Knowledge-Informed Simulated Annealing for Spatial Allocation Problems

Generating prescribed patterns in spatial allocation is a difficult and complex optimization task. Many spatial allocation problems require the arrangement of resources in ways that their patterns promote some desirable landscape functions (e.g., Taylor et al.,2007; De Clercq et al., 2007; Milder et al., 2008). The complexity of the optimization task comes from the simultaneous effects of siting multiple spatial entities that usually require complex formulae to quantify (Tomlin, 1990; Brookes, 2001). Such spatial allocation problems are combinatorial in nature, and often require the use of global optimization algorithms such as simulated annealing or genetic algorithms (Revees, 1993) to find good solutions. Furthermore, spatial allocation problems often exhibit substantial complexity, especially when analyses must consider multiple, often conflicting, objectives (Malczewski, 1999). Despite successful examples of using global optimization algorithms in solving spatial allocation problems (Brookes, 2001; Aerts & Heuvelink, 2002; Xiao et al., 2002), however, an increase in the number of spatial entities involved in allocation deteriorates the performance of the trialand-error mechanism of meta-heuristic algorithms. Recent efforts to solve spatial optimization have been made by developing approaches that use auxiliary rules (i.e., heuristics; e.g., Church et al., 2003; Duh & Brown, 2005; Duh & Brown, 2007). Heuristic approaches, if used appropriately, can greatly improve the performance and utility of spatial optimization algorithms in spatial allocation and interactive spatial decision-making. This chapter describes the design, implementation, and evaluation of a knowledge-informed simulated annealing (KISA) algorithm that applies heuristics in single and multi-objective spatial allocation problems. The discussion at the end of the chapter addresses the potential applications and limitations of the approaches presented.