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A sequential multiobjective optimization tool designed to manage on line a set of varied algorithms

Rodon A., Collette Y., Siarry P.

Foundations of Computing and Decision Sciences

2003

Vol. 28, No. 4

247-271

We present a new sequential multiobjective optimization tool, called SMO, aimed at automatically choosing the most appropriate optimization method to be applied in order to solve a given problem. To make such choices, our program studies the structure of the set of found solutions in objective function space, using a new set of metrics : in particular, we use the Pareto ratio to determine how the solutions are placed in objective function space in relation to the Pareto surface, a correlation metric to compare the shapes of the practical and theoretical Pareto surfaces, and the "segment-dominance metric" to study the convexity of those surfaces. Some tests on academic benchmark problems are presented in this paper. A work under development is the application of SMO to a particular problem, namely the working out of the nuclear fuel loading patterns in pressurized water reactors, which is a difficult combinatorial multiobjective optimization problem.

A systematic comparison of performance of various multiple objective metaheuristics using a common set of analytical test functions

Collette Y., Siarry P., Wong H.-I.

Foundations of Computing and Decision Sciences

2000

Vol. 25, No. 4

249-271

Many multiple objective optimization algorithms have been described in the literature. Some of them use a "metaheuristic" (genetic algorithm, simulated annealing, tabu search and so on) that allow, in principle, to avoid getting trapped into a local minimum of an objective function. We feel that this approach can be advantageously extended to a large set of multiple objective optimization methods. Moreover, it is interesting to perform a systematic comparison between performances of various multiple objective metaheuristics. Such a comparison needs, on the one hand, to adopt a common set of test functions and, on the other hand, to use a common set of performance criteria. In this study, we propose to compare various metaheuristics associated with various multiple objective optimization methods (such as weighted sum of objective functions, goal programming, distance method and so on). These different couples are evaluated using a set of classical test functions. The set of test functions is chosen so as to represent most of the difficulties (multifrontality, discontinuity, non-convexity and so on) that can be met in engineering when handling real multiple objective optimization problems.