Impact of Initial Partial Sequence in the Makespan, in Permutation Flow Shop Scheduling Heuristic Algorithms – An Analysis

The permutation flow-shop scheduling problem (PFSP) is an non-deterministic polynomialtime (NP) hard combinatorial optimization problems and has been widely researched within thescheduling community. In this paper, a memetic gravitation search algorithm (MGSA) is proposedto solve the PFSP for minimizing the makespan measure. The smallest position value (SPV) rule isutilized for converting the continuous number to job permutations for determining the most suitablethe proposed MGSA for the PFSP. The proposed MGSA uses a Nawaz-Enscore-Ham (NEH) heuristicalgorithm for initialization of population, and a simulated annealing (SA) is coupled with the variableneighborhood search (VNS) as the local search method to balance exploitation and exploration. Toverify the robustness of the MGSA, it is compared with three particle swarm optimization (PSO) algorithmson the basis of 12 PFSP instances with different job sizes ranging from 20 to 500. The resultsdemonstrate that the proposed MGSA can outperform other compared algorithms.

The distributed permutation flow shop scheduling (DPFSS) is a permutation flow shop scheduling problem including the multi-factory environment. The processing times of the jobs in a real life scheduling problem cannot be precisely know because of the human factor. In this study, the process times and due dates of the jobs are considered triangular and trapezoidal fuzzy numbers for DPFSS environment. An artificial bee colony (ABC) algorithm is developed to solve the multi-objective distributed fuzzy permutation flow shop (DFPFS) problem. First, the proposed ABC algorithm is calibrated with the well-known DPFSS instances in the literature. Then, the DPFSS instances are fuzzified and solved with the algorithm. According to the results, the proposed ABC algorithm performs well to solve the DFPFS problems.

This paper addresses an n-job, m-machine permutation flow shop scheduling problem (PFSSP) with unlimited intermediate buffers and rework activities. The concept of rework means that processing of a job on a machine may not meet a predefined quality level through its first process. Thus we have a probabilistic cycle of operations for jobs on different machines which is based on two concepts: (1) a failure probability of a job on a machine and, (2) a descent rate that reduces the processing times for rework phase. In this case, the processing times of jobs on machines become random variables with a known probability distribution. The aim of this paper is to examine possible solution approaches for generating the efficient job sequences with the least potential makespan. A wide range of simulation-based approaches are applied to address the proposed problem. These methods contain mathematical formulation, heuristic algorithms, and metaheuristics. The mechanism of the solution approaches is based on firstly using expected processing times to find a job sequence; then evaluating the obtained job sequences by several simulated trials. Using the one-way ANOVA test, these methods have been compared together, and the results show the superiority of metaheuristics, especially simulated annealing, over the other methods

The permutation flow shop scheduling problem (PFSP), which is one of the most important scheduling types, is widespread in the modern industries. With the increase of scheduling scale, the difficulty and computation time of solving the problem will increase exponentially. Adding the knowledge to intelligent algorithms is a good way to solve the complex and difficult scheduling problems in reasonable time. To deal with the complex PFSPs, this paper proposes an improved simulated annealing (SA) algorithm based on residual network (SARes). First, this paper defines the neighborhood of the PFSP and divides its key blocks. Second, the Residual Network (ResNet) is used to extract and train the features of key blocks. And, the trained parameters are stored in the SA algorithm to improve its performance. Afterwards, some key operators, including the initial temperature setting and temperature attenuation function of SA algorithm, are also modified. After every new solution is generated, the parameters trained by the ResNet are used for fast ergodic search until the local optimal solution found in the current neighborhood. Finally, the most famous benchmarks including part of TA benchmark are selected to verify the performance of the proposed SARes algorithm, and the comparisons with the-state-of-art methods are also conducted. The experimental results show that the proposed method has achieved good results by comparing with other algorithms. This paper also conducts experiments on network structure design, algorithm parameter selection, CPU time and other problems, and verifies the advantages of SARes algorithm from the aspects of stability and efficiency.

As a new analogy paradigm of human learning process, reinforcement learning (RL) has become an emerging topic in computational intelligence (CI). The synergy between the RL and CI is an emerging way to develop efficient solution algorithms for solving complex combinatorial optimization (CO) problems like machine scheduling problem. In this paper, we proposed an efficient optimization algorithm based on Deep RL for solving permutation flow-shop scheduling problem (PFSP) to minimize the maximum completion time. Firstly, a new deep neural network (PFSPNet) is designed for the PFSP to achieve the end-to-end output without limitation of problem sizes. Secondly, an actor-critic method of RL is used to train the PFSPNet without depending on the collection of high-quality labelled data. Thirdly, an improvement strategy is designed to refine the solution provided by the PFSPNet. Simulation results and statistical comparison show that the proposed optimization algorithm based on deep RL can obtain better results than the existing heuristics in similar computational time for solving the PFSP.

Scheduling problem has always been an important problem in the industrial sectors since it creates huge impact on the overall performance of the manufacturing. Good scheduling can reduce overall production time which then leads to lower cost and good resource management. The permutation flowshop scheduling (PFSP) is the classic scheduling problems that attracts both business and research area for almost half a century. On research side, a variety of complex algorithms have been introduced to solve the problems and provide high quality of solutions. Nevertheless, these algorithms will be useless if they fail to implement in practice where computational time and complexity of algorithm become an important issue of concern. This research proposes a Node-Based Coincidence Algorithm (NB-COIN) for the permutation flowshop scheduling problems (PFSP) aimed at Makespan minimization. NB-COIN is proved to be an effective algorithm that can provide good quality solutions using small amount of time and resources. The results generated by NB-COIN are also better than other well-known algorithms in consideration. Based on the bench-mark data sets of Taillard, 10% of the solutions provided by the presented algorithm are optimal solutions. Moreover, the solutions found by NB-COIN are also achieve 0.96% gap from upper bound in average. More importantly, those solutions are found within a short time.

This research proposes a revised discrete particle swarm optimization (RDPSO) to solve the permutation flow-shop scheduling problem with the objective of minimizing makespan (PFSP-makespan). The candidate problem is one of the most studied NP-complete scheduling problems. RDPSO proposes new particle swarm learning strategies to thoroughly study how to properly apply the global best solution and the personal best solution to guide the search of RDPSO. A new filtered local search is developed to filter the solution regions that have been reviewed and guide the search to new solution regions in order to keep the search from premature convergence. Computational experiments on Taillard's benchmark problem sets demonstrate that RDPSO significantly outperforms all the existing PSO algorithms.

Permutation flow shop scheduling problem is a complicated global optimum problem. A number of intelligent algorithms have been used for this problem. In this paper, a plant growth simulation algorithm was used to solve permutation flow shop scheduling problem. The algorithm was experimented and the experimental results show that the Plant Growth Simulation Algorithm (PGSA)has better feasibility and validity for solving permutation flow shop scheduling problem.

A constructive heuristic for the permutation flow shop scheduling problem with the objective of minimizing total completion time is proposed in this paper. It is constructed using a population-based technique and also the insertion rule similar to that presented in the Nawaz–Enscore–Ham (Omega 11:91–95, 1983) heuristic for the makespan criterion. We show, through computational results, that the proposed heuristic performs better than the heuristic of Woo and Yim (Comput Oper Res 25:175–182, 1998) for small and large problem sizes and the heuristic of Framinan and Leisten (Omega 31:311–317, 2003) for small and medium problem sizes. However, the relative performance of the heuristic of Framinan and Leisten improves compared to the proposed method when the job size increases. The time complexity of the proposed method has been shown to be less than those required by the existing heuristics. The average CPU time of the proposed heuristic is significantly less than the heuristic of Framinan and Leisten for large jobs.

For the past two decades simulated annealing has been playing a crucial role in the design of optimization strategies for flow shop scheduling applications. This paper presents an efficient simulated annealing algorithm for minimizing the total flow time in permutation flow shop scheduling problems. Empirical results demonstrate the improvement in solution quality obtained by the proposed approach over state-of-the-art methods in the literature.

Energy-efficient scheduling for a permutation flow shop with variable transportation time using an improved discrete whale swarm optimization

In this paper we consider permutation flow shop scheduling problems with batch setup times. Each job has to be processed on each machine once and the technological routes are identical for all jobs. The set of jobs is divided into groups. There are given processing timest ij of jobi on machinej and setup timess rj on machinej when a job of ther-th group is processed after a job of another group. It is assumed that the same job order has to be chosen on each machine. We consider both the problems of minimizing the makespan and of minimizing the sum of completion times, where batch or item availability of the jobs is assumed. For these problems we give various constructive and iterative algorithms. The constructive algorithms are based on insertion techniques combined with beam search. We introduce suitable neighbourhood structures for such problems with batch setup times and describe iterative algorithms that are based on local search and reinsertion techniques. The developed algorithms have been tested on a large collection of problems with up to 80 jobs.

This paper presents two bi-objective simulated annealing proceduresto deal with the classical permutation flow shop scheduling problemconsidering the makespan and the total completion time as criteria.The proposed methods are based on multi-objective simulatedannealing techniques combined with constructive and heuristicalgorithms. A computational experiment has been carried out anddifferent metrics have been computed to check various attributes ofeach method. For all the tested instances a net set of potentiallyefficient schedules has been obtained and compared with previouslypublished results. Results indicate that the proposed algorithmsprovide efficient solutions with little computational effort whichcan serve as input for interactive procedures.

The well-known particle swarm optimization (PSO) proposed by Kennedy and Eberhart has been widely applied to the continuous optimal problems. However, it is still intractable to apply PSO to discrete optimization problems, such as permutation flow shop scheduling problems (PFSSP). In this paper, a new high performing metaheuristic algorithm hybridizing PSO with variable neighborhood search (VNS) is proposed to solve PFSSP with the objective of minimizing makespan. NEH heuristic has been adopted in the first step to generate good solutions in the initial population, and then PSO and VNS are hybridized to search for optimal or near-optimal solutions of the PFSSP. Two effective neighborhood structures concerned with characteristics of PFSSP have been adopted to enhance VNS's performance. Computational experiments have been conducted on benchmarks and comparison results with other existing algorithms show the efficiency of the proposed algorithm.

In order to enhance the performance of shuffled frog leaping algorithm in solving optimization problem, this paper added the mutation operator to original shuffled frog leaping algorithm, an improved shuffled frog-leaping algorithm of solving permutation flow shop scheduling problem was proposed. Simulation results show that the improved algorithm has better feasibility and validity for solving permutation flow shop scheduling problem.