Effects of geographically stratified random sampling initial solutions on solving a continuous surface p-median location problem using the ALTERN heuristic

In the fields of location theory and spatial optimization, heuristic algorithms have been developed to overcome the NP-hard nature of solutions to their problems, which results in an exponential increase in computation time. These algorithms aim to generate good initial solutions, narrow the solution space, and guide the search process to optimality. Geographically stratified random sampling (GSRS) can be regarded as a method to generate such high-quality initial solutions. This study investigates the application of GSRS to solving the p-median location problem on a continuous surface solution space punctuated with weighted demand points, and its impact on the performance of the popular ALTERN heuristic algorithm. Results demonstrate the effectiveness of GSRS in finding optimal p-median solutions, but only for smaller p values: the ALTERN heuristic with initial solutions generated by local spatial means from GSRS for these smaller p always produces optimal final solutions. In contrast, implementing a random search by executing a large number of random initial solutions often produces non-optimal results. Findings reported in this paper also highlight that sample size and degree of positive spatial autocorrelation (PSA) in the geographic distribution of weights influence how close final solutions are to optimality for larger p. Increasing the sample size leads solutions to be concentrated near their optimal counterparts, as does increasing PSA levels.