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To address the challenges of solving the many-objective flexible job-shop scheduling problem, this study proposes a loose non-dominated sorting genetic algorithm III (LNSGA-III), an enhancement of the non-dominated sorting genetic algorithm III (NSGA-III). First, a loose dominance principle is proposed to overcome the shortcomings of low selection pressure and slow convergence under the Pareto dominance principle. Next, a novel crossover operator without repair, named improved order crossover, is presented to fully preserve the characteristics of exchanged operations and enhance the exploration capability of the algorithm. Experimental studies involve testing algorithms on some typical scheduling instances with six simultaneously optimized objectives. The primary metric for algorithm comparison is the hypervolume, with additional investigation for statistical significance. Other metrics, including coverage, convergence and diversity, are also used for comparison. The experimental results demonstrate the effectiveness of the proposed enhancements, showcasing the significant superiority of the algorithm over some state-of-the-art alternatives.
Liu et al. (Fri,) studied this question.