Designing Public Service System with Random Demands Using Truncated Path-Relinking Method

Abstract

Heuristic optimization methods can support the decision-making process in many areas of human activities. Contrary to the exact methods based on mathematical programming principles, the heuristic algorithms are able to produce a near-to-optimal solution in acceptable computational time. However, the accuracy of the produced solution is usually paid for by using the specifics of the solved problem for the development of the algorithm and the careful implementation of related procedures. This paper is focused on a broad class of location problems, which distinguish from other ones by a fixed number of facilities to be located. The studied objective is to deploy the given number of facilities in a given set of possible facility locations so that average user’s disutility is minimal. Within the paper, a special heuristics equipped with the shrinking fence strategy is studied. The strategy consists in the idea that a starting uniformly deployed set of the problem solutions are considered to be a set of stakes of a hypothetical fence, which rounds a flock of animals corresponding to good solutions of the p-location problem. The algorithm inspects the links connecting neighboring stakes and determines set of new stake positions depending on the inspection result. Before a new fence is constituted, the set of new stakes is reduced by elimination of the stakes, positions of which are distant less than a given distance limit. The process of new fence forming is repeated until a termination condition is met and the best found solution obtained by link inspections is returned as the resulting solution. To inspect a fence link, path-relinking method is used. This paper is focused on acceleration of the algorithm by truncation of the inspected link and application of an adaptive termination rule. To find impact of the adjustments on result quality and computational time, a computational study with real-sized benchmarks was performed and associated findings are summarized.