Hybrid Genetic Algorithm and Invasive Weed Optimization via Priority Based Encoding for Location-Allocation Decisions in a Three-Stage Supply Chain

Abstract

In this paper, location–allocation problem of a three-stage supply chain network, including suppliers, plants, distribution centers (DCs) and customers is investigated. With respect to the total cost, the aim is determining opened plants and DCs and designing transportation trees between the facilities. Considering the capacity of suppliers, plants and DCs are limited and there is a limitation on the maximum number of opened plants and DCs, a mixed-integer linear programming (MILP) model of the problem is presented. Since multi-stage supply chain networks have been recognized as NP-hard problems, applying priority-based encoding and a four-step backward decoding procedure, a meta-heuristic algorithm, namely GAIWO, based on the best features of genetic algorithm (GA) and invasive weed optimization (IWO) is designed to solve the problem. In small size problems, the efficiency of the GAIWO is checked by solutions of GAMS software. For larger size problems, the performance of the proposed approach is compared with four evolutionary algorithms in both aspects of the structure of the GAIWO and the efficiency of the proposed encoding–decoding procedure. Besides usual evaluation criteria, Wilcoxon test and a chess rating system are used for evaluating and ranking the algorithms. The results show higher efficiency of the proposed approach.