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

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.

On Solving Large-Size Generalized Cell Formation Problems via a Hard Computing Approach Using the PMP

“…Constraint (21) ensures that the number of machines in each cell does not exceed U machines. Constraint (22) ensures that at most a single copy of a replicate machine type is assigned to each cell. Constraint (23) ensures the binary restriction of variables.…”

“…The other approach aims to indirectly maximize the GE or other alternative performance measures by using the classic or modified p-median problem (PMP). Since Hakimi [20,21] first introduced the PMP on a network of nodes and arcs, the PMP has been widely studied and extended to many practical situations including the location of plants, warehouses, distribution centers, hubs, and public service facilities [22]. Revelle and Swain [23] used Balinski-type constraints [24] to present an integer linear programming (ILP) formulation of the PMP.…”