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Lust T.,Laboratory of Mathematics and Operational Research | Teghem J.,Laboratory of Mathematics and Operational Research
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

We consider the following problem: to decompose a positive integer matrix into a linear combination of binary matrices that respect the consecutive ones property. The positive integer matrix corresponds to fields giving the different radiation beams that a linear accelerator has to send throughout the body of a patient. Due to the inhomogeneous dose levels, leaves from a multi-leaf collimator are used between the accelerator and the body of the patient to block the radiations. The leaves positions can be represented by segments, that are binary matrices with the consecutive ones property. The aim is to find a decomposition that minimizes the irradiation time, and the setup-time to configure the multileaf collimator at each step of the decomposition. We propose for this NP-hard multiobjective problem a heuristic method, based on the Pareto local search method. Experimentations are carried out on different size instances and the results are reported. These first results are encouraging and are a good basis for the design of more elaborated methods. © Springer-Verlag 2009.


Lust T.,Laboratory of Mathematics and Operational Research | Teghem J.,Laboratory of Mathematics and Operational Research | Tuyttens D.,Laboratory of Mathematics and Operational Research
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

Very large-scale neighborhood search (VLSNS) is a technique intensively used in single-objective optimization. However, there is almost no study of VLSNS for multiobjective optimization. We show in this paper that this technique is very efficient for the resolution of multiobjective combinatorial optimization problems. Two problems are considered: the multiobjective multidimensional knapsack problem and the multiobjective set covering problem. VLSNS are proposed for these two problems and are integrated into the two-phase Pareto local search. The results obtained on biobjective instances outperform the state-of-the-art results for various indicators. © 2011 Springer-Verlag.


Besbes W.,British Petroleum | Teghem J.,Laboratory of Mathematics and Operational Research | Loukil T.,Unite de Recherche LOGIQ
European Journal of Industrial Engineering | Year: 2010

In this study, we deal with a k-stage hybrid flow shop scheduling problem under availability constraints (HFSPAC). In such a problem, machines are not continuously available due to preventive maintenance tasks. Our study aims to provide a good approximate solution to this specific problem with the makespan minimisation as the performance measure. Few studies exist in the literature dealing with the HFSPAC. We consider in this paper two variants to tackle this problem. In the first, the starting times of maintenance tasks are fixed, whereas in the second variant, maintenance must be performed on given time windows. In this last case, a theoretical analysis is elaborated based on the machine idle time to decide which action to perform between left-shifting or right-shifting the maintenance task in the window. Due to the NP-hardness of the HFSPAC, an approximate approach, based on a genetic algorithm (GA), is proposed to minimise the makespan. Computational experiments are performed on randomly generated instances to show the efficiency of the proposed variant (flexibility of the starting times of the maintenance tasks) in terms of makespan minimisation. Moreover, a correlation function computation is proposed to statistically analyse these experiments. Copyright © 2010 Inderscience Enterprises Ltd.


Tuyttens D.,Laboratory of Mathematics and Operational Research | Vandaele A.,Laboratory of Mathematics and Operational Research
Computers and Operations Research | Year: 2010

In this paper, the cover printing problem, which consists in the grouping of book covers on offset plates in order to minimize the total production cost, is discussed. As the considered problem is hard, we discuss and propose a greedy random adaptative search procedure (GRASP) to solve the problem. The quality of the proposed procedure is tested on a set of reference instances, comparing the obtained results with those found in the literature. Our procedure improves the best known solutions for some of these instances. Results are also presented for larger, randomly generated problems. © 2009 Elsevier Ltd. All rights reserved.


Lust T.,Laboratory of Mathematics and Operational Research | Teghem J.,Laboratory of Mathematics and Operational Research
Journal of Heuristics | Year: 2010

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 state-of-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. © 2009 Springer Science+Business Media, LLC.


Lust T.,Laboratory of Mathematics and Operational Research | Jaszkiewicz A.,Poznan University of Technology
Computers and Operations Research | Year: 2010

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. © 2009 Elsevier Ltd. All rights reserved.


Lust T.,Laboratory of Mathematics and Operational Research | Teghem J.,Laboratory of Mathematics and Operational Research
Studies in Computational Intelligence | Year: 2010

The traveling salesman problem (TSP) is a challenging problem in combinatorial optimization. In this paper we consider the multiobjective TSP for which the aim is to obtain or to approximate the set of efficient solutions. In a first step, we classify and describe briefly the existing works, that are essentially based on the use of metaheuristics. In a second step, we propose a new method, called two-phase Pareto local search. In the first phase of this method, an initial population composed of an approximation to the extreme supported efficient solutions is generated. The second phase is a Pareto local search applied to all solutions of the initial population. The method does not use any numerical parameter. We show that using the combination of these two techniques-good initial population generation and Pareto local search-gives, on the majority of the instances tested, better results than state-of-the-art algorithms. © 2010 Springer-Verlag Berlin Heidelberg.

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