Multi-Scenario Cooperative Evolutionary Algorithm for the β-Robust p-Median Problem with Demand Uncertainty

Jianmai Shi,Xiaolei Zheng,Rui Wang,Bo Jiao

doi:10.3390/app9194174

Jianmai Shi, Xiaolei Zheng + Show 2 more

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https://doi.org/10.3390/app9194174

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Journal: Applied sciences	Publication Date: Oct 5, 2019
Citations: 2	License type: CC BY 4.0

Affiliation: National University of Defense Technology

Abstract

In this paper, we studied the solution approach for the β-robust p-median problem with a large number of scenarios for the uncertain demands. The concept of neighborhood scenarios was introduced to describe the scenarios with a higher similarity than others. By utilizing knowledge from the solutions of neighborhood scenarios and the parallel search strategy, a novel multi-scenario cooperative evolutionary algorithm was proposed to solve the problem for all scenarios in one run. The proposed algorithm was compared with the widely used location–allocation heuristic and genetic algorithm through two practical cases, which were a network with 95 cities and a network with 668 demand nodes in an urban area. The computational results indicate that our algorithm can obtain better solutions in a much shorter time.

Highlights

The p-median problem is one of the most well-studied facility location problems in the field of management and operation research
In the classical p-median problem, a certain number of p facilities are located among n candidate locations and m demand points are allocated to the p opened facilities, while the objective is to minimize the sum of the transportation cost/distance to serve all of the demand points
When we solved the instances for H-95 and C-668 with p = 10, we found that the statistical results on framework of the genetic algorithm (GA) and the general operators used in Medaglia et al [26] to solve the problem

Summary

Introduction

The p-median problem is one of the most well-studied facility location problems in the field of management and operation research. The p-median problem and its extensions have been widely used in many practical situations including the location of plants, warehouses, distribution centers, hubs, and public service facilities [1]. Previous study has proven that the p-median problem is Non-deterministic Polynomial (NP) hard [2], and that its optimal solution is unlikely to be obtained through an exact approach with polynomial complexity. The genetic algorithm (GA) is a kind of metaheuristic inspired by the biological evolution process, which is one of the most efficient metaheuristics for solving the p-median problem. Hosage and Goodchild [3] first reported the application of the GA for the p-median problem, and showed the advantage of the GA in the generality for approaching difficult optimization problems. Alp et al [4]

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