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.

Hybridization of Particle Swarm Optimization with Variable Neighborhood Search and Simulated Annealing for Improved Handling of the Permutation Flow-Shop Scheduling Problem

“…Once the internal comparison of HPSO with standard PSO, PSO-VNS, and validation against HGA and HGSA was completed, the last part of validation was against other notable techniques already reported in the literature. For this purpose, a more detailed comparison was carried out with WOA [16], Chaotic Whale Optimization (CWA) [17], the BAT-algorithm [18], NEHT (NEH algorithm together with the improvement presented by Taillard) [31], ACO [50], CPSO (Combinatorial PSO) [51], PSOENT (PSO with Expanding Neighborhood Topology) [40], and HAPSO (Hybrid Adaptive PSO) [52]. This comparison was solely based on ARPD values and is shown in Table 6 and graphically illustrated in Figure 8.…”

“…Therefore, the focus of research shifted towards meta-heuristics. Many such approaches, as viable solutions to PFSP, have already been reported in the literature, which includes GA (Genetic Algorithms) [10,11], PSO (Particle Swarm Optimization) [12,13] and ACO (Ant Colony Optimization) [14], Q-Learning algorithms [15], HWOA (Hybrid Whale Optimization Algorithms) [16], CWA (Enhanced Whale Optimization Algorithms) [17], and BAT-algorithms [18]. Metaheuristic-based approaches start with sequences generated randomly by a heuristic and then iterate until a stopping criterion is satisfied [19].…”

A Local Search-Based Generalized Normal Distribution Algorithm for Permutation Flow Shop Scheduling

“…The whale optimization algorithm (WOA) [36] improved using the chaos map and then integrated with the NEH algorithm has been proposed for tackling the PFSSP. In detail, the NEH algorithm and the largest ranked values rule are used in the initialization step of the chaos WOA (CWA) to initialize the solutions in better quality.…”

A discrete whale optimization algorithm for the no-wait flow shop scheduling problem

“…Whereas, it can't be directly applied to the optimization problems with discrete property and has the slower convergence. Although there have been some research results, such as an enhanced WOA 42 and a multi-objective WOA 43 have applied to the production scheduling problems. However, they are not all directly discrete encoding, but individual positions (continuous variables) are converted into scheduling solutions (job permutation) through LPT or ROV rule, which will reduce the optimization performance of the algorithm.…”