Knowledge-informed Pareto simulated annealing for multi-objective spatial allocation

Spatial allocation is the process of assigning different attributes (e.g., land-use or land-cover) to spatial entities (e.g., map polygons or grid cells). It is an exercise that often requires the analysis of multiple, sometimes conflicting, objectives. Multi-objective spatial allocation problems often exhibit substantial computational complexity, especially when spatial pattern characteristics are specified as the allocation objectives. Optimization techniques that incorporate heuristics or knowledge-informed rules have been found to be more effective in solving spatial allocation problem. In this article, we (1) develop and demonstrate a knowledge-informed Pareto simulated annealing approach to tackle specifically multi-objective allocation problems that consider spatial patterns as objectives and (2) determine whether the knowledge-informed approach is more effective than standard Pareto simulation annealing in solving multi-objective spatial allocation problems. Four multi-objective spatial allocation problems were formulated in a gridded two-dimensional discrete space to benchmark the performance of our knowledge-informed algorithms and a standard Pareto simulated annealing algorithm. These four problems, each with two objectives, represent all combinations of cases in which there are (1) conflicting or concordant objectives and (2) two pattern objectives or one pattern objective and one non-pattern objective, representing objectives with similar or different degrees of difficulty. We generated 1200 sets of solutions, represented as allocation maps. Performance indices that measure the computational effectiveness and efficiency were developed for evaluation. The results suggest that the solutions generated by the knowledge-informed approach are more effective in approximating the set of Pareto optimal solutions than those generated by the standard Pareto simulated annealing.