New variants of simulated annealing for solving a biobjective assignment problem

The simulated annealing method (SA) has been applied in many ways to the multiobjective optimization context in order to determinate a set of efficient solutions. In this paper, we develop three approaches of multiobjective simulated annealing. Our first approach consists in acting upstream: the strategy of acceptance or reject of a non improving solution is defined from a dominance relation on the utility vector by simultaneously using all the search directions. In the second approach, we consider the dominance relation, on the cost vector, and we keep the aggregation in the Metropolis's rule. And in the third approach, we eliminate completely the notion of aggregation, by introducing in the Metropolis's rule a dominance relation on the probability vector of acceptance of a lower-quality solution, according to each objective. © 2008 Lavoisier, Paris.