Adaptive stochastic fractal search algorithm for multi-objective optimization

Abstract

Stochastic fractal search algorithm, a relatively efficient algorithm has certain advantages in solving multi-objective optimization problems. Decomposition-based strategy is effective for solving multi-objective optimization, which guarantees the diversity of solutions. On the other hand, a challenge for decomposition-based strategy is to enhance the algorithm’s convergence while maintaining the algorithm’s distribution. This paper proposes a reference vector-guided stochastic fractal search algorithm for multi-objective optimization(RVSFS). In the proposed algorithm, the leader solution of each subspace is selected by reference vectors to assist the generation of new solutions and ensure the convergence of the algorithm. A new selection criterion length–angle distance (LAD) is proposed. Furthermore, the Gaussian walk and Levy flight are conducted in different searching stages to balance the exploration and exploitation ability. To speed up convergence and maintain the diversity of solutions, an adaptive dynamic proportion mechanism is designed when using the random fractals and Gaussian walks to generate offspring. Since information is shared and exchanged among different solutions in each iteration, the searching process is accelerated and the exploration capability can be enhanced contemporary. On top of this, a vector-guided enhanced selection operator is designed in the elite selection step to provide desirable distribution. Our experimental results on 45 benchmarks from UF and WFG test suits show prominent competitiveness compared with five state-of-the-art algorithms. RVSFS is very competitive on all 9 UF benchmarks in terms of the metric inverted generational distance and also performs well on 14 of 36 benchmarks from WFG in terms of the metric inverted generational distance and the metric hypervolume.