A genetic-operator-integrated whale optimization algorithm for solving the flexible job shop scheduling problem

Abstract With the growing emphasis on intelligent and sustainable manufacturing, the flexible job shop scheduling problem (FJSP) has emerged as a critical optimization challenge due to its capability to model complex and dynamic production environments. As an NP-hard problem, FJSP poses significantly greater complexity than the classical job shop scheduling problem, particularly in high-precision domains such as aerospace manufacturing, where traditional optimization methods often fall short. To overcome the limitations of the standard Whale Optimization Algorithm (WOA)–namely its continuous search paradigm and inadequate local search mechanisms–this paper proposes a genetic-operator-integrated whale optimization algorithm (GOI-WOA) tailored for discrete scheduling tasks. The GOI-WOA employs a two-layer discrete encoding strategy to represent operations and machine assignments, and introduces genetic operators, a critical-path-based neighborhood search, and a temporal-entropy-based local search to enhance solution diversity and local exploitation. Furthermore, an elite information-sharing mechanism is incorporated to facilitate the diffusion of high-quality solutions within the population. Comprehensive experiments conducted on standard benchmark instances demonstrate that GOI-WOA consistently outperforms baseline WOA and other state-of-the-art methods in terms of makespan minimization, convergence stability, and computational efficiency. These results validate the effectiveness and robustness of GOI-WOA as a competitive solution framework for complex manufacturing scheduling problems.