Improved Multiverse Optimization Algorithm for Fuzzy Flexible Job-Shop Scheduling Problem

An improved multiverse optimization (IMVO) algorithm is proposed herein for the fuzzy flexible job-shop scheduling problem pertaining to the non-deterministic polynomial-time hard (NP-hard) problem. First, we designed a hybrid initialization method to improve the quality of the initial solution, and thereafter, introduced a self-crossing technique along with an insert-based heuristic algorithm to simulate the process of exchanging objects between black/white holes and wormholes, respectively. Second, a universe selection mechanism is proposed to reduce the possibility of the algorithm falling into a local optimum. Third, four kinds of neighborhood structures were designed to improve the local search ability of the algorithm. In the decoding operation, we adopted the shift-left strategy to completely utilize the idle time of the machine. Finally, numerous experiments were conducted on the three benchmark test sets of various types and sizes to investigate the performance of the proposed IMVO algorithm. The experimental results demonstrated the effectiveness of the algorithm, especially in large-scale instances, displaying a strong superiority with an average maximum enhancement efficiency of 50.44%.