Abstract
The permutation flow shop scheduling problem (PFSP) is a renowned problem in the scheduling research community. It is an NP-hard combinatorial optimization problem that has useful real-world applications. In this problem, finding a useful algorithm to handle the massive amounts of jobs required to retrieve an actionable permutation order in a reasonable amount of time is important. The recently developed crow search algorithm (CSA) is a novel swarm-based metaheuristic algorithm originally proposed to solve mathematical optimization problems. In this paper, a hybrid CSA (HCSA) is proposed to minimize the makespans of PFSPs. First, to make the CSA suitable for solving the PFSP, the smallest position value rule is applied to convert continuous numbers into job sequences. Then, the HCSA uses a Nawaz–Enscore–Ham (NEH) technique to create a population with the required levels of quality and diversity. We apply a local search to enhance the quality of the solutions and avoid premature convergence; simulated annealing enhances the local search of a method based on a variable neighborhood search. Computational tests are used to evaluate the algorithm using PFSP benchmarks with job sizes between 20 and 500. The tests indicate that the performance of the proposed HCSA is significantly superior to that of other algorithms.
Highlights
Several optimization methods have been proposed in artificial intelligence to find interesting patterns or optimization results for larger NP-hard optimization problems within a reasonable amount of time
All programs were implemented in Java and executed on a Windows 10 operating system running on a computer with an AMD Ryzen 3 1200 Quad-Core
Where ARPD is the average percentage relative deviation, BRPD is the best percentage relative deviation, Si is the average values of the makespan found by the algorithm, Sbst is the best makespan found by the algorithm, UB indicates the upper bound of the benchmark, and R is the number of independent runs
Summary
Several optimization methods have been proposed in artificial intelligence to find interesting patterns or optimization results for larger NP-hard optimization problems within a reasonable amount of time. The basic concept of the PFSP is that n jobs need to be processed on a sequence of m machines, such that each job needs to be processed on all machines in the same order Johnson addressed it as a two-machine problem. Metaheuristic approaches are often applied to solve NP-hard combinatorial optimization problems. Various metaheuristic algorithms [23] continue to attract increasing interest in optimization research. In this paper, we propose a hybrid CSA (HCSA) approach to minimize makespan in PFSP problems. HCSA applies the evolutionary searching of CSA to generate the population, individual update, and competition, and effectively find better solutions by utilizing and initializing adaptive local searches to create diversity.
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