Abstract

this paper, we use multiple objective genetic local search (MOGLS) algorithm proposed by us in [11]. The algorithm was tested on multiple objective Travelling Salesperson Problem and outperformed MOGLS algorithm of Ishibuchi and Murata [10], 3 MOGLS based on the idea of MOSA method proposed by Ulungu et al. [19] and Pareto ranking-based evolutionary algorithm [3] proposed by Fonseca and Fleming. Below we describe main ideas of the method. The goal of multiple objective metaheuristics is to generate good approximations to the nondominated set. Of course, the best possible approximation is the whole nondominated set itself. Note that all weighted Tchebycheff scalarizing functions have optima in the nondominated set and each nondominated point is an optimum of a weighted Tchebycheff scalarizing functions (see section II). Thus, finding the whole nondominated set is equivalent to finding optima of all weighted Tchebycheff scalarizing functions. Hence, we reformulate the goal of multiple objective metaheuristics as simultaneous optimization of all weighted Tchebycheff scalarizing functions. In fact, it is enough to consider all weighted Tchebycheff scalarizing functions with normalized weight vectors. MOGLS implements the idea of simultaneous optimization of all weighted Tchebycheff scalarizing functions with normalized weight vectors by random choice of a scalarizing function optimized in each iteration. In other words, in each iteration, MOGLS tries to improve the value of a randomly selected scalarizing function. A single iteration of MOGLS consists of a single recombination of a pair of solutions and application of heuristic that improves locally the value of the current scalarizing function. An approximation of the ideal point composed of the best known values of each...

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