A hybrid combined algorithm based on intelligent water drops and electromagnetism-like algorithms for fuzzy TSP1

Abstract

This paper presents a new combined algorithm for the fuzzy Travelling Salesman Problem (FTSP) based on a composition of the Intelligent Water Drops (IWD) and the Electromagnetism-like (EM) algorithms. In a FTSP, the time consumed distance between cities i and j can be described by vague knowledge, such as fuzzy quantity. The main goal of FTSP is to achieve the minimum distance of Hamilton circuit of G graph, where the Hamilton circuit is a closed route of cities (i.e., nodes) of G that have been visited only once. The proposed algorithm transfers the generated responses by the IWD to the EM, where the best answer is selected. Importantly, the computed results from both algotithm are compared and the best is accumulated. In other words, in each iteration, the best result is collected by comparison between the current and previous hierarchies until the halt condition is fulfilled. Finally, the results of the genetic algorithm (GA), IWD and EM algorithms are compared, so that the efficiency of the proposed combined IWD-EM algorithm is determined.