Yun-Chia Liang

A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem

Abstract In this paper, a particle swarm optimization algorithm (PSO) is presented to solve the permutation flowshop sequencing problem (PFSP) with the objectives of minimizing makespan and the total flowtime of jobs. For this purpose, a heuristic rule called the smallest position value (SPV) borrowed from the random key representation of Bean [J.C. Bean, Genetic algorithm and random keys for sequencing and optimization, ORSA Journal of Computing 6(2) (1994) 154–160] was developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems. In addition, a very efficient local search, called variable neighborhood search (VNS), was embedded in the PSO algorithm to solve the well known benchmark suites in the literature. The PSO algorithm was applied to both the 90 benchmark instances provided by Taillard [E. Taillard, Benchmarks for basic scheduling problems, European Journal of Operational Research, 64 (1993) 278–285], and the 14,000 random, narrow random and structured benchmark instances provided by Watson et al. [J.P. Watson, L. Barbulescu, L.D. Whitley, A.E. Howe, Contrasting structured and random permutation flowshop scheduling problems: Search space topology and algorithm performance, ORSA Journal of Computing 14(2) (2002) 98–123]. For makespan criterion, the solution quality was evaluated according to the best known solutions provided either by Taillard, or Watson et al. The total flowtime criterion was evaluated with the best known solutions provided by Liu and Reeves [J. Liu, C.R. Reeves, Constructive and composite heuristic solutions to the P∥∑Ci scheduling problem, European Journal of Operational Research 132 (2001) 439–452], and Rajendran and Ziegler [C. Rajendran, H. Ziegler, Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs, European Journal of Operational Research, 155(2) (2004) 426–438]. For the total flowtime criterion, 57 out of the 90 best known solutions reported by Liu and Reeves, and Rajendran and Ziegler were improved whereas for the makespan criterion, 195 out of the 800 best known solutions for the random and narrow random problems reported by Watson et al. were improved by the VNS version of the PSO algorithm.

A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem

In this paper, a discrete particle swarm optimization (DPSO) algorithm is presented to solve the no-wait flowshop scheduling problem with both makespan and total flowtime criteria. The main contribution of this study is due to the fact that particles are represented as discrete job permutations and a new position update method is developed based on the discrete domain. In addition, the DPSO algorithm is hybridized with the variable neighborhood descent (VND) algorithm to further improve the solution quality. Several speed-up methods are proposed for both the swap and insert neighborhood structures. The DPSO algorithm is applied to both 110 benchmark instances of Taillard [Benchmarks for basic scheduling problems. European Journal of Operational Research 1993;64:278-85] by treating them as the no-wait flowshop problem instances with the total flowtime criterion, and to 31 benchmark instances provided by Carlier [Ordonnancements a contraintes disjonctives. RAIRO Recherche operationelle 1978;12:333-51], Heller [Some numerical experiments for an MxJ flow shop and its decision-theoretical aspects. Operations Research 1960;8:178-84], and Revees [A genetic algorithm for flowshop sequencing. Computers and Operations Research 1995;22:5-13] for the makespan criterion. For the makespan criterion, the solution quality is evaluated according to the reference makespans generated by Rajendran [A no-wait flowshop scheduling heuristic to minimize makespan. Journal of the Operational Research Society 1994;45:472-8] whereas for the total flowtime criterion, it is evaluated with the optimal solutions, lower bounds and best known solutions provided by Fink and Vosz [Solving the continuous flow-shop scheduling problem by metaheuristics. European Journal of Operational Research 2003;151:400-14]. The computational results show that the DPSO algorithm generated either competitive or better results than those reported in the literature. Ultimately, 74 out of 80 best known solutions provided by Fink and Vosz [Solving the continuous flow-shop scheduling problem by metaheuristics. European Journal of Operational Research 2003;151:400-14] were improved by the VND version of the DPSO algorithm.

An ant colony optimization algorithm for the redundancy allocation problem (RAP)

This paper uses an ant colony meta-heuristic optimization method to solve the redundancy allocation problem (RAP). The RAP is a well known NP-hard problem which has been the subject of much prior work, generally in a restricted form where each subsystem must consist of identical components in parallel to make computations tractable. Meta-heuristic methods overcome this limitation, and offer a practical way to solve large instances of the relaxed RAP where different components can be placed in parallel. The ant colony method has not yet been used in reliability design, yet it is a method that is expressly designed for combinatorial problems with a neighborhood structure, as in the case of the RAP. An ant colony optimization algorithm for the RAP is devised & tested on a well-known suite of problems from the literature. It is shown that the ant colony method performs with little variability over problem instance or random number seed. It is competitive with the best-known heuristics for redundancy allocation.

A discrete differential evolution algorithm for the permutation flowshop scheduling problem

Very recently, Pan et al. [Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, GECCO07, pp. 126-33] presented a new and novel discrete differential evolution algorithm for the permutation flowshop scheduling problem with the makespan criterion. On the other hand, the iterated greedy algorithm is proposed by [Ruiz, R., & Stutzle, T. (2007). A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research, 177(3), 2033-49] for the permutation flowshop scheduling problem with the makespan criterion. However, both algorithms are not applied to the permutation flowshop scheduling problem with the total flowtime criterion. Based on their excellent performance with the makespan criterion, we extend both algorithms in this paper to the total flowtime objective. Furthermore, we propose a new and novel referenced local search procedure hybridized with both algorithms to further improve the solution quality. The referenced local search exploits the space based on reference positions taken from a reference solution in the hope of finding better positions for jobs when performing insertion operation. Computational results show that both algorithms with the referenced local search are either better or highly competitive to all the existing approaches in the literature for both objectives of makespan and total flowtime. Especially for the total flowtime criterion, their performance is superior to the particle swarm optimization algorithms proposed by [Tasgetiren, M. F., Liang, Y. -C., Sevkli, M., Gencyilmaz, G. (2007). Particle swarm optimization algorithm for makespan and total flowtime minimization in permutation flowshop sequencing problem. European Journal of Operational Research, 177(3), 1930-47] and [Jarboui, B., Ibrahim, S., Siarry, P., Rebai, A. (2007). A combinatorial particle swarm optimisation for solving permutation flowshop problems. Computers &Industrial Engineering, doi:10.1016/j.cie.2007.09.006]. Ultimately, for Taillards benchmark suite, four best known solutions for the makespan criterion as well as 40 out of the 90 best known solutions for the total flowtime criterion are further improved by either one of the algorithms presented in this paper.

Particle swarm optimization algorithm for single machine total weighted tardiness problem

In This work we present a particle swarm optimization algorithm to solve the single machine total weighted tardiness problem. A heuristic rule, the smallest position value (SPV) rule, is developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems, which are NP-hard in the literature. A simple but very efficient local search method is embedded in the particle swarm optimization algorithm. The computational results show that the particle swarm algorithm is able to find the optimal and best-known solutions on all instances of widely used benchmarks from the OR library.

An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems

This paper proposes an effective hybrid tabu search algorithm (HTSA) to solve the flexible job-shop scheduling problem. Three minimization objectives - the maximum completion time (makespan), the total workload of machines and the workload of the critical machine are considered simultaneously. In this study, a tabu search (TS) algorithm with an effective neighborhood structure combining two adaptive rules is developed, which constructs improved local search in the machine assignment module. Then, a well-designed left-shift decoding function is defined to transform a solution to an active schedule. In addition, a variable neighborhood search (VNS) algorithm integrating three insert and swap neighborhood structures based on public critical block theory is presented to perform local search in the operation scheduling component. The proposed HTSA is tested on sets of the well-known benchmark instances. The statistical analysis of performance comparisons shows that the proposed HTSA is superior to four existing algorithms including the AL+CGA algorithm by Kacem, Hammadi, and Borne (2002b), the PSO+SA algorithm by Xia and Wu (2005), the PSO+TS algorithm by Zhang, Shao, Li, and Gao (2009), and the Xings algorithm by Xing, Chen, and Yang (2009a) in terms of both solution quality and efficiency.

REDUNDANCY ALLOCATION OF SERIES-PARALLEL SYSTEMS USING A VARIABLE NEIGHBORHOOD SEARCH ALGORITHM

Abstract This paper presents a meta-heuristic algorithm, variable neighborhood search (VNS), to the redundancy allocation problem (RAP). The RAP, an NP-hard problem, has attracted the attention of much prior research, generally in a restricted form where each subsystem must consist of identical components. The newer meta-heuristic methods overcome this limitation and offer a practical way to solve large instances of the relaxed RAP where different components can be used in parallel. Authors’ previously published work has shown promise for the variable neighborhood descent (VND) method, the simplest version among VNS variations, on RAP. The variable neighborhood search method itself has not been used in reliability design, yet it is a method that fits those combinatorial problems with potential neighborhood structures, as in the case of the RAP. Therefore, authors further extended their work to develop a VNS algorithm for the RAP and tested a set of well-known benchmark problems from the literature. Results on 33 test instances ranging from less to severely constrained conditions show that the variable neighborhood search method improves the performance of VND and provides a competitive solution quality at economically computational expense in comparison with the best-known heuristics including ant colony optimization, genetic algorithm, and tabu search.

Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions

This article proposes the hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions. The hybrid NM–PSO algorithm is very easy to implement, in practice, since it does not require gradient computation. This hybrid procedure performed the exploration with PSO and the exploitation with the NM simplex search method. In a suite of 17 multi-optima test functions taken from the literature, the computational results via various experimental studies showed that the hybrid NM–PSO approach is superior to the two original search techniques (i.e. NM and PSO) in terms of solution quality and convergence rate. In addition, the presented algorithm is also compared with eight other published methods, such as hybrid genetic algorithm (GA), continuous GA, simulated annealing (SA), and tabu search (TS) by means of a smaller set of test functions. On the whole, the new algorithm is demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for multimodal functions.

A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search

This paper integrates Nelder-Mead simplex search method (NM) with genetic algorithm (GA) and particle swarm optimization (PSO), respectively, in an attempt to locate the global optimal solutions for the nonlinear continuous variable functions mainly focusing on response surface methodology (RSM). Both the hybrid NM-GA and NM-PSO algorithms incorporate concepts from the NM, GA or PSO, which are readily to implement in practice and the computation of functional derivatives is not necessary. The hybrid methods were first illustrated through four test functions from the RSM literature and were compared with original NM, GA and PSO algorithms. In each test scheme, the effectiveness, efficiency and robustness of these methods were evaluated via associated performance statistics, and the proposed hybrid approaches prove to be very suitable for solving the optimization problems of RSM-type. The hybrid methods were then tested by ten difficult nonlinear continuous functions and were compared with the best known heuristics in the literature. The results show that both hybrid algorithms were able to reach the global optimum in all runs within a comparably computational expense.

Particle Swarm Optimization Algorithm for Permutation Flowshop Sequencing Problem

This paper presents a particle swarm optimization algorithm (PSO) to solve the permutation flowshop sequencing problem (PFSP) with makespan criterion. Simple but very efficient local search based on the variable neighborhood search (VNS) is embedded in the PSO algorithm to solve the benchmark suites in the literature. The results are presented and compared to the best known approaches in the literature. Ultimately, a total of 195 out of 800 best-known solutions in the literature is improved by the VNS version of the PSO algorithm.