On Bounding Fronts and Bounding Vectors in Multi-objective OptimizationJulius Žilinskas
Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania
The main concept of branch and bound is to detect subsets of feasible solutions which cannot contain optimal solutions. In multi-objective optimization a bounding front is used - a set of bounding vectors in the objective space dominating all possible objective vectors corresponding to the subset of feasible solutions. The subset cannot contain Pareto optimal (efficient) solutions if each bounding vector in the bounding front corresponding to this subset is dominated by at least one already known decision vector. The simplest bounding front corresponds to a single ideal vector composed of lower bounds for each objective function. However, the bounding fronts with multiple bounding vectors may be tighter and therefore their use may discard more subsets of feasible solutions. In this seminar we investigate the use of bounding vectors and bounding fronts in multi-objective optimization.
The main concept of branch and bound is to detect subsets of feasible solutions which cannot contain optimal solutions. In multi-objective optimization a bounding front is used - a set of bounding vectors in the objective space dominating all possible objective vectors corresponding to the subset of feasible solutions. The subset cannot contain Pareto optimal (efficient) solutions if each bounding vector in the bounding front corresponding to this subset is dominated by at least one already known decision vector. The simplest bounding front corresponds to a single ideal vector composed of lower bounds for each objective function. However, the bounding fronts with multiple bounding vectors may be tighter and therefore their use may discard more subsets of feasible solutions. In this seminar we investigate the use of bounding vectors and bounding fronts in multi-objective optimization.
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