Geographic Optimization Using Evolutionary Algorithms

During the last two decades, evolutionary algorithms (EAs) have been applied to a wide range of optimization and decision-making problems. Work on EAs for geographic analysis, however, has been conducted in a problem-specific manner, which prevents an EA designed for one type of problem to be used on others. The purpose of this paper is to describe a framework that unifies the design and implementation of EAs for different types of geographic optimization problems. The key element in this framework is a graph representation that can be used to formally define the spatial structure of a broad range of geographic problems. Based on this representation, spatial constraints (e.g., contiguity and adjacency) of optimization problems can be effectively maintained, and general principles of designing evolutionary algorithms for geographic optimization are identified. The framework is applied to an example political redistricting problem.

[1]  David A. Bennett,et al.  Exploring the Solution Space of Semi‐structured Geographical Problems Using Genetic Algorithms , 1999, Trans. GIS.

[2]  John H. Holland,et al.  Outline for a Logical Theory of Adaptive Systems , 1962, JACM.

[3]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[4]  A. Stewart Fotheringham,et al.  Trends in quantitative methods II: stressing the computational , 1998 .

[5]  J. Raper,et al.  Hybrid genetic algorithm for transmitter location in wireless networks , 1999 .

[6]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[7]  William C. Perkins,et al.  Spatial decision support systems: An overview of technology and a test of efficacy , 1995, Decis. Support Syst..

[8]  Herbert A. Simon.  The new science of management decision. , 1960 .

[9]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[10]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[11]  Marc P. Armstrong,et al.  Geography and Computational Science , 2000 .

[12]  Marc P. Armstrong,et al.  Decision support for regionalization: A spatial decision support system for regionalizing service delivery systems , 1991 .

[13]  David A. Bennett,et al.  Using Evolutionary Algorithms to Generate Alternatives for Multiobjective Site-Search Problems , 2002 .

[14]  Allen J. Scott,et al.  Combinatorial programming, spatial analysis and planning , 1971 .

[15]  Leon Cooper,et al.  Heuristic Methods for Location-Allocation Problems , 1964 .

[16]  Stephanie Forrest,et al.  Emergent computation: self-organizing, collective, and cooperative phenomena in natural and artificial computing networks , 1990 .

[17]  H. Miller,et al.  Geographic Information Systems for Transportation: Principles and Applications , 2001 .

[18]  Justin C. Williams.  POLITICAL REDISTRICTING: A REVIEW , 2005 .

[19]  Micah Altman,et al.  Districting principles and democratic representation , 1998 .

[20]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[21]  M. Armstrong.  On Automated Geography , 1993 .

[22]  Michael Bevers,et al.  Spatial Optimization for Managed Ecosystems , 1998 .

[23]  Christopher J. Brookes,et al.  A genetic algorithm for designing optimal patch configurations in GIS , 2001, Int. J. Geogr. Inf. Sci..

[24]  Lewis D. Hopkins,et al.  Evaluation of Methods for Exploring Ill-Defined Problems , 1984 .

[25]  Reza Barkhi,et al.  A REVIEW OF COVERING PROBLEMS IN FACILITY LOCATION. , 1993 .

[26]  I H Osman,et al.  Meta-Heuristics Theory and Applications , 2011 .

[27]  Alan T. Murray,et al.  Measuring the efficacy of adjacency constraint structure in forest planning models , 1995 .

[28]  M. Goodchild,et al.  Discrete space location-allocation solutions from genetic algorithms , 1986 .

[29]  Jeffrey Horn,et al.  Handbook of evolutionary computation , 1997 .

[30]  G. Rushton.  The Roepke Lecture in Economic Geography Location Theory, Location-Allocation Models, and Service Development Planning in the Third World , 1988 .

[31]  Avijit Ghosh,et al.  LOCATION-ALLOCATION MODELS IN THE PRIVATE SECTOR: PROGRESS, PROBLEMS AND PROSPECTS. , 1993 .

[32]  Rajan Batta,et al.  On the use of genetic algorithms to solve location problems , 2002, Comput. Oper. Res..

[33]  Paul J. Densham,et al.  Providing Spatial Decision Support for Rural Public Service Facilities That Require a Minimum Workload , 1996 .

[34]  M. Dorigo,et al.  1 Positive Feedback as a Search Strategy , 1991 .

[35]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[36]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[37]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[38]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[39]  Richard L. Church,et al.  Reserve selection as a maximal covering location problem , 1996 .

[40]  S. Hakimi.  Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems , 1965 .

[41]  Pj Densham,et al.  GENERATING INTERESTING ALTERNATIVES IN GIS AND SDSS USING GENETIC ALGORITHMS , 1993 .

[42]  Anthony K. H. Tung,et al.  Spatial clustering methods in data mining : A survey , 2001 .