Showing papers on "Flow shop scheduling published in 2023"

A Greedy Cooperative Co-Evolutionary Algorithm With Problem-Specific Knowledge for Multiobjective Flowshop Group Scheduling Problems

Abstract: The flowshop sequence-dependent group scheduling problem (FSDGSP) with the production efficiency measures has been extensively studied due to its wide industrial applications. However, energy efficiency indicators are often ignored in the literature. This article considers the FSDGSP to minimize makespan, total flow time, and total energy consumption, simultaneously. After the problem-specific knowledge is extracted, a mixed-integer linear programming model and a critical path-based accelerated evaluation method are proposed. Since the FSDGSP includes multiple coupled subproblems, a greedy cooperative co-evolutionary algorithm (GCCEA) is designed to explore the solution space in depth. Meanwhile, a random mutation operator and a greedy energy-saving strategy are employed to adjust the processing speeds of machines to obtain a potential nondominated solution. A large number of experimental results show that the proposed algorithm significantly outperforms the existing classic multiobjective optimization algorithms, which is due to the usage of problem-related knowledge.

Solving Biobjective Distributed Flow-Shop Scheduling Problems With Lot-Streaming Using an Improved Jaya Algorithm

Abstract: A distributed flow-shop scheduling problem with lot-streaming that considers completion time and total energy consumption is addressed. It requires to optimally assign jobs to multiple distributed factories and, at the same time, sequence them. A biobjective mathematic model is first developed to describe the considered problem. Then, an improved Jaya algorithm is proposed to solve it. The Nawaz-Enscore-Ham (NEH) initializing rule, a job-factory assignment strategy, the improved strategies for makespan and energy efficiency are designed based on the problem's characteristic to improve the Jaya's performance. Finally, experiments are carried out on 120 instances of 12 scales. The performance of the improved strategies is verified. Comparisons and discussions show that the Jaya algorithm improved by the designed strategies is highly competitive for solving the considered problem with makespan and total energy consumption criteria.

Digital twin-based job shop anomaly detection and dynamic scheduling

Abstract: Scheduling scheme is one of the critical factors affecting the production efficiency. In the actual production, anomalies will lead to scheduling deviation and influence scheme execution, which makes the traditional job shop scheduling methods are not sufficient to meet the needs of real-time and accuracy. By introducing digital twin (DT), further convergence between physical and virtual space can be achieved, which enormously reinforces real-time performance of job shop scheduling. For flexible job shop, an anomaly detection and dynamic scheduling framework based on DT is proposed in this paper. Previously, a multi-level production process monitoring model is proposed to detect anomaly. Then, a real-time optimization strategy of scheduling scheme based on rolling window mechanism is explored to enforce dynamic scheduling optimization. Finally, the improved grey wolf optimization algorithm is introduced to solve the scheduling problem. Under this framework, it is possible to monitor the deviation between the actual processing state and the planned processing state in real time and effectively reduce the deviation. An equipment manufacturing job shop is taken as a case study to illustrate the effectiveness and advantages of the proposed framework.

A Hybrid Evolutionary Algorithm Using Two Solution Representations for Hybrid Flow-Shop Scheduling Problem

Abstract: As an extension of the classical flow-shop scheduling problem, the hybrid flow-shop scheduling problem (HFSP) widely exists in large-scale industrial production systems and has been considered to be challenging for its complexity and flexibility. Evolutionary algorithms based on encoding and heuristic decoding approaches are shown effective in solving the HFSP. However, frequently used encoding and decoding strategies can only search a limited area of the solution space, thus leading to unsatisfactory performance during the later period. In this article, a hybrid evolutionary algorithm (HEA) using two solution representations is proposed to solve the HFSP for makespan minimization. First, the proposed HEA searches the solution space by a permutation-based encoding representation and two heuristic decoding methods to find some promising areas. Afterward, a Tabu search (TS) procedure based on a disjunctive graph representation is introduced to expand the searching space for further optimization. Two classical neighborhood structures focusing on critical paths are extended to the problem-specific backward schedules to generate candidate solutions for the TS. The proposed HEA is tested on three public HFSP benchmark sets from the existing literature, including 567 instances in total, and is compared with some state-of-the-art algorithms. Extensive experimental results indicate that the proposed HEA performs much better than the other algorithms. Moreover, the proposed method finds new best solutions for 285 hard instances.

Improved Meta-Heuristics for Solving Distributed Lot-Streaming Permutation Flow Shop Scheduling Problems

Abstract: This paper addresses a distributed lot-streaming permutation flow shop scheduling problem that has various applications in real-life manufacturing systems. We aim to optimally assign jobs to multiple distributed factories and sequence them to minimize the maximum completion time (Makespan). A mathematic model is first developed to describe the considered problem. Then, five meta-heuristics are executed to solve it, including particle swarm optimization, genetic algorithm, harmony search, artificial bee colony, and Jaya algorithm. To improve the performance of these meta-heuristics, we employ Nawaz-Enscore-Ham (NEH) heuristic to initialize populations and propose improved strategies based on the problem’s feature. Finally, experiments are carried out based on 120 instances. The performance of improved strategies is verified. Comparisons and discussions show that the artificial bee colony algorithm with improved strategies has the best competitiveness for solving the proposed problem with makespan criteria. Note to Practitioners—In contemporary manufacturing industry, the traditional single-factory environment is being replaced by a distributed multi-factory environment, as a distributed pattern can effectively improve the production efficiency through the reasonable resource allocation strategies. The distributed lot-streaming permutation flow shop scheduling problem in such a pattern is of significance to practitioners. Although intelligent optimization can provide an effective tool to solve such problems, most of the algorithms are parameter-sensitive. A challenge for engineers is parameter selection, which greatly impacts the algorithm performance. To ensure the robustness of the algorithms, we develop five improved meta-heuristics by employing some strategies. Furthermore, parameter setting test is carried out to select the appropriate parameter values. As a result, the proposed algorithms can obtain resource allocation schemes with high-quality. It is shown that the artificial bee colony algorithm with improved strategies outperforms other algorithms well. The proposed methodology can be readily applied to real distributed scheduling problems.

LS-HH: A Learning-Based Selection Hyper-Heuristic for Distributed Heterogeneous Hybrid Blocking Flow-Shop Scheduling

Abstract: As the development of economic globalization, the distributed manufacturing has become common in modern industries. The scheduling of production resources in multiple production centers becomes an emerging topic. This paper is the first attempt to address a distributed heterogeneous hybrid blocking flow-shop scheduling problem (DHHFSP-B) with the minimization of makespan. Compared with the traditional single flow-shop scheduling, DHHFSP-B considers the collaborative production of multiple hybrid flow lines with heterogeneous layout and processing performance as well as no intermediate buffers. We firstly present a mixed-integer linear programming model to formulate DHHFSP-B and then propose a learning-based selection hyper-heuristic framework (LS-HH) for solving it. The LS-HH contains high-level strategy and low-level heuristics. In the high-level strategy, a learning probability model is built to provide the guidance to choose the suitable perturbation heuristic during the optimization process. A simulated annealing-like move acceptance is employed to determine the updating of incumbent domain solution and prevent the search from trapping into local optimum. In the low-level heuristics, a constructive heuristic is proposed based on a novel assignment rule to create the initial domain solution. Four problem-specific perturbation heuristics and a variable neighborhood search-based improvement operator are employed to search the solution space. A comprehensive computational experiment is conducted. The comparative results show that the LS-HH significantly outperforms the Gurobi solver and several closely relevant optimization methods in solving the DHHFSP-B.

An Improved Artificial Bee Colony Algorithm With Q-Learning for Solving Permutation Flow-Shop Scheduling Problems

Abstract: A permutation flow-shop scheduling problem (PFSP) has been studied for a long time due to its significance in real-life applications. This work proposes an improved artificial bee colony (ABC) algorithm with $Q$ -learning, named QABC, for solving it with minimizing the maximum completion time (makespan). First, the Nawaz–Enscore–Ham (NEH) heuristic is employed to initialize the population of ABC. Second, a set of problem-specific and knowledge-based neighborhood structures are designed in the employ bee phase. $Q$ -learning is employed to favorably choose the premium neighborhood structures. Next, an all-round search strategy is proposed to further enhance the quality of individuals in the onlooker bee phase. Moreover, an insert-based method is applied to avoid local optima. Finally, QABC is used to solve 151 well-known benchmark instances. Its performance is verified by comparing it with the state-of-the-art algorithms. Experimental and statistical results demonstrate its superiority over its peers in solving the concerned problems.

Agent-based simulation and optimization of hybrid flow shop considering multi-skilled workers and fatigue factors

Abstract: In the past few decades, more and more studies have begun to consider the impact of human factors on manufacturing systems. This paper studies a hybrid flow shop scheduling problem considering multi-skilled workers and fatigue factors. An agent-based simulation system is established to cope with the uncertainties in the worker fatigue model. Furthermore, this paper proposes a novel simulation-based optimization (SBO) framework, which combines genetic algorithm (GA) and reinforcement learning (RL) to address the hybrid flow shop scheduling problem. Numerical experiments are conducted on several instances with different production configurations. In particular, a pharmaceutical production facility is modeled as a hybrid flow shop to demonstrate the feasibility and effectiveness of the proposed SBO method.

A Population-Based Iterated Greedy Algorithm for Distributed Assembly No-Wait Flow-Shop Scheduling Problem

Abstract: This article investigates a distributed assembly no-wait flow-shop scheduling problem (DANWFSP), which has important applications in manufacturing systems. The objective is to minimize the total flowtime. A mixed-integer linear programming model of DANWFSP with total flowtime criterion is proposed. A population-based iterated greedy algorithm (PBIGA) is presented to address the problem. A new constructive heuristic is presented to generate an initial population with high quality. For DANWFSP, an accelerated NR3 algorithm is proposed to assign jobs to the factories, which improves the efficiency of the algorithm and saves CPU time. To enhance the effectiveness of the PBIGA, the local search method and the destruction-construction mechanisms are designed for the product sequence and job sequence, respectively. A selection mechanism is presented to determine, which individuals execute the local search method. An acceptance criterion is proposed to determine whether the offspring are adopted by the population. Finally, the PBIGA and seven state-of-the-art algorithms are tested on 810 large-scale benchmark instances. The experimental results show that the presented PBIGA is an effective algorithm to address the problem and performs better than recently state-of-the-art algorithms compared in this article.

A multi-class teaching-learning-based optimization for multi-objective distributed hybrid flow shop scheduling

Abstract: Distributed hybrid flow shop scheduling problem (DHFSP) has attracted some attention. In this study, DHFSP with sequence-dependent setup times is studied and a multi-class teaching–learning-based optimization (MTLBO) is proposed to minimize makespan and maximum tardiness simultaneously. A two-string representation is adopted. s classes are formed to improve search efficiency by implementing reward and punishment mechanism among them. Class evaluation is introduced and two teacher phases and one learner phase are applied in the evolution of each class. Elimination process acts on the worst class to avoid the waste of computing resource. A number of experiments are conducted and the computational results demonstrate that MTLBO is a very competitive method for DHFSP.

An ordered precedence constrained flow shop scheduling problem with machine specific preventive maintenance

Abstract: In reality, the machines may interrupt because of the nature of deterioration of the machines. Thus, it is inevitable to perform maintenance alongside production planning. The preventive maintenance is a schedule of strategic operations that are performed prior to the failure occurring, to retain the system operating at the preferred level of consistency. Thus, preventive maintenance plays a significant role in flow shop scheduling models. With its practical significance, this study addresses a practical three-machine n jobs flow shop-scheduling problem (FSSP) in which machine specific preventive maintenance, where each machine is given with a maintenance schedule is considered. In addition, a practical ordered precedence constraint in which some set of jobs has to process in the specified order irrespective of their processing times is also considered. The problem’s goal is to establish the optimal job sequence and preventive maintenance such that the overall cost of tardiness and preventive maintenance is as minimum as possible. An efficient heuristic approach is designed to tackle the present model, resulting in total cost savings. A comparative analysis is not conducted due to absence of studies on the current problem in the literature. However, Computational experiments are carried out on some test instances and results are reported. The reported results may be useful for future studies.

A Novel Approach for Minimizing Processing Times of Three-Stage Flow Shop Scheduling Problems under Fuzziness

Abstract: The purpose of this research is to investigate a novel three-stage flow shop scheduling problem with an ambiguous processing time. The uncertain information is characterized by Pentagonal fuzzy numbers. To solve the problem, in this paper, two different strategies are proposed; one relies on the idea of a ranking function, and the other on the close interval approximation of the pentagonal fuzzy number. For persons that need to be more specific in their requirements, the close interval approximation of the Pentagonal fuzzy number is judged to be the best appropriate approximation interval. Regarding the rental cost specification, these methods are used to reduce the rental cost for the concerned devices. In addition, a comparison of our suggested approach’s computed total processing time, total machine rental cost, and machine idle time to the existing approach is introduced. A numerical example is shown to clarify the benefits of the two strategies and to help the readers understand it better.

A Novel Hybrid Simulated Annealing for No-Wait Open-Shop Surgical Case Scheduling Problems

Abstract: In this paper, the problem of finding an assignment of “n” surgeries to be presented in one of “m” identical operating rooms (ORs) or machines as the surgical case scheduling problem (SCSP) is proposed. Since ORs are among NP-hard optimization problems, mathematical and metaheuristic methods to address OR optimization problems are used. The job or surgical operation ordering in any OR is a permanent part of all sequencing and scheduling problems. The transportation times between ORs are defined based on the type of surgical operations and do not depend on distance, so there is no surgical operation waiting time for transferring. These problems are called no-wait open-shop scheduling problems (NWOSP) with transportation times. The transportation system for the problems is considered a multi-transportation system with no limitation on the number of transportation devices. Accordingly, this study modeled a novel combined no-wait open-shop surgical case scheduling problem (NWOSP-SCSP) with multi-transportation times for the first time to minimize the maximum percentile of makespan for OR as a single objective model. A mixed-integer linear program (MILP) with small-sized instances is solved. In addition to the small-sized model, a novel metaheuristic based on a hybrid simulated annealing (SA) algorithm to solve large-sized problems in an acceptable computational time is suggested, considering the comparison of the SA algorithm and a new recommended heuristic algorithm. Then, the proposed hybrid SA and SA algorithms are compared based on their performance measurement. After reaching the results with a numerical analysis in Nova Scotia health authority hospitals and health centers, the hybrid SA algorithm has generated significantly higher performance than the SA algorithm.

Hybrid Flow Shop with Setup Times Scheduling Problem

Abstract: The two-stage hybrid flow shop problem under setup times is addressed in this paper. This problem is NP-Hard. on the other hand, the studied problem is modeling different real-life applications especially in manufacturing and high performance-computing. Tackling this kind of problem requires the development of adapted algorithms. In this context, a metaheuristic using the genetic algorithm and three heuristics are proposed in this paper. These approximate solutions are using the optimal solution of the parallel machines under release and delivery times. Indeed, these solutions are iterative procedures focusing each time on a particular stage where a parallel machines problem is called to be solved. The general solution is then a concatenation of all the solutions in each stage. In addition, three lower bounds based on the relaxation method are provided. These lower bounds present a means to evaluate the efficiency of the developed algorithms throughout the measurement of the relative gap. An experimental result is discussed to evaluate the performance of the developed algorithms. In total, 8960 instances are implemented and tested to show the results given by the proposed lower bounds and heuristics. Several indicators are given to compare between algorithms. The results illustrated in this paper show the performance of the developed algorithms in terms of gap and running time.

Survey on Genetic Programming and Machine Learning Techniques for Heuristic Design in Job Shop Scheduling

Abstract: Job shop scheduling is a process of optimising the use of limited resources to improve the production efficiency. Job shop scheduling has a wide range of applications such as order picking in the warehouse and vaccine delivery scheduling under a pandemic. In real-world applications, the production environment is often complex due to dynamic events such as job arrivals over time and machine breakdown. Scheduling heuristics, e.g., dispatching rules, have been popularly used to prioritise the candidates such as machines in manufacturing to make good schedules efficiently. Genetic programming, has shown its superiority in learning scheduling heuristics for job shop scheduling automatically due to its flexible representation. This survey firstly provides comprehensive discussions of recent designs of genetic programming algorithms on different types of job shop scheduling. In addition, we notice that in the recent years, a range of machine learning techniques such as feature selection and multitask learning, have been adapted to improve the effectiveness and efficiency of scheduling heuristic design with genetic programming. However, there is no survey to discuss the strengths and weaknesses of these recent approaches. To fill this gap, this paper provides a comprehensive survey on genetic programming and machine learning techniques on automatic scheduling heuristic design for job shop scheduling. In addition, current issues and challenges are discussed to identify promising areas for automatic scheduling heuristic design in the future.

Multi-stage hybrid evolutionary algorithm for multiobjective distributed fuzzy flow-shop scheduling problem.

Abstract: In the current global cooperative production mode, the distributed fuzzy flow-shop scheduling problem (DFFSP) has attracted much attention because it takes the uncertain factors in the actual flow-shop scheduling problem into account. This paper investigates a multi-stage hybrid evolutionary algorithm with sequence difference-based differential evolution (MSHEA-SDDE) for the minimization of fuzzy completion time and fuzzy total flow time. MSHEA-SDDE balances the convergence and distribution performance of the algorithm at different stages. In the first stage, the hybrid sampling strategy makes the population rapidly converge toward the Pareto front (PF) in multiple directions. In the second stage, the sequence difference-based differential evolution (SDDE) is used to speed up the convergence speed to improve the convergence performance. In the last stage, the evolutional direction of SDDE is changed to guide individuals to search the local area of the PF, thereby further improving the convergence and distribution performance. The results of experiments show that the performance of MSHEA-SDDE is superior to the classical comparison algorithms in terms of solving the DFFSP.

A Dual-Population Genetic Algorithm with Q-Learning for Multi-Objective Distributed Hybrid Flow Shop Scheduling Problem

Abstract: In real-world production processes, the same enterprise often has multiple factories or one factory has multiple production lines, and multiple objectives need to be considered in the production process. A dual-population genetic algorithm with Q-learning is proposed to minimize the maximum completion time and the number of tardy jobs for distributed hybrid flow shop scheduling problems, which have some symmetries in machines. Multiple crossover and mutation operators are proposed, and only one search strategy combination, including one crossover operator and one mutation operator, is selected in each iteration. A population assessment method is provided to evaluate the evolutionary state of the population at the initial state and after each iteration. Two populations adopt different search strategies, in which the best search strategy is selected for the first population and the search strategy of the second population is selected under the guidance of Q-learning. Experimental results show that the dual-population genetic algorithm with Q-learning is competitive for solving multi-objective distributed hybrid flow shop scheduling problems.

An Improved Hyperplane Assisted Multiobjective Optimization for Distributed Hybrid Flow Shop Scheduling Problem in Glass Manufacturing Systems

Abstract: To solve the distributed hybrid flow shop scheduling problem (DHFS) in raw glass manufacturing systems, we investigated an improved hyperplane assisted evolutionary algorithm (IhpaEA). Two objectives are simultaneously considered, namely, the maximum completion time and the total energy consumptions. Firstly, each solution is encoded by a three-dimensional vector, i.e., factory assignment, scheduling, and machine assignment. Subsequently, an efficient initialization strategy embeds two heuristics are developed, which can increase the diversity of the population. Then, to improve the global search abilities, a Pareto-based crossover operator is designed to take more advantage of non-dominated solutions. Furthermore, a local search heuristic based on three parts encoding is embedded to enhance the searching performance. To enhance the local search abilities, the cooperation of the search operator is designed to obtain better non-dominated solutions. Finally, the experimental results demonstrate that the proposed algorithm is more efficient than the other three state-of-the-art algorithms. The results show that the Pareto optimal solution set obtained by the improved algorithm is superior to that of the traditional multiobjective algorithm in terms of diversity and convergence of the solution.

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

Abstract: Permutation flow-shop scheduling is the strategy that ensures the processing of jobs on each subsequent machine in the exact same order while optimizing an objective, which generally is the minimization of makespan. Because of its NP-Complete nature, a substantial portion of the literature has mainly focused on computational efficiency and the development of different AI-based hybrid techniques. Particle Swarm Optimization (PSO) has also been frequently used for this purpose in the recent past. Following the trend and to further explore the optimizing capabilities of PSO, first, a standard PSO was developed during this research, then the same PSO was hybridized with Variable Neighborhood Search (PSO-VNS) and later on with Simulated Annealing (PSO-VNS-SA) to handle Permutation Flow-Shop Scheduling Problems (PFSP). The effect of hybridization was validated through an internal comparison based on the results of 120 different instances devised by Taillard with variable problem sizes. Moreover, further comparison with other reported hybrid metaheuristics has proved that the hybrid PSO (HPSO) developed during this research performed exceedingly well. A smaller value of 0.48 of ARPD (Average Relative Performance Difference) for the algorithm is evidence of its robust nature and significantly improved performance in optimizing the makespan as compared to other algorithms.

Energy-Efficient Iterative Greedy Algorithm for the Distributed Hybrid Flow Shop Scheduling With Blocking Constraints

Abstract: With the global energy shortage, climate anomalies, environmental pollution becoming increasingly prominent, energy saving scheduling has attracted more and more concern than before. This paper studies the energy-efficient distributed hybrid flow-shop scheduling problem (DHFSP) with blocking constraints. Our aim is to find the job sequence with low energy consumption as much as possible in a limited time. In this paper, we formulate a mathematical model of the DHFSP with blocking constraints and propose an improved iterative greedy (IG) algorithm to optimize the energy consumption of job sequence. In the proposed algorithm, first, a problem-specific strategy is presented, namely, the global search strategy, which can assign appropriate jobs to the factory and minimize the energy consumption of each processing factory. Next, a new selection mechanism inspired by Q-learning is proposed to provide strategic guidance for factory scheduling. This selection mechanism provides historical experience for different factories. Finally, five types of local search strategies are designed for blocking constraints of machines and sequence to be scheduled. These proposed strategies can further improve the local search ability of the QIG algorithm and reduce the energy consumption caused by blocking. Simulation results and statistical analysis on 90 test problems show that the proposed algorithm is superior to several high-performance algorithms on convergence rate and quality of solution.

BRCE: bi-roles co-evolution for energy-efficient distributed heterogeneous permutation flow shop scheduling with flexible machine speed

Abstract: Abstract Distributed manufacturing is the mainstream model to accelerate production. However, the heterogeneous production environment makes engineer hard to find the optimal scheduling. This work investigates the energy-efficient distributed heterogeneous permutation flow scheduling problem with flexible machine speed (DHPFSP-FMS) with minimizing makespan and energy consumption simultaneously. In DHPFSP-FMS, the local search misleads the population falling into local optima which reduces the convergence and diversity. To solve this problem, a bi-roles co-evolutionary algorithm is proposed which contains the following improvements: First, the global search and local search is divided into two swarms producer and consumer to balance computation. Second, three heuristic rules are designed to get a high-quality initialization population. Next, five problem-based local search strategies are designed to accelerate converging. Then, an efficient energy-saving strategy is presented to save energy. Finally, to verify the performance of the proposed algorithm, 22 instances are generated based on the Taillard benchmark, and a number of numerical experiments are adopted. The experiment results state that our algorithm is superior to the state-of-arts and more efficient for DHPFSP-FMS.

A Multi-Agent Reinforcement Learning Approach to the Dynamic Job Shop Scheduling Problem

Abstract: In a production environment, scheduling decides job and machine allocations and the operation sequence. In a job shop production system, the wide variety of jobs, complex routes, and real-life events becomes challenging for scheduling activities. New, unexpected events disrupt the production schedule and require dynamic scheduling updates to the production schedule on an event-based basis. To solve the dynamic scheduling problem, we propose a multi-agent system with reinforcement learning aimed at the minimization of tardiness and flow time to improve the dynamic scheduling techniques. The performance of the proposed multi-agent system is compared with the first-in–first-out, shortest processing time, and earliest due date dispatching rules in terms of the minimization of tardy jobs, mean tardiness, maximum tardiness, mean earliness, maximum earliness, mean flow time, maximum flow time, work in process, and makespan. Five scenarios are generated with different arrival intervals of the jobs to the job shop production system. The results of the experiments, performed for the 3 × 3, 5 × 5, and 10 × 10 problem sizes, show that our multi-agent system overperforms compared to the dispatching rules as the workload of the job shop increases. Under a heavy workload, the proposed multi-agent system gives the best results for five performance criteria, which are the proportion of tardy jobs, mean tardiness, maximum tardiness, mean flow time, and maximum flow time.

A modified campbell dudek smith algorithm for flow shop scheduling with parallel machines, batch processors and assembly

Abstract: This paper exhibits an adaptation of Campbell Dudek Smith (CDS) algorithm for a flow shop system whose end product consists of four components, each of which is firstly processed in a single-stage with parallel machines, followed by a number of batch processors, and then finally assembled in one of available assembling stations. The first step of the procedure is to compute equivalent processing times of each stage for each job, and then use the equivalent processing times to find the job sequence using the CDS algorithm. After the job sequence found, the final step is to schedule the jobs considering the parallel machines, the batch processors, and the assembling stations. Numerical example shows that this procedure results a reasonably good schedule for the case studied.

Multi-objective Optimization of the Job Shop Scheduling Problem on Unrelated Parallel Machines with Sequence-Dependent Setup Times

Abstract: Several optimization criteria are involved in the job shop scheduling problems encountered in the engineering area. Multi-objective optimization algorithms are often applied to solve these problems, which become even more complex with the advent of Industry 4.0, mostly due to the increase of data from industrial systems. In this work, several instances of the multi-objective job shop scheduling problem on unrelated parallel machines with sequence-dependent setup times are solved using evolutionary approaches. In this problem, the goal is to assign a set of N jobs on M unrelated machines considering sequence-dependent setup times. Several objectives such as makespan, average completion time, cost and energy consumption can be optimized. In this work, single and multi-objective optimization problems are solved considering the minimization of makespan and the average completion time. Preliminary results for the comparison of algorithms on different instances of the problems are presented and statistically analysed. Future work will include problems with more objectives, and to extend this approach to the distributed job shop problem.

Hybrid Flow-Shop Scheduling Problems with Missing and Re-Entrant Operations Considering Process Scheduling and Production of Energy Consumption

Abstract: A hybrid flow shop scheduling model with missing and re-entrant operations was designed to minimize the maximum completion time and the reduction in energy consumption. The proposed dual-population genetic algorithm was enhanced with a range of improvements, which include the design of a three-layer gene coding method, hierarchical crossover and mutation techniques, and the development of an adaptive operator that considered gene similarity and chromosome fitness values. The optimal and worst individuals were exchanged between the two subpopulations to improve the exploration ability of the algorithm. An orthogonal experiment was performed to obtain the optimal horizontal parameter set of the algorithm. Furthermore, an experiment was conducted to compare the proposed algorithm with a basic genetic algorithm, particle swarm optimization algorithm, and ant colony optimization, which were all performed on the same scale. The experimental results show that the fitness value of the proposed algorithm is above 15% stronger than the other 4 algorithms on a small scale, and was more than 10% stronger than the other 4 algorithms on a medium and large scale. Under the condition close to the actual scale, the results of ten repeated calculations showed that the proposed algorithm had higher robustness.