An Improved MOEA/D with an Auction-Based Matching Mechanism

Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing these subproblems in a collaborative manner. However, most existing MOEA/Ds maintain population diversity by limiting the replacement region or scale, which come at the cost of decreasing convergence. To better balance convergence and diversity, we introduce auction theory into algorithm design and propose an auction-based matching (ABM) mechanism to coordinate the replacement procedure in MOEA/D. In the ABM mechanism, each subproblem can be associated with its preferred individual in a competitive manner by simulating the auction process in economic activities. The integration of ABM into MOEA/D forms the proposed MOEA/D-ABM. Furthermore, to make the appropriate distribution of weight vectors, a modified adjustment strategy is utilized to adaptively adjust the weight vectors during the evolution process, where the trigger timing is determined by the convergence activity of the population. Finally, MOEA/D-ABM is compared with six state-of-the-art multi-objective evolutionary algorithms (MOEAs) on some benchmark problems with two to ten objectives. The experimental results show the competitiveness of MOEA/D-ABM in the performance of diversity and convergence. They also demonstrate that the use of the ABM mechanism can greatly improve the convergence rate of the algorithm.