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Constraint propagation using dominance in interval branch & bound for nonlinear biobjective optimization. (English) Zbl 1403.90612

Summary: Constraint propagation has been widely used in nonlinear single-objective optimization inside interval branch & bound algorithms as an efficient way to discard infeasible and non-optimal regions of the search space. On the other hand, when considering two objective functions, constraint propagation is uncommon. It has mostly been applied in combinatorial problems inside particular methods. The difficulty is in the exploitation of dominance relations in order to discard the so-called non-Pareto optimal solutions inside a decision domain, which complicates the design of complete and efficient constraint propagation methods exploiting dominance relations. In this paper, we present an interval branch & bound algorithm which integrates dominance contractors, constraint propagation mechanisms that exploit an upper bound set using dominance relations. This method discards from the decision space values yielding solutions dominated by some solutions from the upper bound set. The effectiveness of the approach is shown on a sample of benchmark problems.

MSC:

90C29 Multi-objective and goal programming
90C30 Nonlinear programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
65K05 Numerical mathematical programming methods
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