Achievement scalarizing function sorting for strength Pareto evolutionary algorithm in many-objective optimization

Multi-objective evolutionary algorithms (MOEAs) have proven their effectiveness in solving two or three objective problems. However, recent research shows that Pareto-based MOEAs encounter selection difficulties facing many similar non-dominated solutions in dealing with many-objective problems. In order to reduce the selection pressure and improve the diversity, we propose achievement scalarizing function sorting strategy to make strength Pareto evolutionary algorithm suitable for many-objective optimization. In the proposed algorithm, we adopt density estimation strategy to redefine a new fitness value of a solution, which can select solution with good convergence and distribution. In addition, a clustering method is used to classify the non-dominated solutions, and then, an achievement scalarizing function ranking method is designed to layer different frontiers and eliminate redundant solutions in the environment selection stage, thus ensuring the convergence and diversity of non-dominant solutions. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems with 3, 5, 8, 10 objectives. Experimental studies demonstrate that the proposed algorithm shows very competitive performance.