ND-Tree-based update: a Fast Algorithm for the Dynamic Non-Dominance Problem

In this paper we propose a new method called ND-Tree-based update (or shortly ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online update of a Pareto archive composed of mutually non-dominated points. It uses a new ND-Tree data structure in which each node represents a subset of points contained in a hyperrectangle defined by its local approximate ideal and nadir points. By building subsets containing points located close in the objective space and using basic properties of the local ideal and nadir points we can efficiently avoid searching many branches in the tree. ND-Tree may be used in multiobjective evolutionary algorithms and other multiobjective metaheuristics to update an archive of potentially non-dominated points. We prove that the proposed algorithm has sub-linear time complexity under mild assumptions. We experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front methods using artificial and realistic benchmarks with up to 10 objectives and show that with this new method substantial reduction of the number of point comparisons and computational time can be obtained. Furthermore, we apply the method to the non-dominated sorting problem showing that it is highly competitive to some recently proposed algorithms dedicated to this problem.Comment: 15 pages, 21 figures, 3 table

MEMOTS : a memetic algorithm integrating tabu search for combinatorial multiobjective optimization

We present in this paper a new multiobjective memetic algorithm scheme called MEMOX. In current multiobjective memetic algorithms, the parents used for recombination are randomly selected. We improve this approach by using a dynamic hypergrid which allows to select a parent located in a region of minimal density. The second parent selected is a solution close, in the objective space, to the first parent. A local search is then applied to the offspring. We experiment this scheme with a new multiobjective tabu search called PRTS, which leads to the memetic algorithm MEMOTS. We show on the multidimensional multiobjective knapsack problem that if the number of objectives increase, it is preferable to have a diversified research rather using an advanced local search. We compare the memetic algorithm MEMOTS to other multiobjective memetic algorithms by using different quality indicators and show that the performances of the method are very interesting

RIGA: A Regret-Based Interactive Genetic Algorithm

In this paper, we propose an interactive genetic algorithm for solving multi-objective combinatorial optimization problems under preference imprecision. More precisely, we consider problems where the decision maker's preferences over solutions can be represented by a parameterized aggregation function (e.g., a weighted sum, an OWA operator, a Choquet integral), and we assume that the parameters are initially not known by the recommendation system. In order to quickly make a good recommendation, we combine elicitation and search in the following way: 1) we use regret-based elicitation techniques to reduce the parameter space in a efficient way, 2) genetic operators are applied on parameter instances (instead of solutions) to better explore the parameter space, and 3) we generate promising solutions (population) using existing solving methods designed for the problem with known preferences. Our algorithm, called RIGA, can be applied to any multi-objective combinatorial optimization problem provided that the aggregation function is linear in its parameters and that a (near-)optimal solution can be efficiently determined for the problem with known preferences. We also study its theoretical performances: RIGA can be implemented in such way that it runs in polynomial time while asking no more than a polynomial number of queries. The method is tested on the multi-objective knapsack and traveling salesman problems. For several performance indicators (computation times, gap to optimality and number of queries), RIGA obtains better results than state-of-the-art algorithms

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

International audienceIn 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

Méthodes en deux phases pour la détermination des solutions Lorenz-optimales en optimisation combinatoire biobjectif

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A General Interactive Approach for Solving Multi-Objective Combinatorial Optimization Problems with Imprecise Preferences

International audienceWe consider multi-objective combinatorial optimization problems where preferences can be represented by a parameterized scalarizing function that is linear in its parameters. Assuming that the parameters are initially not known, we iteratively collect preference information from the decision maker until being able to identify her preferred solution. To obtain informative preference information, we ask the decision maker to compare two promising solutions generated using the extreme points of the polyhedron representing the admissible parameters. Moreover, our stopping criterion guarantees that the returned solution is optimal (or near-optimal) according to the decision maker's preferences. Finally, we provide numerical results to demonstrate the practical efficiency of our approach