In this work, we present a method, called Two-Phase Pareto Local Search, to find a good approximation of the efficient set of the biobjective traveling salesman problem. In the first phase of the method, an initial population composed of a good approximation of the extreme supported efficient solutions is generated. We use as second phase a Pareto Local Search method applied to each solution of the initial population. We show that using the combination of these two techniques: good initial population generation plus Pareto Local Search gives better results than stateof-the-art algorithms. Two other points are introduced: the notion of ideal set and a simple way to produce near-efficient solutions of multiobjective problems, by using an efficient single-objective solver with a data perturbation technique.
The knapsack problem (KP) and its multidimensional version (MKP) are basic problems in combinatorial optimization. In this paper, we consider their multiobjective extension (MOKP and MOMKP), for which the aim is to obtain or approximate the set of efficient solutions. In the first step, we classify and briefly describe the existing works that are essentially based on the use of metaheuristics. In the second step, we propose the adaptation of the two‐phase Pareto local search (2PPLS) to the resolution of the MOMKP. With this aim, we use a very large scale neighborhood in the second phase of the method, that is the PLS. We compare our results with state‐of‐the‐art results and show that the results we obtained were never reached before by heuristics for biobjective instances. Finally, we consider the extension to three‐objective instances.
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