Genetic algorithms and the corridor location problem: multiple objectives and alternative solutions

Corridor planning problems are challenging because their solution often requires the participation of multiple stakeholders with different interests and emphases. Though such problems fall into the domain of multiobjective evaluation, existing corridor location models often search for a single global optimum by collapsing multiple objectives into a single one using a weighting method. In multiobjective problems with competing objectives, however, optimality will often have different interpretations among decision makers, and, as a consequence, no single optimal solution will satisfy all participants. This paper describes the design and implementation of a multiobjective genetic algorithm for corridor selection problems (MOGADOR). This new approach generates a large set of Pareto-optimal and near-optimal solutions that can be evaluated with respect to the untargeted or imprecisely modeled characteristics of ill-structured corridor location problems. Experimental results suggest that the MOGADOR approach outperforms traditional shortest-path methods in both computation time and solution quality. An analytical and visualization tool is provided to help decision makers identify good candidates and evaluate trade-offs among alternatives. DOI:10.1068/b32167 ôCorrespondence address: Global Navigation Group, ESRI Professional Services, 380 New York Street, Redlands, CA 92373, USA; e-mail: [email protected] Owing to the lack of suitable multiobjective problem-solving techniques in planning, researchers have often used a weighted linear combination method to reduce a multiobjective problem to one with a single objective. Exact or heuristic methods are then used to generate alternative solutions by varying combinations of weights. These approaches, however, become problematic when underlying planning problems have a nonlinear or nonconvex solution space. Moreover, a substantial amount of computation time is required to generate a set of trade-off solutions, since traditional methods can at best find one solution in a single simulation run. There is a mismatch between the needs of problem solvers and existing corridor location methods. The purpose of this paper is to elucidate a set of important characteristics of corridor location problems and to present a multiobjective genetic algorithm (MOGA) approach to their solution on raster surfaces. A focus is placed on the geographical representation of corridor location problems and the design of the crossover and mutation operators used by this type of genetic algorithm (GA). Researchers have used MOGA to solve multiobjective problems in various applications and their superiority for `wicked' or ill-structured problems has been widely recognized (see Coello et al, 2002; Deb, 2001). Applications of MOGA to spatial problems include location-allocation models (Dibble and Densham, 1993), environmental policy analysis (Bennett et al, 2004), and site selection (Xiao et al, 2002) to name a few. However, the power of MOGA as an effective objective function optimizer and alternative generator for corridor location problems has not been fully investigated. The work presented in this paper is intended to fill this gap. The MOGA-based corridor location model (MOGADOR) described in this paper outperforms conventional SP-based methods both in computational intensity and in solution quality, thus demonstrating the effectiveness and robustness of this approach to spatial analysis and multiobjective decision making. The remainder of the paper is organized as follows. In the next section we review classical shortest-path algorithms (SPAs), existing techniques for corridor-alternative generation, and the principles of MOGA. The detailed design of the MOGADOR modelöincluding the formulation of the problem, the design of a genetic representation and operators, and the valuation of solution fitnessöis described in section 3. In section 4 we discuss the effectiveness and efficiency of MOGADOR, based on the results of computational experiments, including a performance comparison between MOGADOR and a SPA-based multiobjective analytical method (denoted as SPAM). The paper concludes with some summary remarks and recommendations for further work on MOGA-based corridor location models. 2 Background This section provides a review of several commonly used SPAs in GIS. Existing techniques for alternative generation in corridor location problems are then described and compared. After an evaluation of those methods, the basic concepts and characteristics of GAs and MOGA are described. 2.1 Shortest-path algorithms Existing corridor location models are often based on SPAs. Traditionally, path-finding and route-planning problems have fallen within the domain of network analysis in vector GIS. Though numerous SPAs have been proposed, the most commonly used in GIS was developed by Dijkstra (1959). Different from brute-force graph algorithms, which must search the entire space exhaustively for a global optimal solution, Dijkstra's algorithm works in a greedy manner. It computes optimal solutions to problems by acting in the best way at each stage to reduce search effort. The performance of Dijkstra's 2 X Zhang, M P Armstrong