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.

在位置理论和空间优化领域，已经开发了启发式算法来克服问题解决方案的NP困难性质，这导致计算时间呈指数增长。这些算法的目的是生成良好的初始解，缩小解空间，并引导搜索过程达到最优。地理分层随机抽样（GSRS）可以被视为生成这种高质量初始解决方案的方法。本研究探讨了 GSRS 在解决问题中的应用-连续表面解空间上的中值位置问题，其间断有加权需求点，及其对流行的 ALTERN 启发式算法性能的影响。结果证明了 GSRS 在寻找最佳p中值解方面的有效性，但仅适用于较小的p值：对于这些较小的p值，ALTERN 启发式的初始解由 GSRS 的局部空间平均值生成总是产生最佳的最终解决方案。相反，通过执行大量随机初始解决方案来实现随机搜索通常会产生非最佳结果。本文报告的结果还强调，样本大小和权重地理分布中的正空间自相关 (PSA) 程度会影响最终解决方案与较大 p 的最优性的接近程度。增加样本量会导致溶液浓度接近最佳对应物，增加 PSA 水平也是如此。