A strength pareto evolutionary algorithm based on reference direction for multi-objective and many-objective optimization
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Abstract
While Pareto-based multi-objective 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 multi- 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 multi- and many-objective problems considered in this study. 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.