An improved multiobjective evolutionary algorithm based on decomposition and adaptive multi-reference points

Many real-world optimization problems such as engineering design are finally modeled as a multiobjective optimization problem (MOP) which must be solved to get a set of trade-offs. Multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been regarded as a very promising approach for solving MOPs, which offers a general algorithmic framework of evolutionary multiobjective optimization. Recent studies have shown that MOEA/D with uniformly distributed weight vectors is well-suited to MOPs with regular Pareto optimal front, but its performance in terms of diversity deteriorates on MOPs with irregular Pareto optimal front such as highly nonlinear and convex. In this way, the solution set obtained by the algorithm can not provide more reasonable choices for decision makers. In order to efficiently overcome this shortcoming, in this paper, we propose an improved MOEA/D algorithm by virtue of the well-known Pascoletti-Serafini scalarization method and a new strategy of multi-reference points. Specifically, this strategy consists of the setting and adaptation of reference points generated by the techniques of equidistant partition and projection. For performance assessment, the proposed algorithm is compared with existing four state-of-the-art multiobjective evolutionary algorithms on both benchmark test problems with various types of Pareto optimal fronts and two real-world MOPs including the hatch cover design and the rocket injector design in engineering optimization. Experimental results reveal that the proposed algorithm is better than that of the other compared algorithms in diversity.