A novel local search mechanism based on the reflected ray tracing method coupled to MOEA/D

In recent years, the use of decomposition methods has become a popular choice to solve complex multi-objective optimization problems. One possible approach to enhance the performance of a decomposition method is to couple it to a local search engine that speeds up convergence to the true Pareto front of a problem. Here, we propose a new local search strategy for continuous search spaces, which is based on the law of reflection of light. Our proposed approach computes reflected rays in order to explore and exploit promising subregions of the search space. The local search engine uses information of the Penalty Boundary Intersection method to create a scene with three elements: 1) a light source defined by the solution which is farthest from the ideal point, 2) a hyperspherical structure built by non-dominated neighboring solutions and 3) a set of reflected rays located in decision variable space. Our proposed local search engine is coupled to MOEA/D (a popular decomposition-based multi-objective optimizer) and is able to outperform three state-of-the-art multi-objective evolutionary algorithms, particularly in multifrontal problems.