by applying an indexation procedure (whenever the different types of flow have different orders of magnitude) or by just considering the economic flow (whenever the different types of flow have similar orders of magnitude). The optimization starts by investigating non-inferior land-use shifts in each area of influence through a systematic search procedure. The solution for the whole region is then found by combining non-inferior alternative mixes found for each area of influence.
Definition of non-inferior alternative solutions for each area of influence (1) Enumeration and screening of alternative mixes. The enumeration of the different alternative land-use mixes for each area of influence is the first step in the search process. It should be mentioned that the number of these may be, in some cases, still very high despite the elimination stage mentioned above. To enumerate and screen the most promising alternative mixes, the model uses another network theoretic application. To illustrate it, let us assume that the area of influence only has three cells, 1, 2 and 3, each cell having three possible alternative land uses (one of which is the current land use). Let us suppose that each alternative land use is a node in a network. The connection rules are the following: (a) the nodes corresponding to a cell cannot be connected among themselves; and (b) nodes of cell 1 are only connected to nodes of cell 2 and nodes of cell 3 are only connected to nodes of cell 2. The graph is shown in Fig. 4. Now, let us assume that this is a node-oriented network and the measure of each node is the weighted sum of valuations for economic, social, ecologic and aesthetic variables obtained for that node with the expert advice given in the previous stage (note that these valuations are obtained through mass-balance type calculations involving the internal, incoming and departing flows). Using a k-shortest path algorithm, one can then enumerate and rank the alternative land-use mixes. The clearly inferior combinations may then be eliminated from further analysis. (2) Economic, social, ecologic and aesthetic impacts. To evaluate the
299 CELLSi, 2 and 3 i USES
o
2
3
o
o
U R B A N ~ R ~ I D U S T R Y
INDUS
0"r AGRC I ULTURE
I~ R B A N "0" CONSERVATO IN
.0 AGRC I ULTURE
Fig. 4. Network scheme to enumerate and screen land-use mixes for each area of influence. alternative land-use mixes in each area of influence, one has to estimate their economic, social, ecologic and aesthetic impacts measured in terms of the objective function variables defined above, that may be represented for a period T, as vectors [IVtk]. These impacts result from the aggregation of the economic, social, ecologic and aesthetic valuations assumed by each cell i, derived by assessing the internal, incoming and departing multicommodity (economic, social, ecologic and aesthetic) arcs i, ji and ik. The economic impacts are estimated by applying input-output analyses to the area's economic activities (corresponding to each cell i). These analyses are made for each alternative mix and provide the basis for dynamic compartment-type models. The outputs of the model are, for each alternative j, the levels of the economic variables IVjk over period T. The 'behavior' of the different alternatives j in relation to the social objective function variables [IVk]j is assessed by a weighting process, repeated for each step DT over period T. The weighting is done by experts following Saaty's approach. (Saaty, 1980). To facilitate their contribution, relevant information on existing and forecasted social statistics is provided. To determine the ecological impacts, a three-step procedure is applied for each alternative j: (a) point and non-point water and air pollution generation rates are estimated over time; (b) state-of-the-art impact models are used; and (c) water and air quality indices are established. These indices, defined over period T represent the ecologic [IVtk]/. Finally the aesthetic [IVtk]j are evaluated using an approach similar to the one followed to define the social [IVtk]j. Again to facilitate the experts' intervention, complete descriptions on ecologic (water and air quality impacts) and visual disturbing elements introduced by each alternative j are provided. (3) Definition of non-inferior alternative mixes. To select the non-inferior alternative land-use mixes for each area of influence, one has to solve a
300
multiobjective programming problem. The solution process consists of two steps: (1) For each alternative j, translate vector [IVtk] into a vector [IV~]j by aggregating each vector [IVtk] into a scalar IV ~'. This is done by dividing simulation period T into sub-periods t 1, t 2, t3, . . . , tn, synthesizing sub-vectors [IVan] into a scalar by computing the summation, mean, median, mode, maximum or minimum for the values of [IVt~], depending on the nature of IV ~', assigning weights W, to the sub-periods to assess their relative importance, applying Saaty's method, and finally calculating [IVk]j = E.Wt; [IVt~]j Kk. (2) Using a value display method and the calculated [IVk]j, define the non-inferior alternatives j. The value display method adopted by Schilling (1976) consists of displaying value paths which are lines drawn for each alternative to indicate the level of achievement of each objective: a line high up on the scale for an objective indicates a high value for that objective.
Definition of non-inferior alternative land-use mixes for the region The definition of non-inferior alternative land-use mixes for the regions follows an approach similar to the one applied to each area of influence. The model deals with the non-inferior alternatives j as it did with cell i. First of all, the alternatives to be evaluated may well be enumerated, ranked and screened as done. It should be mentioned that a constraint on the compatibility of control strategies may be used, in some cases, to eliminate alternatives from further consideration. The impact assessment stage is mostly confined to the determination of economic and ecologic impacts. In the evaluation of the former, special attention is paid to the input-output analysis now done between areas of influence with the dynamic model built accordingly. Again a value-path display method is applied to find the non-inferior combinations of non-inferior alternatives for each area of influence. By simple backtracking to the step of the generation of alternatives, one may then find the outputs of the model: the control strategies that will allow the implementation of those combinations. The responsibility of selecting one mix from these non-inferior combinations rests with the decision-makers. APPLICATION
The model is being applied to a pilot Portuguese region. So far, comments may be focused on three points: computational efficiency; conceptual soundness; and application to land-use planning. Computationally, its current implementation in Basic on a single processor is clearly inefficient. It is obvious that the use of a logic programming
301
language in some segments of the model (mainly in all of those that are strictly logical in nature) would greatly enhance the program's efficiency and interactive capabilities. Similarly, the use of concurrent processors would be particularly effective to perform the search of non-inferior alternatives for each area of influence (i.e., each area could be allocated to a processor). Conceptually, and apart from the 'software-led' improvements that should be obtained by using a logic programming language and parallel processing, there is a need to take into account the uncertainties associated with economic and ecologic phenomena. It also seems that the model needs to evolve from hybrid simulation-optimization to optimal-control, theory-based formulations, to better represent the dynamic nature of planning. Data and dimensionality problems are, at the present time, serious obstacles to the implementation of these considerations. Concerning its application in land-use planning, the major problems result either from data deficiencies or the traditional difficulty in dealing with qualitative (i.e., social, aesthetic) variables. So far, the model has proved to be a good 'laboratory' to analyse the land-use planning process and a testing ground for land-use policies. SUMMARY AND CONCLUSIONS
A computer mathematical model developed to guide regional land-use planning in Portugal was introduced in this paper. The model determines the land-use mixes optimizing a pre-defined multi-objective function, including economic and ecologic variables, and defines the control strategies necessary to achieve the optimal mixes, at a given point in time. The model considers the region as a network, each node representing a land use, each arc, internal, incoming or departing economic, ecologic, social or aesthetic flows between nodes. For each node, alternative land uses are generated using suitability analysis models. Unfeasible alternative uses are then eliminated by applying economic, social, ecological and political criteria. To facilitate the search for non-inferior mixes, the region is decomposed into areas of influence using network theory-based concepts. For each area, alternative mixes are enumerated, their economic, ecologic, social and aesthetic impacts over time are screened and assessed. Using multi-objective formulations, one then selects non-inferior mixes for each area of influence. Dealing with the non-inferior alternatives for each area, the way it did with the alternative land uses for each node, applying dynamic models and multiple objective analysis, non-inferior alternatives mixes for the region are found. By simple backtracking, one then determines the control strategies that will allow the implementation of those mixes.
302 A discussion on the results of its application focused on the model's computational efficiency, conceptual soundness and application in land-use planning. The incorporation of logic p r o g r a m m i n g and stochastic optimal control theoretic concepts are suggested, to overcome some of the current computational and conceptual deficiencies. It is pointed out that despite the existing limitations, the model has proved to be a good 'laboratory' for land-use planning. REFERENCES Saaty, T.L., 1980. The Analytic Hierarchy Process. McGraw Hill, New York, NY, 228 pp. Schilling, D., 1976. Multiobjective and temporal considerations in public facility location. Ph.D. Thesis, Johns Hopkins University, Baltimore, MD.
293
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
AN E C O N O M I C - E C O L O G I C A L M O D E L FOR REGIONAL LAND-USE PLANNING
ANTONIO S. C,~MARA, ANTON10 P. MANO, M. GRA~A MARTINHO, M. PAULA MARQUES
College of Sciences and Technology, New University of Lisbon, and Direc~o-Geral do Ordenamento, Lisbon (Portugal) JOAO F. NUNES, TERESA C. LOPES and ANTONIO CABELEIRA
Instituto Superior de Agronomia, Technical University of Lisbon, and Direcq~to-Geral do Ordenamento, Lisbon (Portugal)
ABSTRACT Camara, A.S., Mano, A.P., Martinho, M.G., Marques, M.P., Nunes, J.F., Lopes, T.C. and Cabeleira A., 1986. An economic-ecological model for regional land-use planning. Ecol. Modelling, 31: 293-302. A computer mathematical model developed to guide regional land-use planning in Portugal was introduced in this paper. The model determines the land-use mixes optimizing a pre-defined multi-objective function, including economic and ecologic variables, and defines control strategies necessary to achieve the optimal mixes at a given point in time. It is essentially based on heuristics, network theoretic concepts, dynamic simulation and multi-objective programming. The incorporation of logic programming is one of the major improvements currently being sought.
INTRODUCTION
The land-use planning process consists of defining and implementing, at given points in time, control strategies necessary to achieve a land-use mix optimizing a pre-defined multi-objective function, including economic and ecologic variables. Computer mathematical models have been developed in the past to guide land-use planning but, in general, they fail to include, simultaneously, spatial, dynamic and multi-objective considerations and do not define explicitly the plan implementation strategies. They are therefore unrealistic 0304-3800/86/$03.50
© 1986 Elsevier Science Publishers B.V.
294
and do not provide the planner with information on the means to achieve his ends. This paper introduces a model developed for Portugal's regional land-use planning that attempts to overcome these flaws. Its major features include: the consideration of economic and ecologic indicators to assess the different land-use mix alternatives, whose behavior in time is simulated by applying dynamic models; the definition of the control strategies required to implement the optimal land-use mix (or more generally the non-inferior set of land-use mixes); the possibility of accommodating dynamic input conditions; and, finally, its interactive nature. The structure, development and application of the model are discussed below. Possible improvements on the model regarding the application of artificial intelligence methods and stochastic control theory are also presented. M O D E L S T R U C T U R E A N D DEVELOPMENT
The model considers the region represented in a polygon map where each cell stands for a land use. Each cell may be visualized as a node in a network, each node having three types of multicommodity arcs: (a) arcs describing the internal economic, social, ecologic and aesthetic processes in cell i; (b) arcs describing the economic, social, ecologic and aesthetic impacts of i upon cells k; and (c) incoming arcs representing the impacts of cells j on cell i (Fig. la and b). Mass-balance type calculations including these processes enable one to define a vector including economic, social, ecologic and aesthetic valuations for each node at a given point in time. The knowledge of this vector and the definition of the objective function variables are the inputs to the model. Subsequent stages include (Fig. 2): (a) the generation of alternatives - - the enumeration of the alternative land uses for each cell i; (b) the elimination of alternatives - - a preliminary screening of the alternative land uses for cell i; (c) determination of non-inferior alternative mixes - - a search for non-inferior land-use mixes applying composition and screening processes, dynamic models and multiobjective programming formulations; and (d) definition of control strategies to implement the non-inferior alternatives by simple backtracking procedures. A detailed discussion of these modeling phases is presented below.
Inputs The first requirement of the model is the definition of cells i, i.e., the definition of land uses to be considered. Portugal's model considers, at this
295 arc d e s c r i b i n g the i n t e r n a l economic, s o c i a l , e c o l o g i c a l and a e s t h e t i c processes i n c e l l i J
• incoming arcs representing the impacts of c e l l s j upon c e l l i
~
the impacts o f i upon c e l l s k
Go \
\
\ _J
J
(b)
(a)
Fig. 1. (a) Network representation of a cell. (b) Network representation of a region.
point: agriculture, forests, conservation, recreation, urban and industrial land uses. Data inputs on the internal, incoming and departing multicommodity arcs from every cell i are also necessary. Special attention should be paid to the corresponding land uses-economic activities to provide a spatial dimension to subsequent economic analyses.
(I)
INPUTS D e f i n i t i o n of c e l l i Corresponding land uses - economic a t i v l t i e s Data On the i n t e r n a l , departing and incoming arcs i , j on p h y s i c a l , soeio-economic and ecological processes D e f i n i t i o n of the o b j e c t i v e f u n c t i o n v a r i a b l e s
I
(2) GENERATION OF ALTERNATIVES S u i t a b i l i t y analysis to generate a l t e r n a t i v e land uses for each c e l l i
I
(3) ELIMINATION OF ALTERNATIVES Screening f o r i n f e r i o r a l t e r n a t i v e land uses f o r c e l l i applying socio-economic, a e s t h e t i c , p o l i t i c a l and feasibility criteria
I (4)
DEFINITION OF NON-INFERIOR At.TERNATIVE LAND-USE MIXES D e f i n i t i o n of areas of i n f l u e n c e For each area of i n f l u e n c e : - enumeration and screening of a l t e r n a t i v e mixes analysis of economic, s o c i a l , ecological and a e s t h e t i c impacts - definition of n o n - i n f e r i o r a l t e r n a t i v e s o l u t i o n s for the area of influence D e f i n i t i o n of n o n - a l t e r n a t i v e land-Jse mixes f o r the region
I (5) OUTPUTS D e f i n i t i o n of control s t r a t e g i e s to implement the noninferior alternatives
Fig. 2. Portugal's model structure.
296
IV2 ~
---
BV4
"
~
IV3
IV4
/
-
"
~
DV2
DV3
DV4
Fig. 3. Graph model for the generation of alternative land uses for cell i. BV, base variables; IV, interaction variables; DV, determinant variables.
The other input to the model is the specification of the objective function variables which, at the moment, are in Portugal's model: economic variables - - income, employment and investment levels; ecologic variables - - water and air quality indexes; aesthetic variable - - aesthetic quality index; and social variables - - an index measuring housing, health and education levels and another index measuring leisure and cultural levels.
Generation of alternatives The generation of alternative land uses for each cell i is based on a graph model of the suitability analysis process, the nodes representing variables and the arcs relationships between variables (Fig. 3). These are divided into: base variables - - variables that characterize cell i physically (i.e. slopes, ridge lines, soil fertility); interaction variables - - variables that characterize cell i, but knowledge of which is only relevant if a given land use is going to be implemented in i, and that are related to the base variables (i.e., erosion potential, geotechnical factors, scenic sensitivity), and determinant variables variables determining the suitability levels of cell i to land use a, b, c . . . . . Z, and that are related to base and interaction variables. A systematic classification of the variables and relationships of the model, in terms of its measurement characteristics and types of mathematical functions, clarifies the nature of the suitability analysis model. Basically, the variables are of three types: (1) Nominal - - variables in which measurement is categorical in nature (i.e., land use, existence of ridge lines). Note that a number can be assigned to these variables (i.e., 1, industry; 2, .agriculture). (2) Ordinal - - variables in which measurement can be considered as the result of a ranking process (i.e., soil fertility). (3) Ratio - - variables having a given, fixed interval size and an absolute zero point (i.e., slopes, rainfall). -
-
297
On the other hand, the relationships can be divided into four categories: (1) y = f ( x ) : x = ai ~ y = Ki
(i.e., soil = a ~ geotechnical capacity = b)
(2) y = f ( x ) : x ~ [ ai, bi] =, y = K/ (3) y = f ( x ) : x = ai ~ y ~ [ Kl, Km] (4) y = Kx:
(i.e., slope ~ [ a, b] = construction suitability = c) (i.e.,soilfertitily=a=,land value ~ [ c, d] )
(i.e., slope = a ~ erosion = Ka)
Given data on the base variables and on the model relationships, the application of the graph model provides information on alternative land uses for each cell i. In the process, insights are also gained on the 'dominance' of variables and 'strength' of relationships. These will be helpful in designing more efficient, less redundant data bases for land-use planning. A final step in this phase consists of assigning to each alternative land use the control strategy required to implement it (i.e., zoning, incentives).
Elimination of alternatives In the previous stage, alternative land uses a, b, c , . . . , Z were generated for each cell i. The search for an optimal land-use mix could well become an almost unsolvable combinatorial optimization problem if the clearly inferior alternatives were not eliminated in a preliminary analysis. The elimination process involves two analytical steps: (a) analysis of the alternative land uses for each cell i per se by evaluating its internal arcs, providing a first screening; and (b) analysis of the incompatibility between adjacent land uses by evaluating incoming and departing arcs ji and ik, respectively, which provides a second preliminary selection. In both steps, the evaluations are based o n expert advice rather than on more detailed studies. A systematic selection of the experts' opinions provides elimination rules expressed in logical form (i.e., if ... then). These rules conform not only to economic, social, ecologic and aesthetic criteria, but also to political considerations and to the implementation feasibility. They are becoming more and more an important c o m p o n e n t of the model.
Definition of non-inferior alternative land-use mixes Definition of areas of influence The analysis of the network representing a region shows that 'strongly connected nodes' usually represent urban centers and that it is possible to
298 divide the region into 'sheds' around those centers by using as dividers the arcs that are loosely connected to the centers. This division facilitates the optimization search procedure. In regional planning terminology, these 'sheds' correspond to areas of influence, These may be found by applying to the regional network graph-theoretic concepts (strength of connection), Kirchoff laws, visualizing the network as an electric circuit where the centers are irradiators of electricity, or gravitational models. The multicommodity network (i.e., there are economic, social and ecologic flows) is converted into a single commodity graph by applying an indexation procedure (whenever the different types of flow have different orders of magnitude) or by just considering the economic flow (whenever the different types of flow have similar orders of magnitude). The optimization starts by investigating non-inferior land-use shifts in each area of influence through a systematic search procedure. The solution for the whole region is then found by combining non-inferior alternative mixes found for each area of influence.
Definition of non-inferior alternative solutions for each area of influence (1) Enumeration and screening of alternative mixes. The enumeration of the different alternative land-use mixes for each area of influence is the first step in the search process. It should be mentioned that the number of these may be, in some cases, still very high despite the elimination stage mentioned above. To enumerate and screen the most promising alternative mixes, the model uses another network theoretic application. To illustrate it, let us assume that the area of influence only has three cells, 1, 2 and 3, each cell having three possible alternative land uses (one of which is the current land use). Let us suppose that each alternative land use is a node in a network. The connection rules are the following: (a) the nodes corresponding to a cell cannot be connected among themselves; and (b) nodes of cell 1 are only connected to nodes of cell 2 and nodes of cell 3 are only connected to nodes of cell 2. The graph is shown in Fig. 4. Now, let us assume that this is a node-oriented network and the measure of each node is the weighted sum of valuations for economic, social, ecologic and aesthetic variables obtained for that node with the expert advice given in the previous stage (note that these valuations are obtained through mass-balance type calculations involving the internal, incoming and departing flows). Using a k-shortest path algorithm, one can then enumerate and rank the alternative land-use mixes. The clearly inferior combinations may then be eliminated from further analysis. (2) Economic, social, ecologic and aesthetic impacts. To evaluate the
299 CELLSi, 2 and 3 i USES
o
2
3
o
o
U R B A N ~ R ~ I D U S T R Y
INDUS
0"r AGRC I ULTURE
I~ R B A N "0" CONSERVATO IN
.0 AGRC I ULTURE
Fig. 4. Network scheme to enumerate and screen land-use mixes for each area of influence. alternative land-use mixes in each area of influence, one has to estimate their economic, social, ecologic and aesthetic impacts measured in terms of the objective function variables defined above, that may be represented for a period T, as vectors [IVtk]. These impacts result from the aggregation of the economic, social, ecologic and aesthetic valuations assumed by each cell i, derived by assessing the internal, incoming and departing multicommodity (economic, social, ecologic and aesthetic) arcs i, ji and ik. The economic impacts are estimated by applying input-output analyses to the area's economic activities (corresponding to each cell i). These analyses are made for each alternative mix and provide the basis for dynamic compartment-type models. The outputs of the model are, for each alternative j, the levels of the economic variables IVjk over period T. The 'behavior' of the different alternatives j in relation to the social objective function variables [IVk]j is assessed by a weighting process, repeated for each step DT over period T. The weighting is done by experts following Saaty's approach. (Saaty, 1980). To facilitate their contribution, relevant information on existing and forecasted social statistics is provided. To determine the ecological impacts, a three-step procedure is applied for each alternative j: (a) point and non-point water and air pollution generation rates are estimated over time; (b) state-of-the-art impact models are used; and (c) water and air quality indices are established. These indices, defined over period T represent the ecologic [IVtk]/. Finally the aesthetic [IVtk]j are evaluated using an approach similar to the one followed to define the social [IVtk]j. Again to facilitate the experts' intervention, complete descriptions on ecologic (water and air quality impacts) and visual disturbing elements introduced by each alternative j are provided. (3) Definition of non-inferior alternative mixes. To select the non-inferior alternative land-use mixes for each area of influence, one has to solve a
300
multiobjective programming problem. The solution process consists of two steps: (1) For each alternative j, translate vector [IVtk] into a vector [IV~]j by aggregating each vector [IVtk] into a scalar IV ~'. This is done by dividing simulation period T into sub-periods t 1, t 2, t3, . . . , tn, synthesizing sub-vectors [IVan] into a scalar by computing the summation, mean, median, mode, maximum or minimum for the values of [IVt~], depending on the nature of IV ~', assigning weights W, to the sub-periods to assess their relative importance, applying Saaty's method, and finally calculating [IVk]j = E.Wt; [IVt~]j Kk. (2) Using a value display method and the calculated [IVk]j, define the non-inferior alternatives j. The value display method adopted by Schilling (1976) consists of displaying value paths which are lines drawn for each alternative to indicate the level of achievement of each objective: a line high up on the scale for an objective indicates a high value for that objective.
Definition of non-inferior alternative land-use mixes for the region The definition of non-inferior alternative land-use mixes for the regions follows an approach similar to the one applied to each area of influence. The model deals with the non-inferior alternatives j as it did with cell i. First of all, the alternatives to be evaluated may well be enumerated, ranked and screened as done. It should be mentioned that a constraint on the compatibility of control strategies may be used, in some cases, to eliminate alternatives from further consideration. The impact assessment stage is mostly confined to the determination of economic and ecologic impacts. In the evaluation of the former, special attention is paid to the input-output analysis now done between areas of influence with the dynamic model built accordingly. Again a value-path display method is applied to find the non-inferior combinations of non-inferior alternatives for each area of influence. By simple backtracking to the step of the generation of alternatives, one may then find the outputs of the model: the control strategies that will allow the implementation of those combinations. The responsibility of selecting one mix from these non-inferior combinations rests with the decision-makers. APPLICATION
The model is being applied to a pilot Portuguese region. So far, comments may be focused on three points: computational efficiency; conceptual soundness; and application to land-use planning. Computationally, its current implementation in Basic on a single processor is clearly inefficient. It is obvious that the use of a logic programming
301
language in some segments of the model (mainly in all of those that are strictly logical in nature) would greatly enhance the program's efficiency and interactive capabilities. Similarly, the use of concurrent processors would be particularly effective to perform the search of non-inferior alternatives for each area of influence (i.e., each area could be allocated to a processor). Conceptually, and apart from the 'software-led' improvements that should be obtained by using a logic programming language and parallel processing, there is a need to take into account the uncertainties associated with economic and ecologic phenomena. It also seems that the model needs to evolve from hybrid simulation-optimization to optimal-control, theory-based formulations, to better represent the dynamic nature of planning. Data and dimensionality problems are, at the present time, serious obstacles to the implementation of these considerations. Concerning its application in land-use planning, the major problems result either from data deficiencies or the traditional difficulty in dealing with qualitative (i.e., social, aesthetic) variables. So far, the model has proved to be a good 'laboratory' to analyse the land-use planning process and a testing ground for land-use policies. SUMMARY AND CONCLUSIONS
A computer mathematical model developed to guide regional land-use planning in Portugal was introduced in this paper. The model determines the land-use mixes optimizing a pre-defined multi-objective function, including economic and ecologic variables, and defines the control strategies necessary to achieve the optimal mixes, at a given point in time. The model considers the region as a network, each node representing a land use, each arc, internal, incoming or departing economic, ecologic, social or aesthetic flows between nodes. For each node, alternative land uses are generated using suitability analysis models. Unfeasible alternative uses are then eliminated by applying economic, social, ecological and political criteria. To facilitate the search for non-inferior mixes, the region is decomposed into areas of influence using network theory-based concepts. For each area, alternative mixes are enumerated, their economic, ecologic, social and aesthetic impacts over time are screened and assessed. Using multi-objective formulations, one then selects non-inferior mixes for each area of influence. Dealing with the non-inferior alternatives for each area, the way it did with the alternative land uses for each node, applying dynamic models and multiple objective analysis, non-inferior alternatives mixes for the region are found. By simple backtracking, one then determines the control strategies that will allow the implementation of those mixes.
302 A discussion on the results of its application focused on the model's computational efficiency, conceptual soundness and application in land-use planning. The incorporation of logic p r o g r a m m i n g and stochastic optimal control theoretic concepts are suggested, to overcome some of the current computational and conceptual deficiencies. It is pointed out that despite the existing limitations, the model has proved to be a good 'laboratory' for land-use planning. REFERENCES Saaty, T.L., 1980. The Analytic Hierarchy Process. McGraw Hill, New York, NY, 228 pp. Schilling, D., 1976. Multiobjective and temporal considerations in public facility location. Ph.D. Thesis, Johns Hopkins University, Baltimore, MD.