A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization

While Pareto-based multiobjective optimization algorithms continue to show effectiveness for a wide range of practical problems that involve mostly two or three objectives, their limited application for many-objective problems, due to the increasing proportion of nondominated solutions and the lack of sufficient selection pressure, has also been gradually recognized. In this paper, we revive an early developed and computationally expensive strength Pareto-based evolutionary algorithm by introducing an efficient reference direction-based density estimator, a new fitness assignment scheme, and a new environmental selection strategy, for handling both multiobjective and many-objective problems. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed method shows very competitive performance on both multiobjective and many-objective problems considered in this paper. Besides, our extensive investigations and discussions reveal an interesting finding, that is, diversity-first-and-convergence-second selection strategies may have great potential to deal with many-objective optimization.