Two-phase Pareto Local Search Research Articles

Proper balance between search towards and along Pareto front: biobjective TSP case study

In this paper we propose simple yet efficient version of the two-phase Pareto local search (2PPLS) for solving the biobjective traveling salesman problem (bTSP). In the first phase the powerful Lin–Kernighan heuristic is used to generate some high quality solutions being very close to the Pareto front. Then Pareto local search is used to generate more potentially Pareto efficient solutions along the Pareto front. Instead of previously used method of Aneja and Nair we use uniformly distributed weight vectors in the first phase. We show experimentally that properly balancing the computational effort in the first and second phase we can obtain results better than previous versions of 2PPLS for bTSP and at least comparable to the state-of-the art results of more complex MOMAD method. Furthermore, we propose a simple extension of 2PPLS where some additional solutions are generated by Lin–Kernighan heuristic during the run of PLS. In this way we obtain a method that is more robust with respect to the number of initial solutions generated in the first phase.

Variable and large neighborhood search to solve the multiobjective set covering problem

In this paper, we study the multiobjective version of the set covering problem. To our knowledge, this problem has only been addressed in two papers before, and with two objectives and heuristic methods. We propose a new heuristic, based on the two-phase Pareto local search, with the aim of generating a good approximation of the Pareto efficient solutions. In the first phase of this method, the supported efficient solutions or a good approximation of these solutions is generated. Then, a neighborhood embedded in the Pareto local search is applied to generate non-supported efficient solutions. In order to get high quality results, two elaborate local search techniques are considered: a large neighborhood search and a variable neighborhood search. We intensively study the parameters of these two techniques. We compare our results with state-of-the-art results and we show that with our method, better results are obtained for different indicators.

Multi-objective approaches for the open-pit mining operational planning problem

This work presents three multi-objective heuristic algorithms based on Two-phase Pareto Local Search with VNS (2PPLS-VNS), Multi-objective Variable Neighborhood Search (MOVNS) and Non-dominated Sorting Genetic Algorithm II (NSGA-II). The algorithms were applied to the open-pit-mining operational planning problem with dynamic truck allocation (OPMOP). Approximations to Pareto sets generated by the developed algorithms were compared considering the hypervolume and spacing metrics. Computational experiments have shown the superiority of the algorithms based on VNS methods, which were able to find better sets of non-dominated solutions, more diversified and with an improved convergence.

Two-phase Pareto local search for the biobjective traveling salesman problem

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 m...

Speed-up techniques for solving large-scale biobjective TSP

In this paper, we present the Two-Phase Pareto Local Search ( 2PPLS) method with speed-up techniques for the heuristic resolution of the biobjective traveling salesman problem. The 2PPLS method is a state-of-the-art method for this problem. However, because of its running time that strongly grows with the instances size, the method can be hardly applied to instances with more than 200 cities. We thus adapt some speed-up techniques used in single-objective optimization to the biobjective case. The proposed method is able to solve instances with up to 1000 cities in a reasonable time with no, or very small, reduction of the quality of the generated approximations.