Design and application of MOEA/D with adaptive penalty strategy

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and optimizes them in a collaborative manner. In MOEA/D, decomposition mechanisms are used to push the population to approach the Pareto optimal front (POF), whilst a set of uniformly distributed weight vectors are applied to maintain the diversity of the population. MOEA/D has been shown to be very efficient in solving MOPs. However, the POF of many MOPs has complex characteristics, which significantly degrades the performance of MOEA/D. Penalty-based boundary intersection (PBI) is one of the frequently used decomposition approaches. In PBI approach, penalty factor plays a crucial role in balancing convergence and diversity. This paper proposes an adaptive penalty strategy (APS) which can dynamically adjust the value of the penalty factor for each weight vector during the evolutionary process. The diversity of approximated Pareto front can be enhanced by using this APS approach. The performance of the proposed MOEA/D-APS algorithm is investigated on six newly designed benchmark MOPs with complex POF shapes and the multiobjective optimization of space truss structure.