Jacques Teghem

MOSA method: a tool for solving multiobjective combinatorial optimization problems

The success of modern heuristics (Simulated Annealing (S.A.), Tabu Search, Genetic Algorithms, …) in solving classical combinatorial optimization problems has drawn the attention of the research community in multicriteria methods. In fact, for large-scale problems, the simultaneous difficulties of -hard complexity and of multiobjective framework make most Multiobjective Combinatorial Optimization (MOCO) problems intractable for exact methods. This paper develops the so-called MOSA (Multiobjective Simulated Annealing) method to approximate the set of efficient solutions of a MOCO problem. Different options for the implementation are illustrated and extensive experiments prove the efficiency of the approach. Its results are compared to exact methods on bi-objective knapsack problems. Copyright

Two-phases Method and Branch and Bound Procedures to Solve the Bi–objective Knapsack Problem

The classical 0–1 knapsack problem is considered with two objectives. Two methods of the “two–phases” type are developed to generate the set of efficient solutions. In the first phase, the set of supported efficient solutions is determined by optimizing a parameterized single-objective knapsack problem. Two versions are proposed for a second phase, determining the non-supported efficient solutions: both versions are Branch and Bound approaches, but one is “breadth first”, while the other is “depth first”. Extensive numerical experiments have been realized to compare the results of both methods.

Control of the service process in a queueing system

Queueing systems already have a long life, and right from their birth they have been used to solve certain practical problems such as job-scheduling, the organisation of telephone exchanges,. . . . Nevertheless, although some optimization problems were introduced in queueing models early on, the majority of them where static or design problems in which the system characteristics do not change over time. Clearly, this type of model did not meet the requirements of the majority of the practical queueing applications, such as those related to the management of large scale systems in various domains: distribution, transportation, administration, informatics, . . . . It is particularly so in many communication and computer applications, in which the performance of the studied system may be improved if some system parameters are adjusted as the system state changes. Hence, one has a dynamic or control problem in which the system characteristics are allowed to change over time.

Solving multi-objective production scheduling problems using metaheuristics

Abstract Most of research in production scheduling is concerned with the optimization of a single criterion. However the analysis of the performance of a schedule often involves more than one aspect and therefore requires a multi-objective treatment. In this paper we first present ( Section 1 ) the general context of multi-objective production scheduling, analyze briefly the different possible approaches and define the aim of this study i.e. to design a general method able to approximate the set of all the efficient schedules for a large set of scheduling models. Then we introduce ( Section 2 ) the models we want to treat––one machine, parallel machines and permutation flow shops––and the corresponding notations. The method used––called multi-objective simulated annealing––is described in Section 3 . Section 4 is devoted to extensive numerical experiments and their analysis. Conclusions and further directions of research are discussed in the last section.

Strange: An interactive method for multi-objective linear programming under uncertainty

Abstract In the field of investment planning within a time horizon, problems typically involve multiple objectives, and basic data are uncertain. In a large number of cases, these decision problems can be written as linear programming problems in which time dependent uncertainties affect the coefficients and the right hand side of constraints. Given the possibility of defining plausible scenarios on basic data, discrete sets of such coefficients are given, each with its subjective probability of occurrence. The corresponding structure is then characteristic for Multi-Objective Stochastic Linear Programming (MOSLP). In the paper, an interactive procedure is described to obtain a best compromise for such a MOSLP problem. This algorithm, called Strange , extends the Stem method to take the random aspects into account. It involves in particular, the concepts of stochastic programming with recourse. In its interactive steps, the efficiency projection techniques are used to provide the decision-maker with detailed graphical information on efficient solution families. As an illustration of the successive steps, a didactic example is solved in some detail, and the results of a case study in energy planning are given.

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 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.

A multi-objective production scheduling case study solved by simulated annealing

Abstract During several decades, research in production scheduling mainly concerns a single criterion to optimize. However, the analysis of the performance of a schedule often involves more than one aspect and therefore requires multi-objective analysis. Such situation appears in the real case study considered here. This paper deals with a production scheduling problem in a flexible (or hybrid) job-shop with particular constraints: batch production; existence of two steps: production of several sub-products followed by the assembly of the final product; possible overlaps for the processing periods of two successive operations of a same job. At the end of the production step, different objectives should be considered simultaneously, among the makespan, the mean completion time, the maximal tardiness, the mean tardiness. The research is based on a real case study, concerning a Tunisian firm. We propose a multi-objective simulated annealing approach to tackle this problem and to propose to the manager an approximation of the set of efficient schedules. Several numerical results are reported.

The multiobjective multidimensional knapsack problem: a survey and a new approach

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.

Performance of the MOSA Method for the Bicriteria Assignment Problem

The classical linear Assignment problem is considered with two objectives. The aim is to generate the set of efficient solutions. An exact method is first developed based on the two-phase approach. In the second phase a new upper bound is proposed so that larger instances can be solved exactly. The so-called MOSA (Multi-Objective Simulated Annealing) is then recalled; its efficiency is improved by initialization with a greedy approach. Its results are compared to those obtained with the exact method. Extensive numerical experiments have been realized to measure the performance of the MOSA method.

Comparison of methodologies for fuzzy and stochastic multi-objective programming

Abstract Methods for solving a multicriteria linear program with coefficients of the objective functions and the constraints being flat fuzzy numbers and those dealing with a stochastic multicriteria linear program where imprecision of some data is modelled by probability distributions are surveyed. The methodologies are compared and evaluated. Some ideas for future research are emphasized.