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An experimental ant colony approach for the geolocation of verbal route descriptions
Knowledge-Based Systems 24 (2011) 484–491
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Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys
An experimental ant colony approach for the geolocation of verbal route descriptions David Brosset a,⇑, Christophe Claramunt b a b
Géomer LETG UMR 6554 IUEM, 29280 Plouzané, France Naval Academy Research Institute, BP 600, 29240 Brest Naval, France
a r t i c l e
i n f o
Article history: Received 4 August 2009 Received in revised form 17 December 2010 Accepted 19 December 2010 Available online 24 December 2010 Keywords: Verbal route description Route finding Ant colony algorithm Genetic algorithm S-patial information
a b s t r a c t This paper introduces an experimental cooperative and stochastic algorithm for the derivation of spatial routes that fits the semantics of a verbal route description in natural environments. The algorithm mimics the behavior of ants, where positive feedbacks consist of pheromone trails, deposited on attractive paths. The novelty of the approach relies on the integration of the semantics of a verbal route description within the heuristic of the search algorithm. A route is modeled using a graph-based description where landmarks and spatial relationships play a central role. The algorithm is experimented and illustrated by a prototype implementation applied to foot orienteering. Preliminary computational experiments show that the ant colony developed and applied to route finding in natural environments performs relatively well when compared with other meta-heuristics. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Modeling navigation knowledge is a process that still requires a better link between common sense perceptions of space and formal models that integrate this kind of knowledge [11]. This implies an evaluation of how human beings conceptualize space and their displacements. Navigation knowledge is closely related to the notion of mental map where multiple representations of space are associated by cognitive associations [26,16]. These mental representations are mediated by structural elements, often language-based, categorized as image schemata built upon human experiences and practices with the environment [17]. The qualitative components of these cognitive perceptions are closely related to human knowledge, but difficult to manipulate directly when searching for map-based representations. This has generated a rich amount of work in the structural analysis of verbal descriptions oriented to the modeling of urban and natural environments [4,23,10]. A landmark is commonly defined in navigation as a decision point, or assimilated to a decision point, and where decisions are taken [24,13]. Actions expressed by verbs convey the dynamic component of human navigation [6]. Several empirical studies have revealed the prominent roles played by landmarks and actions [7,28]. Their role and salience in navigation knowledge have been investigated [24,22], and their potential for the derivation of computational models of navigation tasks have been formally ⇑ Corresponding author. E-mail addresses: [email protected] (D. Brosset), [email protected] (C. Claramunt). 0950-7051/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.knosys.2010.12.006
investigated, and applied to street networks in urban contexts [15,5,25]. The research presented in this paper introduces a modeling and computational framework whose objective is to explore a conceptual and logical bridge between the way humans conceptualize navigation knowledge and quantitative representations. In a previous work, we introduced a structural and logical approach that applies graph principles to the modeling of verbal route descriptions [3]. The main assumption of this approach is that a route description can be modeled as a path made of locations and actions, and semantically qualified by landmarks and qualitative spatial relationships. Based on this logical and semantic representation, this paper develops a stochastic algorithm whose objective is to derive plausible geo-referenced representations of a verbal route description (Fig. 1). This algorithm belongs to a class of solutions, so-called Ant Colony System (ACS), introduced as a new computational paradigm to solve combinatorial optimization problems, and for rapid discovery of satisfactory solutions [9,8,20]. These algorithms reproduce the behavior of a colony of ants, i.e., agents with very basic capabilities, that move essentially at random, and deposit rewards on the ground, i.e., pheromone trails, when satisfied by the route they have followed. Therefore, an ant encountering a route with a previously deposited pheromone will decide with a higher probability to follow this route. This generates positive feedback loops, where the probability of having ants following this route progressively increases. These algorithms have been inspired by the observation of termite communication [14]. Termites use a form of indirect communication, so-called stigmergy, where the
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Fig. 1. Geo-referencing principles.
environment acts as the exchange support. The advantage of these algorithms when applied to route finding problems is that they facilitate convergence. Implementations of these algorithms to spatial environments have been applied to conventional shortest paths or the classical Traveling Salesman Problem, and where the search space is predefined with specific constraints. The algorithm presented in this paper differs in many aspects to current ACS implementations. First, the constraints of the search process are derived from a verbal description which is imprecise per nature. Secondly, the number of candidate paths is very large, these paths being not predefined by the structure of the environment. This is due to the fact that our algorithm is experimented in a natural environment non constrained by a street network. The aim of the algorithm is to search for a plausible mapping of a route description toward a geo-referenced representation. Potential applications are varied as such route finding problems cover a wide range of situations from rescue operations to orienteering processes in natural environment. Overall, the computational algorithm developed relies on a stochastic approach, but it is able to model and create a solution to a complex and somehow vague problem thus favouring or generating a form of computational creativity as recently suggested in [2]. The remainder of this paper is organized as follows. Section 2 introduces the principles of the structural and graph based modeling approach of a verbal route description. Section 3 develops the algorithm initialization and execution. A prototype implementation is presented in Section 4 together with some preliminary computational experiments and comparison with a genetic algorithm. Finally, a discussion and some concluding remarks are given in Section 5. 2. Route description modeling approach This modeling approach is experimented in the context of path finding applied to foot orienteering course descriptions. Foot orienteering has been created in 1857, and was first used by the Scandinavian army as a training method. Orienteers have to visit a set of control points in a given order and within the shortest possible time. The objective of each orienteer is to find the correct control
points according to a route description given at the start of the orienteering course. Control points are colored flags distributed randomly in the exercise area. Route descriptions are made of sequences of sentences, where landmarks and actions are successively identified and qualified (e.g., Fig. 1). Actions and landmarks are the core elements of this modeling approach. Landmarks model salient points where decision are taken (e.g., ‘‘go to the green1 control point’’), whereas other saliences in the environment not acting as decision are hereafter considered as spatial entities. An action describes an elementary displacement and can be schematized by a directed path between two locations. A navigation process can be modeled as a path in the sense of graph principles, where the nodes of the path represent locations qualified by a landmark or a spatial entity or not, edges of the path actions between these locations. More formally, a route is modeled as an oriented graph G(NG, EG, lG, dG) where NG denotes the set of nodes, EG the set of edges, lG a function that associates a location to a node, and dG a function that associates an action to an edge. A route description is modeled by an ordered set of connected 3-tuples (pi, ai, pi+1), named route segments, where pi, pi+1 2 LG and ai 2 AG, and where LG denotes the set of locations, AG the set of actions. An action starts and terminates at a location, that might be close to or on a landmark. Similarly, an action might interact with a landmark during its execution. At a finer level of granularity, actions in the environment can be also qualitatively described by orientation terms. An action can be qualified by its cardinal or relative directions (e.g., go to the north, turn to the right). Similarly, landmarks are qualified when present in the route descriptions according to their proximity to a decision point. We make the difference between two cases: either, the decision point is on a landmark (e.g., ‘‘go to the green control point’’) or in the proximity of a landmark (e.g., ‘‘start near the red control point’’). While qualitative terms give an additional component to route descriptions, landmark categories complement route descriptions. For each kind of environment and navigation, a set 1 For interpretation of colour in Fig. 1, the reader is referred to the web version of this article.
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Fig. 2. Graphic representation of a verbal route description.
of landmark categories are identified and derived from an ontology that applies to the environment considered. The one used in our case study is derived from the orienteering symbols set defined by the International Orienteering Federation (IOF). The route description modeling approach has been experimented with a prototype and an interface that provides a schematic representation of a route description (Fig. 1). This interface models a route description, and supplies a Boolean-based and schematic view of a directed path between two locations. Verbal route descriptions are mapped to equivalent schematic representations at the interface level. Fig. 1 shows a verbal route description taken from an orienteering course exercise: ‘‘Go to the North to a Red control point. Go to the West for five hundred meters, then go to the South to arrive near a Green control point. Finally, go to the East to a Red control point’’. This description is modeled according to the approach introduced. It contains four route segments and three landmarks, each action being qualified by an orientation term, and one of them by a distance. Fig. 2 illustrates the modeling approach where the graph description of the verbal route description previously introduced is mapped towards a schematic representation. The nodes and edges of the graph are described by appropriate symbols whereas cardinal, direction and other semantic information constitute labels that enrich the graphic presented. Overall the schematic representation complements the graph model by providing a user-oriented interface that presents the main semantic components of a route description. 3. Algorithm model principles The algorithm presented is based on the principles of ant colony algorithms, but introduces additional spatial semantics derived from a qualitative and structural representation of a verbal route description. The main differences with conventional ant algorithms are as follows: the network that constitutes the search space is not explicitly defined, but the result of systematic exploration of the search space, as we preferably consider a natural terrain non constrained by a predefined network structure (without loss of generality we consider a natural terrain being not constrained by physical obstacles), proximity to landmarks, when present in route descriptions, constrains the searching process,
additional spatial relationships, i.e., edges direction and length, and when also present in route descriptions, also constrain the searching process, flexibility of the algorithm is guaranteed by regulation of its execution at the interface level. The search problem is qualitative per nature, the objective is not to find a minimal length (closed) route that passes through each node once, but rather to find the ones that fulfill as much as possible the route description given, and particularly its semantics. This also implies to develop an algorithm that provides a relative diversity of solutions in order to avoid emergence of local solutions. The algorithm is made of two parts: an initialization and an execution. The initialization generates the search space, that is, the candidate points for the route finding process. The algorithm execution triggers the ant colony search process where a balance between exploration and confirmation of candidate solutions is maintained. After a number of iterations the algorithm should discover several route solutions. 3.1. Algorithm initialization principles The algorithm is initialized by a stochastic generation of M paths of length n, and where n + 1 denotes the number of nodes of the route description (M is parameterized at the interface level, and preferably very large). These paths are generated taking into account a minimal and maximal length derived from the environment characteristics, and valued at the interface level. We assume that the route description is semantically rich, that is, most of the nodes are qualified by landmarks. We consider route descriptions of reasonable length, that is, less than ten nodes, this corresponding to most common cases found in pedestrian route descriptions. The landmarks are those identified on a reference map according to a semantic classification. This ensures that the node selection process and the generation of layers do not overshadow candidate solutions. A layer represents a set of candidate nodes that represent possible solutions for a given node of the route description. For each path iði 2 N; 1 6 i 6 MÞ, an evaluation process is applied to each vertex v ij ðj 2 N; 1 6 j 6 n þ 1Þ as follows: for a given vertex v ij of the path i and when the jth node of the route given is labeled by a landmark, the algorithm searches for similar landmarks in the neighborhood defined by a distance a around the vertex v ij . The distance a is parameterized at the interface level, it should reflect the topography characteristics and the average visibility (the distance a is valued at the interface level during the execution of the algorithm). When no landmark labels the node in the description, the vertex v ij is added to the set of candidate nodes Nj. when several landmarks are found, one of them is selected randomly, when one landmark is found, it is selected. Two cases are then considered (Fig. 3):
Fig. 3. Candidate node selection: principle.
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Fig. 4. Layers derivation example (Case 2).
Case 1: The node j is a landmark explicitly given by the route description (e.g., ‘‘go to a Red control point’’). The vertex v ij is relocated to the location of the landmark and retained. Case 2: The node j is in the neighborhood of a landmark given by the route description (e.g., ‘‘arrive near of a Green control point’’). The vertex v ij is retained. the vertex retained by the application of either Case 1 or Case 2 is added to the set of candidate nodes Nj, when no landmarks are found for this vertex, the algorithm passes to the next vertex v ij if any, otherwise passes to the next path i + 1 if any, otherwise terminates. The algorithm generates a number n + 1 of layers where each layer Lj ðj 2 N; 1 6 j 6 n þ 1Þ is associated to a set Nj of Kj candidate nodes that represent possible solutions for the jth node of the route description. Fig. 4 shows the principles of a node selection for one of the layers, and according to case 2 described above. A landmark is first selected as a candidate for the third node of the route description (I), a node in the neighborhood is then selected as candidate (II), and finally integrated in the third layer L3(III). 3.2. Algorithm execution principles The algorithm execution applies an ant-based colony optimization process to solve the route finding problem. The main steps of the algorithm execution are as follows: 1. at each iteration of the algorithm, each ant of the colony population generates a path amongst the set of candidate nodes, 2. these paths are initialized using a probabilistic process that maintains a balance between exploration of novel solutions and confirmation of good solutions, and using the candidate nodes selected by the algorithm initialization, 3. at each iteration of the algorithm, pheromone trails on the candidate edges are rewarded according to the evaluation of the routes followed by the ants. At the first iteration of the algorithm, the candidate edges of every layer Lj are incremented with a pheromone null value. Each ant builds a path of length n. At each decision point, i.e., each node jðj 2 N; 1 6 j 6 n þ 1Þ, each ant selects stochastically the next
node amongst the set Nj+1. Then the probability Probj,j+1(t) of choosing the node j + 1 amongst the set Nj+1 from j at the time t is given by
sj;jþ1 ðtÞ ; jþ1 k¼1 sj;kðtÞ
Probj;jþ1 ðtÞ ¼ PK
ð1Þ
where sj,j+1(t) gives the pheromone value of the edge (j, j + 1) at t. This approach maintains a balance between the necessity of favoring good solutions to a certain degree, while allowing the exploration of novel paths. At each iteration of the algorithm, two valuations are performed. First, a pheromone evaporation ensures that routes not followed by the ants are progressively forgotten. Secondly, the amount of pheromone deposited on each edge (j, j + 1) is derived. The pheromone value for an edge (j, j + 1) is given by
sj;jþ1 ðt þ 1Þ ¼ sj;jþ1 ðtÞð1 qÞ þ dj;jþ1 ðt þ 1Þ;
ð2Þ
where the evaporation rate q is valued in the unit interval [0, 1]. The value given to q should ensure a balance between the necessity of exploring new solutions (i.e., values that tend to 1), and the confirmation of good solutions (i.e., values that tend to 0). The reward on each edge (j, j + 1) is given by the valuation of the pheromone dj,j+1 at each step of the algorithm, while constraining these values in order to give a chance to each edge to be selected. The quantity of pheromone dj,j+1 laid on the edge (j, j + 1) at t + 1 is given by
dj;jþ1 ðt þ 1Þ ¼
Q X
dqj;jþ1 ðt þ 1Þ;
ð3Þ
q¼1
where Q denotes the number of ants, and dqj;jþ1 the quantity of pheromone laid on the edge (nj, nj+1) at t + 1 by the ant q. Next the pheromone deposited on each edge (j, j + 1) should be evaluated. This evaluation is local to a given edge, but should reflect the positive rewards of the ants that pass through this edge to complete their route. For each edge on a given route we make the difference between three cases, from the best to the worst ones: Case A: The starting node j and the ending node j + 1 fit the semantics of the route description, i.e., each node is associated to a landmark of similar class.
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Case B: Either the starting node j or the ending node j + 1 fit the semantics of the route description, i.e., one node only is associated to a landmark of similar class. Case C: None of the nodes j and j + 1 fit the semantics of the route description. In order to give representative scores to these cases, they are qualified by a coefficient bj,j+1 whose value is given by the unit interval [0, 1], and that tends to 1 for case A, 0.5 for case B and null for case C. Compliances to the direction relationship (lj,j+1) and the length (kj,j+1) of each edge (j, j + 1) are also evaluated. These mappings are scored according to their degree of match given by a Gaussian membership function. This allows to not eliminate paths close enough to the directions or distances given. The compliance lj,j+1 is given by values that range from 0 (the edge (j, j + 1) does not fit the direction given) to 1 (the edge (j, j + 1) fits the direction given, or no direction information is given). Similarly, the length of each edge is evaluated by a coefficient kj,j+1 2 [0, 1] that ranges from 1 when the length of the edge fits the length given by the route description or no distance information is given, to the null value when the difference of the length of the edge with the length of the route description is larger than a threshold value. Overall, the amount of pheromone deposited on an edge (j, j + 1) at t + 1 by an ant q is given by
dqj;jþ1 ðt þ 1Þ ¼
n X bj;jþ1 j¼1
n
lj;jþ1 kj;jþ1 :
ð4Þ
The algorithm is terminated when the best solutions do not change, or the number of ants following this route does not evolve significantly, or the number of iterations given as a limit is reached. 4. Algorithm computation and comparison The algorithm has been implemented and validated by a prototype written using Java and the Geotools library. The algorithm implementation is illustrated on top of the example of route description introduced in Section 2. We consider a large-scale environment of approximately one square kilometer size, mostly
wooded with a few barriers and a relatively large diversity of landmarks. This environment is initialized with around ten to twenty landmarks categorized into three different classes. Fig. 5 shows the prototype interface. The verbal route description and its graphic representation are presented at the top-left of the interface. The geographical environment that constitutes the search space appears at the right part of the interface. Last, the control parameters constitute the interaction part of the interface to the left. The landmarks identified are categorized according to the classes they belong to. The algorithm is first initialized. After a stochastic generation of a relative high number of paths, and generation of n + 1 layers where each layer Lj contains the Nj candidate nodes of the jth node of the path of length n. The algorithm is ready to process its execution, when all the parameters required have been valued by the user in control at the interface level. The valuation of these parameters should maintain a balance between the necessity of ensuring convergence and the need for a search space large enough to avoid local solutions. The algorithm parameters are calibrated at the experimentation level in order to ensure a balance between the necessity of implementing a performing algorithm, and the need for a sufficient level of exploration. They are as follows: the spatial parameters employed during the algorithm initialization: the distance a used for the neighborhood analysis to relocate the vertices when required, the pheromone evaporation rate q, the number of ants Q, although its influence should be marginal as far as its value is large enough, the maximum number of iterations. The algorithm applied to the example of route description previously introduced in Fig. 2 has produced the following results. The algorithm initialization has created several layers of landmarks with around four hundred to five hundred points per layer. We initialized the algorithm execution with one hundred ants. The experiments have been conducted with a neighborhood distance a = 100 m which is acceptable considering the topography of the terrain considered, and a pheromone evaporation value (q = 0.2). The experiments reveal that the algorithm converges after a few
Fig. 5. Algorithm solutions example.
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Fig. 6. Maximum score values per length l of the route description.
iterations. This shows that, while based on minimal knowledge and local behavior, the ant colony algorithm evolves toward solutions that comply with the route description given. Four best solutions have been identified with respect to the semantics of the route description provided (Fig. 5). It is worth noting that, although these solutions fit to the route given as input, they are relatively different. The main difference relies in the length of the four paths generated, whose value if described, can also help to differentiate these solutions. This is a result of the fact that distances are often not provided in route descriptions, this introducing ambiguity in the evaluation of distances and a relative degree of liberty with respect to that criteria and the solutions that emerge. Overall, providing several solutions favors the emergence of a sufficient number of solutions and alternatives, without being limited to local solutions. Several experiments have been conducted in order to evaluate the different role played by the algorithm parameters during computation and its complexity. Several initial constraints should be taken into account. The number of ants should be relatively high at the initialization level, it can be reduced at the execution level. The level of pheromone evaporation should be balanced in order to allow both exploration and confirmation. Several route finding problems have been tested and executed on top of the environment chosen as the case study, but considering routes of different
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lengths and of similar semantics. A notable result shows that when the length of the route description increases, the initial number of solutions increases while the final number of candidate solutions decreases toward a low number of solutions (see Fig. 6). The performances of this ACS inspired algorithm have been comparatively studied with respect to another meta-heuristic, a genetic-based algorithm. Genetic algorithms have been widely introduced and applied to the resolution of complex search problems, and where their basic principles mimic natural selection processes of species evolution [12]. One of the advantage of genetic algorithms is that they also avoid local solutions, while being inspired by biological processes as ACS-based algorithms [21,18,27]. A genetic-based algorithm has been implemented with the functions usually applied: selection, crossover and mutation. For instance, the crossing function randomly selects a sample of half of possible routes and cross these solutions in order to generate novel route solutions. Best route solutions are then taken into account, either parents or children solution. The way route solutions are combined is also performed randomly(see Fig. 7). The computational comparison of the ant-based and genetic algorithms are performed on top of the experimental environment previously presented. Every experiment is made of one hundred random route finding tests that has been summarized. Two parameters have been evaluated: performance with respect to the number of nodes of a given route finding process, and the size of the environment. For each algorithm, computational parameters have been optimized in order to produce the best results (i.e., 100 ants and 1500 individuals, respectively for the ant-based and genetic algorithms). Several observations can be made from the emerging computational results. First, there is an evidence of satisfactory computational convergence for each algorithm. Next, it appears clearly that under the conditions of the experiment made, the ant-based algorithm has a better convergence than the genetic-based algorithm, this being even more noteworthy when the complexity of the search space increases with the number of nodes (cf. Fig. 8). This confirms the observed fact that the ant-based algorithm is particularly adapted when the complexity of the search space does increase. This is also the result of the local knowledge applied by the ants during the execution of the algorithm, and thus refinement, while the genetic algorithm does not encompass any form of experience during execution. The formal computational evaluation of the ACS-based and genetic-based algorithm is a non straightforward task as these algorithms are generally terminated long before their formal
Fig. 7. Genetic-based algorithm: example of a route of length = 5.
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Fig. 8. Computational performance: number of nodes – route length.
convergence. Nonetheless, the computations experimented clearly show that the complexity is mainly determined by the qualitative properties of the route description and not directly by the length of the description whose influence is variable, and by the number of points in the search space (cf. Figs. 6 and 8). The computational experiments also show that the ACS-based algorithm has a faster convergence than the genetic-based algorithm. Overall, the ACSbased algorithm can be considering as performing better than the genetic-based algorithm under the conditions of the experiment. These promising results encourage further applications of the ACS-based algorithms to larger search space and longer route descriptions from a quantitative point of view. Qualitative extensions will be also studied by considering additional spatial constraints. The ACS-based algorithm design appears particularly adapted to route descriptions qualified by landmarks and directions, this favouring the search process. Also, the number of candidate solutions should be large enough to justify a stochastic approach while being reasonable regarding its length. The main advantage of the algorithm is that although it combines a stochastic approach with a local knowledge of the environment exhibited by the ant during the algorithm execution, this being the result of the semantic derived from the route problem. It guarantees the emergence of acceptable solutions to a relatively complex way-finding problem in satisfactory computational time. The fact that the algorithm converges toward several potential solutions does not ensure a satisfactory solution to the route finding problem. Rather it provides an input for a human-based expertise whose objective will be to study and identify possible solutions with respect to the verbal route description given as an input. These route should be considered as possible solutions, including sequences of nodes and edges in order to favor cross-comparison of verbal descriptions derived from natural environments, and study of the emerging structural and linguistic properties. This provides a cognitive dimension
and perspective to the application of this algorithm that will be the object of further extension of our research.
5. Conclusions The integration of biologically inspired algorithms into computational processes offers stimulating perspectives for solving complex problems [19,1]. Way-finding typically belongs to this class of problems as developing a bridge between cognitive models and spatial representation is still an open avenue of research. The research introduced in this paper applies an experimental ant colony algorithm whose objective is to derive a plausible solution to a way-finding problem. The algorithm considers as an input a graph and logical based representation of a verbal route description, where landmarks and actions are the main constructs identified. The exploratory algorithm stochastically explores the geographical space support of the route finding task, and selects potential decision points to constitute a search space. The ant colony model is applied on top of this search space, according to the spatial semantics of the verbal route description, rewarding good solutions, and progressively converges toward what should appear as the most satisfactory solution. Preliminary comparison with another meta-heuristic, namely a genetic-based algorithm, confirms the satisfactory performances of our algorithm, and this particularly when the complexity of the search process and the environment considered increase. The algorithm design and its implementation are at their initial stage. The algorithm is flexible enough to integrate additional spatial semantics and constraints with some minor adaptations. Barriers in the environment can be integrated as restricting variables at the initialization stage of the algorithm and the generation of paths. Elevation can also constitute an additional topographic variable for pheromone valuations. We also plan to conduct further
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experiments in order to compare computational solutions with paths followed by orienteers. References [1] B. Alatas, E. Akin, Multi-objective rule mining using a chaotic particle swarm optimization algorithm, Knowl. Based Syst. 22 (6) (2009) 455–460. [2] C. Bento, A. Cardoso, Creative systems, Knowl. Based Syst. 19 (7) (2006) 447– 448. [3] D. Brosset, C. Claramunt, E. Saux, A location and action-based model for route descriptions, in: F. Fonseca, M. Rodríguez (Eds.), GeoS 2007, Lecture Notes in Computer Science, vol. 4853, Springer-Verlag, Berlin Heidelberg, 2007, pp. 146–159. [4] D. Brosset, C. Claramunt, E. Saux, Wayfinding in natural and urban environments: a comparative study, Cartographica 43 (1) (2008) 21–30. [5] C. Claramunt, S. Winter, Structural salience of elements of the city, Environ. Plann. B 34 (6) (2007) 1030–1050. [6] M. Denis, F. Pazzaglia, C. Cornoldi, L. Bertolo, Spatial discourse and navigation: an analysis of route directions in the city of Venice, Appl. Cognitive Psych. 13 (1999) 145–174. [7] M. Denis, The description of routes: a cognitive approach to the production of spatial discourse, Curr. Psych. Cognition 16 (1997) 409–458. [8] M. Dorigo, M. Birattari, T. Stützle, Ant colony optimization: artificial ants as a computational intelligence technique, IEEE Comput. Intel. Mag. 1 (4) (2006) 28–39. [9] M. Dorigo, T. Stützle, Ant Colony Optimization, MIT Press, Cambridge, MA, 2004. [10] M. Duckham, S. Winter, M. Robinson, Including landmarks in routing instructions, J. Location Based Serv. 4 (1) (2010) 28–52. [11] M.J. Egenhofer, D.M. Mark, Naive geography, in: A.U. Frank, W. Kuhn (Eds.), Proceedings of the Conference on Spatial Information Theory, Lecture Notes in Computer Science, vol. 988, Springer, 1995, pp. 1–15. ISBN: 3-540-60392-1. [12] D. Goldberg, K. Sastry, Genetic algorithms, in: The Design of Innovation, Springer, Berlin, 2008. [13] R.G. Golledge, Human wayfinding and cognitive maps, Wayfinding behavior: cognitive mapping and other spatial processes, 1999, pp. 5–45. [14] P.P. Grassé, La reconstruction du nid et les coordinations interindividuelles chez bellicositermes natalensis et cubitermes sp. la théorie de la stigmergie: Essai d’interprétation du comportement des termites constructeurs, Insectes Sociaux 6 (1959) 41–80.
491
[15] S. Hansen, K.-F. Richter, A. Klippel, Landmarks in openls – a data structure for cognitive ergonomic route directions, in: M. Raubal, H.J. Miller, A.U. Frank, M.F. Goodchild (Eds.), GIScience, Lecture Notes in Computer Science, vol. 4197, Springer, 2006, pp. 128–144. ISBN: 3-540-44526-9. [16] S.C. Hirtle, J. Jonides, Evidence of hierarchies in cognitive maps, Memory Cognition 13 (1985) 208–217. [17] M. Johnson, The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason, The University of Chicago Press, Chicago, 1987. [18] K. Li, L. Kang, W. Zhang, B. Li, Comparative analysis of genetic algorithm and ant colony algorithm on solving traveling salesman problem, in: WSCS ’08: Proceedings of the IEEE International Workshop on Semantic Computing and Systems, IEEE Computer Society, Washington, DC, USA, 2008, pp. 72–75. [19] A. Misevicius, Genetic algorithm hybridized with ruin and recreate procedure: application to the quadratic assignment problem, Knowl. Based Syst. 16 (5–6) (2003) 261–268. ISSN: 0950-7051. [20] L. Nolle, On a novel aco-estimator and its application to the target motion analysis problem, Knowl. Based Syst. 21 (3) (2008) 225–231. [21] M. Pilat, T. White, Using genetic algorithms to optimize ACS-TSP, Lect. Notes Comput. Sci. (2002) 282–287. [22] M. Raubal, S. Winter, Enriching wayfinding instructions with local landmarks, in: M.J. Egenhofer, D.M. Mark (Eds.), GIScience, Lecture Notes in Computer Science, vol. 2478, Springer, 2002, pp. 243–259. ISBN: 3-540-44253-7. [23] K. Rehrl, S. Leitinger, G. Gartner, F. Ortag, An analysis of direction and motion concepts in verbal descriptions of route choices, in: K.S. Hornsby, C. Claramunt, M. Denis, G. Ligozat (Eds.), COSIT, Lecture Notes in Computer Science, vol. 5756, Springer, 2009, pp. 471–488. ISBN: 978-3-642-03831-0. [24] M.E. Sorrows, S.C. Hirtle, The nature of landmarks for real and electronic spaces, in: C. Freksa, D.M. Mark (Eds.), COSIT, Lecture Notes in Computer Science, vol. 1661, Springer, 1999, pp. 37–50. ISBN: 3-540-66365-7. [25] M. Tomko, S. Winter, C. Claramunt, Experiential hierarchies of streets, Environment and Urban Systems 32 (1) (2008) 41–52. [26] B. Tversky, Cognitive maps, cognitive collages, and spatial mental models, in: A.U. Frank, I. Campari (Eds.), COSIT, Lecture Notes in Computer Science, vol. 716, Springer, 1993, pp. 14–24. ISBN: 3-540-57207-4. [27] J. Ware, I. Wilson, J. Ware, A knowledge based genetic algorithm approach to automating cartographic generalisation, Knowl. Based Syst. 16 (5-6 SPEC.) (2003) 295–303. [28] S. Winter, Route adaptive selection of salient features, Spatial Inform. Theory 2825 (2003) 320–334.
Contents lists available at ScienceDirect
Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys
An experimental ant colony approach for the geolocation of verbal route descriptions David Brosset a,⇑, Christophe Claramunt b a b
Géomer LETG UMR 6554 IUEM, 29280 Plouzané, France Naval Academy Research Institute, BP 600, 29240 Brest Naval, France
a r t i c l e
i n f o
Article history: Received 4 August 2009 Received in revised form 17 December 2010 Accepted 19 December 2010 Available online 24 December 2010 Keywords: Verbal route description Route finding Ant colony algorithm Genetic algorithm S-patial information
a b s t r a c t This paper introduces an experimental cooperative and stochastic algorithm for the derivation of spatial routes that fits the semantics of a verbal route description in natural environments. The algorithm mimics the behavior of ants, where positive feedbacks consist of pheromone trails, deposited on attractive paths. The novelty of the approach relies on the integration of the semantics of a verbal route description within the heuristic of the search algorithm. A route is modeled using a graph-based description where landmarks and spatial relationships play a central role. The algorithm is experimented and illustrated by a prototype implementation applied to foot orienteering. Preliminary computational experiments show that the ant colony developed and applied to route finding in natural environments performs relatively well when compared with other meta-heuristics. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Modeling navigation knowledge is a process that still requires a better link between common sense perceptions of space and formal models that integrate this kind of knowledge [11]. This implies an evaluation of how human beings conceptualize space and their displacements. Navigation knowledge is closely related to the notion of mental map where multiple representations of space are associated by cognitive associations [26,16]. These mental representations are mediated by structural elements, often language-based, categorized as image schemata built upon human experiences and practices with the environment [17]. The qualitative components of these cognitive perceptions are closely related to human knowledge, but difficult to manipulate directly when searching for map-based representations. This has generated a rich amount of work in the structural analysis of verbal descriptions oriented to the modeling of urban and natural environments [4,23,10]. A landmark is commonly defined in navigation as a decision point, or assimilated to a decision point, and where decisions are taken [24,13]. Actions expressed by verbs convey the dynamic component of human navigation [6]. Several empirical studies have revealed the prominent roles played by landmarks and actions [7,28]. Their role and salience in navigation knowledge have been investigated [24,22], and their potential for the derivation of computational models of navigation tasks have been formally ⇑ Corresponding author. E-mail addresses: [email protected] (D. Brosset), [email protected] (C. Claramunt). 0950-7051/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.knosys.2010.12.006
investigated, and applied to street networks in urban contexts [15,5,25]. The research presented in this paper introduces a modeling and computational framework whose objective is to explore a conceptual and logical bridge between the way humans conceptualize navigation knowledge and quantitative representations. In a previous work, we introduced a structural and logical approach that applies graph principles to the modeling of verbal route descriptions [3]. The main assumption of this approach is that a route description can be modeled as a path made of locations and actions, and semantically qualified by landmarks and qualitative spatial relationships. Based on this logical and semantic representation, this paper develops a stochastic algorithm whose objective is to derive plausible geo-referenced representations of a verbal route description (Fig. 1). This algorithm belongs to a class of solutions, so-called Ant Colony System (ACS), introduced as a new computational paradigm to solve combinatorial optimization problems, and for rapid discovery of satisfactory solutions [9,8,20]. These algorithms reproduce the behavior of a colony of ants, i.e., agents with very basic capabilities, that move essentially at random, and deposit rewards on the ground, i.e., pheromone trails, when satisfied by the route they have followed. Therefore, an ant encountering a route with a previously deposited pheromone will decide with a higher probability to follow this route. This generates positive feedback loops, where the probability of having ants following this route progressively increases. These algorithms have been inspired by the observation of termite communication [14]. Termites use a form of indirect communication, so-called stigmergy, where the
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Fig. 1. Geo-referencing principles.
environment acts as the exchange support. The advantage of these algorithms when applied to route finding problems is that they facilitate convergence. Implementations of these algorithms to spatial environments have been applied to conventional shortest paths or the classical Traveling Salesman Problem, and where the search space is predefined with specific constraints. The algorithm presented in this paper differs in many aspects to current ACS implementations. First, the constraints of the search process are derived from a verbal description which is imprecise per nature. Secondly, the number of candidate paths is very large, these paths being not predefined by the structure of the environment. This is due to the fact that our algorithm is experimented in a natural environment non constrained by a street network. The aim of the algorithm is to search for a plausible mapping of a route description toward a geo-referenced representation. Potential applications are varied as such route finding problems cover a wide range of situations from rescue operations to orienteering processes in natural environment. Overall, the computational algorithm developed relies on a stochastic approach, but it is able to model and create a solution to a complex and somehow vague problem thus favouring or generating a form of computational creativity as recently suggested in [2]. The remainder of this paper is organized as follows. Section 2 introduces the principles of the structural and graph based modeling approach of a verbal route description. Section 3 develops the algorithm initialization and execution. A prototype implementation is presented in Section 4 together with some preliminary computational experiments and comparison with a genetic algorithm. Finally, a discussion and some concluding remarks are given in Section 5. 2. Route description modeling approach This modeling approach is experimented in the context of path finding applied to foot orienteering course descriptions. Foot orienteering has been created in 1857, and was first used by the Scandinavian army as a training method. Orienteers have to visit a set of control points in a given order and within the shortest possible time. The objective of each orienteer is to find the correct control
points according to a route description given at the start of the orienteering course. Control points are colored flags distributed randomly in the exercise area. Route descriptions are made of sequences of sentences, where landmarks and actions are successively identified and qualified (e.g., Fig. 1). Actions and landmarks are the core elements of this modeling approach. Landmarks model salient points where decision are taken (e.g., ‘‘go to the green1 control point’’), whereas other saliences in the environment not acting as decision are hereafter considered as spatial entities. An action describes an elementary displacement and can be schematized by a directed path between two locations. A navigation process can be modeled as a path in the sense of graph principles, where the nodes of the path represent locations qualified by a landmark or a spatial entity or not, edges of the path actions between these locations. More formally, a route is modeled as an oriented graph G(NG, EG, lG, dG) where NG denotes the set of nodes, EG the set of edges, lG a function that associates a location to a node, and dG a function that associates an action to an edge. A route description is modeled by an ordered set of connected 3-tuples (pi, ai, pi+1), named route segments, where pi, pi+1 2 LG and ai 2 AG, and where LG denotes the set of locations, AG the set of actions. An action starts and terminates at a location, that might be close to or on a landmark. Similarly, an action might interact with a landmark during its execution. At a finer level of granularity, actions in the environment can be also qualitatively described by orientation terms. An action can be qualified by its cardinal or relative directions (e.g., go to the north, turn to the right). Similarly, landmarks are qualified when present in the route descriptions according to their proximity to a decision point. We make the difference between two cases: either, the decision point is on a landmark (e.g., ‘‘go to the green control point’’) or in the proximity of a landmark (e.g., ‘‘start near the red control point’’). While qualitative terms give an additional component to route descriptions, landmark categories complement route descriptions. For each kind of environment and navigation, a set 1 For interpretation of colour in Fig. 1, the reader is referred to the web version of this article.
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Fig. 2. Graphic representation of a verbal route description.
of landmark categories are identified and derived from an ontology that applies to the environment considered. The one used in our case study is derived from the orienteering symbols set defined by the International Orienteering Federation (IOF). The route description modeling approach has been experimented with a prototype and an interface that provides a schematic representation of a route description (Fig. 1). This interface models a route description, and supplies a Boolean-based and schematic view of a directed path between two locations. Verbal route descriptions are mapped to equivalent schematic representations at the interface level. Fig. 1 shows a verbal route description taken from an orienteering course exercise: ‘‘Go to the North to a Red control point. Go to the West for five hundred meters, then go to the South to arrive near a Green control point. Finally, go to the East to a Red control point’’. This description is modeled according to the approach introduced. It contains four route segments and three landmarks, each action being qualified by an orientation term, and one of them by a distance. Fig. 2 illustrates the modeling approach where the graph description of the verbal route description previously introduced is mapped towards a schematic representation. The nodes and edges of the graph are described by appropriate symbols whereas cardinal, direction and other semantic information constitute labels that enrich the graphic presented. Overall the schematic representation complements the graph model by providing a user-oriented interface that presents the main semantic components of a route description. 3. Algorithm model principles The algorithm presented is based on the principles of ant colony algorithms, but introduces additional spatial semantics derived from a qualitative and structural representation of a verbal route description. The main differences with conventional ant algorithms are as follows: the network that constitutes the search space is not explicitly defined, but the result of systematic exploration of the search space, as we preferably consider a natural terrain non constrained by a predefined network structure (without loss of generality we consider a natural terrain being not constrained by physical obstacles), proximity to landmarks, when present in route descriptions, constrains the searching process,
additional spatial relationships, i.e., edges direction and length, and when also present in route descriptions, also constrain the searching process, flexibility of the algorithm is guaranteed by regulation of its execution at the interface level. The search problem is qualitative per nature, the objective is not to find a minimal length (closed) route that passes through each node once, but rather to find the ones that fulfill as much as possible the route description given, and particularly its semantics. This also implies to develop an algorithm that provides a relative diversity of solutions in order to avoid emergence of local solutions. The algorithm is made of two parts: an initialization and an execution. The initialization generates the search space, that is, the candidate points for the route finding process. The algorithm execution triggers the ant colony search process where a balance between exploration and confirmation of candidate solutions is maintained. After a number of iterations the algorithm should discover several route solutions. 3.1. Algorithm initialization principles The algorithm is initialized by a stochastic generation of M paths of length n, and where n + 1 denotes the number of nodes of the route description (M is parameterized at the interface level, and preferably very large). These paths are generated taking into account a minimal and maximal length derived from the environment characteristics, and valued at the interface level. We assume that the route description is semantically rich, that is, most of the nodes are qualified by landmarks. We consider route descriptions of reasonable length, that is, less than ten nodes, this corresponding to most common cases found in pedestrian route descriptions. The landmarks are those identified on a reference map according to a semantic classification. This ensures that the node selection process and the generation of layers do not overshadow candidate solutions. A layer represents a set of candidate nodes that represent possible solutions for a given node of the route description. For each path iði 2 N; 1 6 i 6 MÞ, an evaluation process is applied to each vertex v ij ðj 2 N; 1 6 j 6 n þ 1Þ as follows: for a given vertex v ij of the path i and when the jth node of the route given is labeled by a landmark, the algorithm searches for similar landmarks in the neighborhood defined by a distance a around the vertex v ij . The distance a is parameterized at the interface level, it should reflect the topography characteristics and the average visibility (the distance a is valued at the interface level during the execution of the algorithm). When no landmark labels the node in the description, the vertex v ij is added to the set of candidate nodes Nj. when several landmarks are found, one of them is selected randomly, when one landmark is found, it is selected. Two cases are then considered (Fig. 3):
Fig. 3. Candidate node selection: principle.
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Fig. 4. Layers derivation example (Case 2).
Case 1: The node j is a landmark explicitly given by the route description (e.g., ‘‘go to a Red control point’’). The vertex v ij is relocated to the location of the landmark and retained. Case 2: The node j is in the neighborhood of a landmark given by the route description (e.g., ‘‘arrive near of a Green control point’’). The vertex v ij is retained. the vertex retained by the application of either Case 1 or Case 2 is added to the set of candidate nodes Nj, when no landmarks are found for this vertex, the algorithm passes to the next vertex v ij if any, otherwise passes to the next path i + 1 if any, otherwise terminates. The algorithm generates a number n + 1 of layers where each layer Lj ðj 2 N; 1 6 j 6 n þ 1Þ is associated to a set Nj of Kj candidate nodes that represent possible solutions for the jth node of the route description. Fig. 4 shows the principles of a node selection for one of the layers, and according to case 2 described above. A landmark is first selected as a candidate for the third node of the route description (I), a node in the neighborhood is then selected as candidate (II), and finally integrated in the third layer L3(III). 3.2. Algorithm execution principles The algorithm execution applies an ant-based colony optimization process to solve the route finding problem. The main steps of the algorithm execution are as follows: 1. at each iteration of the algorithm, each ant of the colony population generates a path amongst the set of candidate nodes, 2. these paths are initialized using a probabilistic process that maintains a balance between exploration of novel solutions and confirmation of good solutions, and using the candidate nodes selected by the algorithm initialization, 3. at each iteration of the algorithm, pheromone trails on the candidate edges are rewarded according to the evaluation of the routes followed by the ants. At the first iteration of the algorithm, the candidate edges of every layer Lj are incremented with a pheromone null value. Each ant builds a path of length n. At each decision point, i.e., each node jðj 2 N; 1 6 j 6 n þ 1Þ, each ant selects stochastically the next
node amongst the set Nj+1. Then the probability Probj,j+1(t) of choosing the node j + 1 amongst the set Nj+1 from j at the time t is given by
sj;jþ1 ðtÞ ; jþ1 k¼1 sj;kðtÞ
Probj;jþ1 ðtÞ ¼ PK
ð1Þ
where sj,j+1(t) gives the pheromone value of the edge (j, j + 1) at t. This approach maintains a balance between the necessity of favoring good solutions to a certain degree, while allowing the exploration of novel paths. At each iteration of the algorithm, two valuations are performed. First, a pheromone evaporation ensures that routes not followed by the ants are progressively forgotten. Secondly, the amount of pheromone deposited on each edge (j, j + 1) is derived. The pheromone value for an edge (j, j + 1) is given by
sj;jþ1 ðt þ 1Þ ¼ sj;jþ1 ðtÞð1 qÞ þ dj;jþ1 ðt þ 1Þ;
ð2Þ
where the evaporation rate q is valued in the unit interval [0, 1]. The value given to q should ensure a balance between the necessity of exploring new solutions (i.e., values that tend to 1), and the confirmation of good solutions (i.e., values that tend to 0). The reward on each edge (j, j + 1) is given by the valuation of the pheromone dj,j+1 at each step of the algorithm, while constraining these values in order to give a chance to each edge to be selected. The quantity of pheromone dj,j+1 laid on the edge (j, j + 1) at t + 1 is given by
dj;jþ1 ðt þ 1Þ ¼
Q X
dqj;jþ1 ðt þ 1Þ;
ð3Þ
q¼1
where Q denotes the number of ants, and dqj;jþ1 the quantity of pheromone laid on the edge (nj, nj+1) at t + 1 by the ant q. Next the pheromone deposited on each edge (j, j + 1) should be evaluated. This evaluation is local to a given edge, but should reflect the positive rewards of the ants that pass through this edge to complete their route. For each edge on a given route we make the difference between three cases, from the best to the worst ones: Case A: The starting node j and the ending node j + 1 fit the semantics of the route description, i.e., each node is associated to a landmark of similar class.
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Case B: Either the starting node j or the ending node j + 1 fit the semantics of the route description, i.e., one node only is associated to a landmark of similar class. Case C: None of the nodes j and j + 1 fit the semantics of the route description. In order to give representative scores to these cases, they are qualified by a coefficient bj,j+1 whose value is given by the unit interval [0, 1], and that tends to 1 for case A, 0.5 for case B and null for case C. Compliances to the direction relationship (lj,j+1) and the length (kj,j+1) of each edge (j, j + 1) are also evaluated. These mappings are scored according to their degree of match given by a Gaussian membership function. This allows to not eliminate paths close enough to the directions or distances given. The compliance lj,j+1 is given by values that range from 0 (the edge (j, j + 1) does not fit the direction given) to 1 (the edge (j, j + 1) fits the direction given, or no direction information is given). Similarly, the length of each edge is evaluated by a coefficient kj,j+1 2 [0, 1] that ranges from 1 when the length of the edge fits the length given by the route description or no distance information is given, to the null value when the difference of the length of the edge with the length of the route description is larger than a threshold value. Overall, the amount of pheromone deposited on an edge (j, j + 1) at t + 1 by an ant q is given by
dqj;jþ1 ðt þ 1Þ ¼
n X bj;jþ1 j¼1
n
lj;jþ1 kj;jþ1 :
ð4Þ
The algorithm is terminated when the best solutions do not change, or the number of ants following this route does not evolve significantly, or the number of iterations given as a limit is reached. 4. Algorithm computation and comparison The algorithm has been implemented and validated by a prototype written using Java and the Geotools library. The algorithm implementation is illustrated on top of the example of route description introduced in Section 2. We consider a large-scale environment of approximately one square kilometer size, mostly
wooded with a few barriers and a relatively large diversity of landmarks. This environment is initialized with around ten to twenty landmarks categorized into three different classes. Fig. 5 shows the prototype interface. The verbal route description and its graphic representation are presented at the top-left of the interface. The geographical environment that constitutes the search space appears at the right part of the interface. Last, the control parameters constitute the interaction part of the interface to the left. The landmarks identified are categorized according to the classes they belong to. The algorithm is first initialized. After a stochastic generation of a relative high number of paths, and generation of n + 1 layers where each layer Lj contains the Nj candidate nodes of the jth node of the path of length n. The algorithm is ready to process its execution, when all the parameters required have been valued by the user in control at the interface level. The valuation of these parameters should maintain a balance between the necessity of ensuring convergence and the need for a search space large enough to avoid local solutions. The algorithm parameters are calibrated at the experimentation level in order to ensure a balance between the necessity of implementing a performing algorithm, and the need for a sufficient level of exploration. They are as follows: the spatial parameters employed during the algorithm initialization: the distance a used for the neighborhood analysis to relocate the vertices when required, the pheromone evaporation rate q, the number of ants Q, although its influence should be marginal as far as its value is large enough, the maximum number of iterations. The algorithm applied to the example of route description previously introduced in Fig. 2 has produced the following results. The algorithm initialization has created several layers of landmarks with around four hundred to five hundred points per layer. We initialized the algorithm execution with one hundred ants. The experiments have been conducted with a neighborhood distance a = 100 m which is acceptable considering the topography of the terrain considered, and a pheromone evaporation value (q = 0.2). The experiments reveal that the algorithm converges after a few
Fig. 5. Algorithm solutions example.
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Fig. 6. Maximum score values per length l of the route description.
iterations. This shows that, while based on minimal knowledge and local behavior, the ant colony algorithm evolves toward solutions that comply with the route description given. Four best solutions have been identified with respect to the semantics of the route description provided (Fig. 5). It is worth noting that, although these solutions fit to the route given as input, they are relatively different. The main difference relies in the length of the four paths generated, whose value if described, can also help to differentiate these solutions. This is a result of the fact that distances are often not provided in route descriptions, this introducing ambiguity in the evaluation of distances and a relative degree of liberty with respect to that criteria and the solutions that emerge. Overall, providing several solutions favors the emergence of a sufficient number of solutions and alternatives, without being limited to local solutions. Several experiments have been conducted in order to evaluate the different role played by the algorithm parameters during computation and its complexity. Several initial constraints should be taken into account. The number of ants should be relatively high at the initialization level, it can be reduced at the execution level. The level of pheromone evaporation should be balanced in order to allow both exploration and confirmation. Several route finding problems have been tested and executed on top of the environment chosen as the case study, but considering routes of different
489
lengths and of similar semantics. A notable result shows that when the length of the route description increases, the initial number of solutions increases while the final number of candidate solutions decreases toward a low number of solutions (see Fig. 6). The performances of this ACS inspired algorithm have been comparatively studied with respect to another meta-heuristic, a genetic-based algorithm. Genetic algorithms have been widely introduced and applied to the resolution of complex search problems, and where their basic principles mimic natural selection processes of species evolution [12]. One of the advantage of genetic algorithms is that they also avoid local solutions, while being inspired by biological processes as ACS-based algorithms [21,18,27]. A genetic-based algorithm has been implemented with the functions usually applied: selection, crossover and mutation. For instance, the crossing function randomly selects a sample of half of possible routes and cross these solutions in order to generate novel route solutions. Best route solutions are then taken into account, either parents or children solution. The way route solutions are combined is also performed randomly(see Fig. 7). The computational comparison of the ant-based and genetic algorithms are performed on top of the experimental environment previously presented. Every experiment is made of one hundred random route finding tests that has been summarized. Two parameters have been evaluated: performance with respect to the number of nodes of a given route finding process, and the size of the environment. For each algorithm, computational parameters have been optimized in order to produce the best results (i.e., 100 ants and 1500 individuals, respectively for the ant-based and genetic algorithms). Several observations can be made from the emerging computational results. First, there is an evidence of satisfactory computational convergence for each algorithm. Next, it appears clearly that under the conditions of the experiment made, the ant-based algorithm has a better convergence than the genetic-based algorithm, this being even more noteworthy when the complexity of the search space increases with the number of nodes (cf. Fig. 8). This confirms the observed fact that the ant-based algorithm is particularly adapted when the complexity of the search space does increase. This is also the result of the local knowledge applied by the ants during the execution of the algorithm, and thus refinement, while the genetic algorithm does not encompass any form of experience during execution. The formal computational evaluation of the ACS-based and genetic-based algorithm is a non straightforward task as these algorithms are generally terminated long before their formal
Fig. 7. Genetic-based algorithm: example of a route of length = 5.
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Fig. 8. Computational performance: number of nodes – route length.
convergence. Nonetheless, the computations experimented clearly show that the complexity is mainly determined by the qualitative properties of the route description and not directly by the length of the description whose influence is variable, and by the number of points in the search space (cf. Figs. 6 and 8). The computational experiments also show that the ACS-based algorithm has a faster convergence than the genetic-based algorithm. Overall, the ACSbased algorithm can be considering as performing better than the genetic-based algorithm under the conditions of the experiment. These promising results encourage further applications of the ACS-based algorithms to larger search space and longer route descriptions from a quantitative point of view. Qualitative extensions will be also studied by considering additional spatial constraints. The ACS-based algorithm design appears particularly adapted to route descriptions qualified by landmarks and directions, this favouring the search process. Also, the number of candidate solutions should be large enough to justify a stochastic approach while being reasonable regarding its length. The main advantage of the algorithm is that although it combines a stochastic approach with a local knowledge of the environment exhibited by the ant during the algorithm execution, this being the result of the semantic derived from the route problem. It guarantees the emergence of acceptable solutions to a relatively complex way-finding problem in satisfactory computational time. The fact that the algorithm converges toward several potential solutions does not ensure a satisfactory solution to the route finding problem. Rather it provides an input for a human-based expertise whose objective will be to study and identify possible solutions with respect to the verbal route description given as an input. These route should be considered as possible solutions, including sequences of nodes and edges in order to favor cross-comparison of verbal descriptions derived from natural environments, and study of the emerging structural and linguistic properties. This provides a cognitive dimension
and perspective to the application of this algorithm that will be the object of further extension of our research.
5. Conclusions The integration of biologically inspired algorithms into computational processes offers stimulating perspectives for solving complex problems [19,1]. Way-finding typically belongs to this class of problems as developing a bridge between cognitive models and spatial representation is still an open avenue of research. The research introduced in this paper applies an experimental ant colony algorithm whose objective is to derive a plausible solution to a way-finding problem. The algorithm considers as an input a graph and logical based representation of a verbal route description, where landmarks and actions are the main constructs identified. The exploratory algorithm stochastically explores the geographical space support of the route finding task, and selects potential decision points to constitute a search space. The ant colony model is applied on top of this search space, according to the spatial semantics of the verbal route description, rewarding good solutions, and progressively converges toward what should appear as the most satisfactory solution. Preliminary comparison with another meta-heuristic, namely a genetic-based algorithm, confirms the satisfactory performances of our algorithm, and this particularly when the complexity of the search process and the environment considered increase. The algorithm design and its implementation are at their initial stage. The algorithm is flexible enough to integrate additional spatial semantics and constraints with some minor adaptations. Barriers in the environment can be integrated as restricting variables at the initialization stage of the algorithm and the generation of paths. Elevation can also constitute an additional topographic variable for pheromone valuations. We also plan to conduct further
D. Brosset, C. Claramunt / Knowledge-Based Systems 24 (2011) 484–491
experiments in order to compare computational solutions with paths followed by orienteers. References [1] B. Alatas, E. Akin, Multi-objective rule mining using a chaotic particle swarm optimization algorithm, Knowl. Based Syst. 22 (6) (2009) 455–460. [2] C. Bento, A. Cardoso, Creative systems, Knowl. Based Syst. 19 (7) (2006) 447– 448. [3] D. Brosset, C. Claramunt, E. Saux, A location and action-based model for route descriptions, in: F. Fonseca, M. Rodríguez (Eds.), GeoS 2007, Lecture Notes in Computer Science, vol. 4853, Springer-Verlag, Berlin Heidelberg, 2007, pp. 146–159. [4] D. Brosset, C. Claramunt, E. Saux, Wayfinding in natural and urban environments: a comparative study, Cartographica 43 (1) (2008) 21–30. [5] C. Claramunt, S. Winter, Structural salience of elements of the city, Environ. Plann. B 34 (6) (2007) 1030–1050. [6] M. Denis, F. Pazzaglia, C. Cornoldi, L. Bertolo, Spatial discourse and navigation: an analysis of route directions in the city of Venice, Appl. Cognitive Psych. 13 (1999) 145–174. [7] M. Denis, The description of routes: a cognitive approach to the production of spatial discourse, Curr. Psych. Cognition 16 (1997) 409–458. [8] M. Dorigo, M. Birattari, T. Stützle, Ant colony optimization: artificial ants as a computational intelligence technique, IEEE Comput. Intel. Mag. 1 (4) (2006) 28–39. [9] M. Dorigo, T. Stützle, Ant Colony Optimization, MIT Press, Cambridge, MA, 2004. [10] M. Duckham, S. Winter, M. Robinson, Including landmarks in routing instructions, J. Location Based Serv. 4 (1) (2010) 28–52. [11] M.J. Egenhofer, D.M. Mark, Naive geography, in: A.U. Frank, W. Kuhn (Eds.), Proceedings of the Conference on Spatial Information Theory, Lecture Notes in Computer Science, vol. 988, Springer, 1995, pp. 1–15. ISBN: 3-540-60392-1. [12] D. Goldberg, K. Sastry, Genetic algorithms, in: The Design of Innovation, Springer, Berlin, 2008. [13] R.G. Golledge, Human wayfinding and cognitive maps, Wayfinding behavior: cognitive mapping and other spatial processes, 1999, pp. 5–45. [14] P.P. Grassé, La reconstruction du nid et les coordinations interindividuelles chez bellicositermes natalensis et cubitermes sp. la théorie de la stigmergie: Essai d’interprétation du comportement des termites constructeurs, Insectes Sociaux 6 (1959) 41–80.
491
[15] S. Hansen, K.-F. Richter, A. Klippel, Landmarks in openls – a data structure for cognitive ergonomic route directions, in: M. Raubal, H.J. Miller, A.U. Frank, M.F. Goodchild (Eds.), GIScience, Lecture Notes in Computer Science, vol. 4197, Springer, 2006, pp. 128–144. ISBN: 3-540-44526-9. [16] S.C. Hirtle, J. Jonides, Evidence of hierarchies in cognitive maps, Memory Cognition 13 (1985) 208–217. [17] M. Johnson, The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason, The University of Chicago Press, Chicago, 1987. [18] K. Li, L. Kang, W. Zhang, B. Li, Comparative analysis of genetic algorithm and ant colony algorithm on solving traveling salesman problem, in: WSCS ’08: Proceedings of the IEEE International Workshop on Semantic Computing and Systems, IEEE Computer Society, Washington, DC, USA, 2008, pp. 72–75. [19] A. Misevicius, Genetic algorithm hybridized with ruin and recreate procedure: application to the quadratic assignment problem, Knowl. Based Syst. 16 (5–6) (2003) 261–268. ISSN: 0950-7051. [20] L. Nolle, On a novel aco-estimator and its application to the target motion analysis problem, Knowl. Based Syst. 21 (3) (2008) 225–231. [21] M. Pilat, T. White, Using genetic algorithms to optimize ACS-TSP, Lect. Notes Comput. Sci. (2002) 282–287. [22] M. Raubal, S. Winter, Enriching wayfinding instructions with local landmarks, in: M.J. Egenhofer, D.M. Mark (Eds.), GIScience, Lecture Notes in Computer Science, vol. 2478, Springer, 2002, pp. 243–259. ISBN: 3-540-44253-7. [23] K. Rehrl, S. Leitinger, G. Gartner, F. Ortag, An analysis of direction and motion concepts in verbal descriptions of route choices, in: K.S. Hornsby, C. Claramunt, M. Denis, G. Ligozat (Eds.), COSIT, Lecture Notes in Computer Science, vol. 5756, Springer, 2009, pp. 471–488. ISBN: 978-3-642-03831-0. [24] M.E. Sorrows, S.C. Hirtle, The nature of landmarks for real and electronic spaces, in: C. Freksa, D.M. Mark (Eds.), COSIT, Lecture Notes in Computer Science, vol. 1661, Springer, 1999, pp. 37–50. ISBN: 3-540-66365-7. [25] M. Tomko, S. Winter, C. Claramunt, Experiential hierarchies of streets, Environment and Urban Systems 32 (1) (2008) 41–52. [26] B. Tversky, Cognitive maps, cognitive collages, and spatial mental models, in: A.U. Frank, I. Campari (Eds.), COSIT, Lecture Notes in Computer Science, vol. 716, Springer, 1993, pp. 14–24. ISBN: 3-540-57207-4. [27] J. Ware, I. Wilson, J. Ware, A knowledge based genetic algorithm approach to automating cartographic generalisation, Knowl. Based Syst. 16 (5-6 SPEC.) (2003) 295–303. [28] S. Winter, Route adaptive selection of salient features, Spatial Inform. Theory 2825 (2003) 320–334.