A Parallel Tabu Search Heuristic to Approximate Uniform Designs for Reference Set Based MOEAs

Recent Multi-objective Optimization (MO) algorithms such as MOEA/D or NSGA-III make use of an uniformly scattered set of reference points indicating search directions in the objective space in order to achieve diversity. Apart from the mixture-design based techniques such as the simplex lattice, the mixture-design based techniques, there exists the Uniform Design (DU) approach, which is based on based on the minimization of a discrepancy metric, which measures how well equidistributed the points are in a sample space. In this work, this minimization problem is tackled through the \(L_2\) discrepancy function and solved with a parallel heuristic based on several Tabu Searches, distributed over multiple processors. The computational burden does not allow us to perform many executions but the solution technique is able to produce nearly Uniform Designs. These point sets were used to solve some classical MO test problems with two different algorithms, MOEA/D and NSGA-III. The computational experiments proves that, when the dimension increases, the algorithms working with a set generated by Uniform Design significantly outperform their counterpart working with other state-of-the-art strategies, such as the simplex lattice or two layer designs.