Enhancing Whale Optimization Algorithm with Chaotic Theory for Permutation Flow Shop Scheduling Problem

Abstract

The permutation flow shop scheduling problem (PFSSP) is a typical production scheduling problem and it has been proved to be a nondeterministic polynomial (NP-hard) problem when its scale is larger than 3. The whale optimization algorithm (WOA) is a new swarm intelligence algorithm which performs well for PFSSP. But the stability is still low, and the optimization results are not too good. On this basis, we optimize the parameters of WOA through chaos theory, and put forward a chaotic whale algorithm (CWA). Firstly, in this paper, the proposed CWA is combined with Nawaz–Ensco–Ham (NEH) and largest-rank-value (LRV) rule to initialize the population. Next, chaos theory is applied to WOA algorithm to improve its convergence speed and stability. On this basis, we also use cross operator and reversal-insertion operator to enhance the search ability of the algorithm. Finally, the improved local search algorithm is used to optimize the job sequence to find the minimum makespan. In several experiments, different benchmarks are used to investigate the performance of CWA. The experimental results show that CWA has better performance than other scheduling algorithms.

Keywords

• Whale optimization algorithm
• Chaotic maps
• Flow shop scheduling
• Makespan
• Local search
• Cross selection