A Neighborhood Operator for Continuous Multi-Objective Optimization Problems

Abstract

Path-metaheuristics have been used successfully in combinatorial optimization. However, in continuous optimization problems, the lack of neighborhood definitions makes them difficult to design and implement. This paper proposes a neighborhood operator based on first order linear approximation of the gradient. In order to adapt the linear approximation to multi-objective optimization, we use the multi-objective decomposition approach so the operator can be used for single and multi-objective continuous optimization problems. The proposed approach is validated using a Threshold Accepting algorithm based on decomposition and a set of benchmark problems for multi-objective optimization. Results show a significant improvement over Pareto lineal sets.