Evolutionary Hybrid Particle Swarm Optimization Algorithm for Solving NP-Hard No-Wait Flow Shop Scheduling Problems
The no-wait flow shop is a flowshop in which the scheduling of jobs is continuous and simultaneous through all machines without waiting for any consecutive machines. The scheduling of a no-wait flow shop requires finding an appropriate sequence of jobs for scheduling, which in turn reduces total processing time. The classical brute force method for finding the probabilities of scheduling for improving the utilization of resources may become trapped in local optima, and this problem can hence be
... roblem can hence be observed as a typical NP-hard combinatorial optimization problem that requires finding a near optimal solution with heuristic and metaheuristic techniques. This paper proposes an effective hybrid Particle Swarm Optimization (PSO) metaheuristic algorithm for solving no-wait flow shop scheduling problems with the objective of minimizing the total flow time of jobs. This Proposed Hybrid Particle Swarm Optimization (PHPSO) algorithm presents a solution by the random key representation rule for converting the continuous position information values of particles to a discrete job permutation. The proposed algorithm initializes population efficiently with the Nawaz-Enscore-Ham (NEH) heuristic technique and uses an evolutionary search guided by the mechanism of PSO, as well as simulated annealing based on a local neighborhood search to avoid getting stuck in local optima and to provide the appropriate balance of global exploration and local exploitation. Extensive computational experiments are carried out based on Taillard's benchmark suite. Computational results and comparisons with existing metaheuristics show that the PHPSO algorithm outperforms the existing methods in terms of quality search and robustness for the problem considered. The improvement in solution quality is confirmed by statistical tests of significance. the start of a job by the first machine is delayed, if required, and the scheduling of such a "no-wait" constraint has attracted many researchers. A No-Wait Flow Shop Scheduling Problem (NWFSSP) has found applications in various processing industries, such as the chemical industry , food , concrete ware production , pharmaceuticals , etc. Allahverdi  reviewed scheduling problems with the no-wait constraint with respect to different shop environments, performance measures, setup types, and optimal scheduling criteria. Among various optimality criteria, viz. makespan, Total Flow Time (TFT), tardiness, lateness, number of tardy jobs, etc., makespan  and TFT [7,10] are of major interest for solving scheduling problems of no-wait type of flow shops, because makespan and TFT determine the total processing time for an entire pool of jobs and the total processing times for individual jobs respectively. This paper addresses TFT as an objective function for solving NWFSSP. TFT is considered to be an important performance measure that, when optimized, reflects a stable or uniform utilization of resources, a rapid turn-around on jobs, and the minimization of in-process inventory  . The main objective of planning a production schedule is to discover the sequence of jobs, which minimizes TFT. The classical brute force method for finding such job sequences fails for large-sized problems, as computational complexity rises exponentially as n!, where "n" is number of jobs; thus, NWFSSP is treated as combinatorial optimization problem. Because of computational complexity, researchers    have concluded that NWFSSP with more than two machines is NP-hard. The solutions to solve such NP-hard problems consist of an approximate algorithm which uses constructive heuristics, local search methods, and metaheuristics. Generally, heuristic algorithms can obtain near-optimal solutions in an acceptable amount of time. Earlier researchers      have developed efficient constructive heuristic algorithms for TFT minimization; however, these attempts are not useful for identifying near optimal solutions for larger-sized problems, as these developed algorithms usually get trapped in local optima for large-problem sizes  . Local search methods can find the solutions, but the quality of a solution and computational time depends to a great extent on appropriate initial populations  . Due to the advent of computation techniques, metaheuristics can be used to solve problems in less time so that the limitation of computational complexity can be resolved through metaheuristic applications. The field of metaheuristics, for application in combinatorial optimization problems of the scientific and industrial worlds, is growing rapidly ; on the other hand, attempts to use metaheuristics for solving combinatorial optimization problems began late. The recent past has witnessed a remarkable shift towards the hybridization of metaheuristics for optimization. The current trend focuses more on problem-specific approaches that lead to hybridization  . This paper attempts to use a metaheuristic technique, viz. Particle Swarm Optimization (PSO) algorithm, and its hybridization with Simulated Annealing (SA) to solve NWFSSP with a consideration of the Total Flow Time (TFT) of jobs as an objective criterion. Through extensive computational analysis using the well-known Taillard benchmark suite, we demonstrate that the Proposed Hybrid PSO (PHPSO) algorithm outperforms the recent best-performing algorithms available in the literature. The remainder of this paper is organized as follows. Section 2 provides a comparative review of various metaheuristics for solving NWFSSP. Section 3 formally defines and formulates NWFSSP. Section 4 describes metaheuristic PSO and SA along with a detailed procedure for implementing the proposed metaheuristic PHPSO. Section 5 describes PHPSO on Taillard benchmark suites, and then compares the performance of the proposed metaheuristics with that of the best-so-far algorithms. Finally, concluding remarks are given in Section 6. Literature Review Various metaheuristics have been proposed for solving NWFSSP for different objective criteria. This section provides a comparative review of various metaheuristics, used by earlier researchers, for solving NWFSSP for TFT as an optimization criterion, along with various hybridization techniques for the improvement of results obtained via metaheuristics over the last decade.