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In this paper, a bi-population competition adaptive interior search algorithm (BCAISA) based on a reinforcement learning strategy is proposed for the classical flexible job shop scheduling problem (FJSP) to optimize the makespan. First, the scheduling solution is represented using a machine-job-based two-segment integer encoding method, and various heuristic rules are then applied to generate the initial population. Secondly, a bi-population mechanism is introduced to partition the population into two distinct sub-populations. These sub-populations are specifically tailored for machine assignment and operation permutation, employing different search strategies respectively, aiming to facilitate an efficient implementation of parallel search. A competition mechanism is introduced to facilitate the information exchange between the two sub-populations. Thirdly, the ISA is adapted for the discrete scheduling problem by discretizing a series of search operators, which include composition optimization, mirror search, and random walk. A Q-learning-based approach is proposed to dynamically adjust a key parameter, aiming to strike a balance between the capacity for global exploration and local exploitation. Finally, extensive experiments are conducted based on 10 well-known benchmark instances of the FJSP. The design of the experiment (DOE) method is employed to determine the algorithm’s parameters. Based on the computational results, the effectiveness of four improvement strategies is first validated. The BCAISA is then compared with fifteen published algorithms. The comparative data demonstrate that our algorithm outperforms other algorithms in 50% of benchmark instances. Additionally, according to the relative percentage deviation (RPD) from the state-of-the-art results, the BCAISA also exhibits superior performance. This highlights the effectiveness of our algorithm for solving the classical FJSP. To enhance the practical application, the scope of the ISA will be broadened in future work to more complex problems in real-world scenarios. [ABSTRACT FROM AUTHOR]

Energy-aware scheduling has been viewed as a feasible way to reduce energy consumption during the production process. Recently, energy-aware job shop scheduling problems (EAJSPs) have received wide attention in the manufacturing area. However, the majority of previous literature about EAJSPs supposed that all jobs are fabricated in the in-house workshop, while the outsourcing of jobs to some available subcontractors is neglected. To get close to practical production, the outsourcing and scheduling are simultaneously determined in an energy-aware job shop problem with outsourcing option (EAJSP-OO). To formulate the considered problem, a novel mathematical model is constructed to minimize the sum of completion time cost, outsourcing cost and energy consumption cost. Considering the strong complexity, a self-learning interior search algorithm (SLISA) is developed based on reinforcement learning. In the SLISA, a new Q-learning algorithm is embedded to dynamically select search strategies to prevent blind search in the iteration process. Extensive experiments are carried out to evaluate the performance of the proposed algorithm. Simulation results indicate that the SLISA is superior to the compared existing algorithms in more than 50% of the instances of the considered EAFJSP-OO problem. [ABSTRACT FROM AUTHOR]

Due to the increasing demand for green manufacturing, energy-saving scheduling problems have garnered significant attention. These problems aim to reduce energy consumption at the production system level within workshops. To simulate a realistic production environment, this study addresses an energy-saving flexible job shop scheduling problem that considers two types of speed-adjustable resources, namely machines and transporters. The optimization objective is to minimize the comprehensive energy consumption of the workshop. A novel mathematical model is initially constructed based on the specific characteristics of the problem at hand. Given its NP-hard nature, a new Q-learning-based biology migration algorithm (QBMA) is proposed, which encompasses diverse search strategies and employs a Q-learning algorithm to dynamically select search strategies, thereby preventing blind search during the evolutionary process. The experimental results of our study demonstrate the promising efficacy of QBMA in effectively addressing the aforementioned problem, while also highlighting the positive impact of considering resources with adjustable speed. [ABSTRACT FROM AUTHOR]

The energy-saving scheduling problem (ESSP) has gained increasing attention of researchers in the manufacturing field. However, there is a lack of studies on ESSPs in the assembly job shop environment. In contrast with traditional scheduling problems, the assembly job shop scheduling problem (AJSP) adds the additional consideration of hierarchical precedence constraints between different jobs of each final product. This paper focuses on developing a methodology for an energy-saving assembly job shop scheduling problem with job transportation times. Firstly, a mathematical model is constructed with the objective of minimizing total energy consumption. Secondly, an improved elephant herding optimization (IEHO) is proposed by considering the problem's characteristics. Finally, thirty-two different instances are designed to verify the performance of the proposed algorithm. Computational results and statistical data demonstrate that the IEHO has advantages over other algorithms in terms of the solving accuracy for the considered problem. [ABSTRACT FROM AUTHOR]

Energy-saving scheduling has been pointed out as an interesting research issue in the manufacturing field, by which energy consumption can be effectively reduced through production scheduling from the operational management perspective. In recent years, energy-saving scheduling problems in flexible job shops (ESFJSPs) have attracted considerable attention from scholars. However, the majority of existing work on ESFJSPs assumed that the processing of any two consecutive operations in a job cannot be overlapped. In order to be close to real production, the processing overlapping of consecutive operations is allowed in this paper, while the job transportation tasks are also involved between different machines. To formulate the problem, a mathematical model is set up to minimize total energy consumption. Due to the NP-hard nature, a new interior search algorithm (NISA) is elaborately proposed following the feature of the problem. A number of experiments are conducted to verify the effectiveness of the NISA algorithm. The experimental results demonstrate that the NISA provides promising results for the considered problem. In addition, the computational results indicate that the increasing transportation time and sub-lot number will increase the transportation energy consumption, which is largely responsible for the increase in total energy consumption. [ABSTRACT FROM AUTHOR]

This paper presents a discrete animal migration optimization (DAMO) to solve the dual-resource constrained energy-saving flexible job shop scheduling problem (DRCESFJSP), with the aim of minimizing the total energy consumption in the workshop. A job-resource-based two-vector encoding method is designed to represent the scheduling solution, and an energy-saving decoding approach is given based on the left-shift rule. To ensure the quality and diversity of initial scheduling solutions, a heuristic approach is employed for the resource assignment, and some dispatching rules are applied to acquire the operation permutation. In the proposed DAMO, based on the characteristics of the DRCESFJSP problem, the search operators of the basic AMO are discretized to adapt to the problem under study. An animal migration operator is presented based on six problem-based neighborhood structures, which dynamically changes the search scale of each animal according to its solution quality. An individual updating operator based on crossover operation is designed to obtain new individuals through the crossover operation between the current individual and the best individual or a random individual. To evaluate the performance of the proposed algorithm, the Taguchi design of experiment method is first applied to obtain the best combination of parameters. Numerical experiments are carried out based on 32 instances in the existing literature. Computational data and statistical comparisons indicate that both the left-shift decoding rule and population initialization strategy are effective in enhancing the quality of the scheduling solutions. It also demonstrate that the proposed DAMO has advantages against other compared algorithms in terms of the solving accuracy for solving the DRCESFJSP. [ABSTRACT FROM AUTHOR]

For the job shop with variable processing speeds, the aim of energy saving and consumption reduction is implemented from the perspective of production scheduling. By analyzing the characteristics of the workshop, a multi-objective mathematical model is established with the objective of reducing the total energy consumption and shortening the makespan. A multi-objective discrete water wave optimization (MODWWO) algorithm is proposed for solving the problem. Firstly, a two-vector encoding method is adopted to divide the scheduling solution into two parts, which represent speed selection and operation permutation in the scheduling solution, respectively. Secondly, some dispatching rules are used to initialize the population and obtain the initial scheduling solutions. Then, three operators of the basic water wave optimization algorithm are redesigned to make the algorithm adaptive for the multi-objective discrete scheduling problem under study. A new propagation operator is presented with the ability of balancing global exploration and local exploitation based on individual rank and neighborhood structures. A novel refraction operator is designed based on crossover operation, by which each individual can learn from the current best individual to absorb better information. And a breaking operator is modified based on the local search strategy to enhance the exploitation ability. Finally, extensive simulation experiments demonstrate that the proposed MODWWO algorithm is effective for solving the considered energy-saving scheduling problem. [ABSTRACT FROM AUTHOR]

The conventional production scheduling problem has mainly emphasized the time-related metrics, such as makespan, machine workload and tardiness/earliness, and so on. With the advent of the sustainable manufacturing, the green scheduling problem has been received more and more attention from scholars and researchers. In this paper, we investigate a green flexible job shop scheduling problem (GFJSP) with the consideration of environmental factors. To formulate the GFJSP problem, a mathematical model is first established to minimize the amount of total energy-consumption. To solve the model, a kind of improved African buffalo optimization (IABO) algorithm is proposed based on the characteristics of the problem. In the proposed IABO, a two-vector solution representation method is first designed, and a population initialization method is adopted to generate the initial solutions with certain quality and diversity. Based on the original ABO, several improvement strategies are introduced to enhance the performance of the algorithm, i.e., the modified individual learning mechanism and the aging-based re-initializaiton mechanism. In addition, in order to adapt our algorithm to the scheduling problem, a discrete individual updating method is developed to ensure the algorithm search directly in a discrete domain. Finally, a number of experiments have been conducted to test the performance of the proposed IABO algorithm. The simulation data demonstrate the effectiveness of the proposed IABO for the considered GFJSP. [ABSTRACT FROM AUTHOR]

The workshop scheduling has historically emphasized the production metrics without involving any environmental considerations. Low-carbon scheduling has attracted the attention of many researchers after the promotion of green manufacturing. In this paper, we investigate the low-carbon scheduling problem in a job shop environment. A mathematical model is first established with the objective to minimize the sum of energy-consumption cost and completion-time cost. A discrete genetic-grey wolf optimization algorithm (DGGWO) is developed to solve the problem in this study. According to the characteristics of the problem, a job-based encoding method is first employed. Then a heuristic approach and the random generation rule are combined to fulfill the population initialization. Based on the original GWO, a discrete individual updating method the crossover operation of the genetic algorithm is adopted to make the algorithm directly work in a discrete domain. Meanwhile, a mutation operator is adopted to enhance the population diversity and avoid the algorithm from getting trapped into the local optima. In addition, a variable neighborhood search is embedded to further improve the search ability. Finally, extensive simulations are conducted based on 43 benchmark instances. The experimental data demonstrate that the proposed algorithm can yield better results than the other published algorithms. [ABSTRACT FROM AUTHOR]

This paper aims to develop a hybrid grey wolf optimization algorithm (HGWO) for solving the job shop scheduling problem (JSP) with the objective of minimizing the makespan. Firstly, to make the GWO suitable for the discrete nature of JSP, an encoding mechanism is proposed to implement the continuous encoding of the discrete scheduling problem, and a ranked-order value (ROV) rule is used to conduct the conversion between individual position and operation permutation. Secondly, a heuristic algorithm and the random rule are combined to implement the population initialization in order to ensure the quality and diversity of initial solutions. Thirdly, a variable neighborhood search algorithm is embedded to improve the local search ability of our algorithm. In addition, to further improve the solution quality, genetic operators (crossover and mutation) are introduced to balance the exploitation and exploration ability. Finally, experimental results demonstrate the effectiveness of the proposed algorithm based on 23 benchmark instances. [ABSTRACT FROM AUTHOR]

• A mathematical model of the energy-conscious FJSP with transportation time and deterioration effect is built. • A modified animal migration optimization algorithm is elaborately designed by considering the characteristics of the problem. • Comprehensive computational experiments demonstrate that the MAMO algorithm is effective for the consider problem. In recent years, research on green manufacturing has received much attention to the increasing environmental problems. Production scheduling is viewed as an effective way of saving energy in manufacturing system from the operation management point of view. This paper investigates an energy-conscious flexible job shop scheduling problem with transportation time and deterioration effect simultaneously (ECFJSP-TD). To begin with, a mathematical model is built with the objective of optimizing total energy consumption. A modified animal migration optimization algorithm (MAMO) is elaborately designed by considering the characteristics of the problem. In the MAMO, a two-vector encoding is designed to represent the scheduling solution, and a left-shift decoding approach is proposed to ensure the operation permutation on each machine as compact as possible. In addition, a new animal migration operator is designed based on the problem-specific neighborhood structures, which can dynamically adjust the search scope along with the iteration process to balance global exploration and local exploitation. A new population updating operator is developed based on the crossover operation to generate new individuals by absorbing some information about the best individuals as well as two random individuals. Finally, comprehensive experiments are carried out to test the performance of the proposed MAMO algorithm. According to the comparison data, the MAMO is more effective for solving the considered problem than some published algorithms. [ABSTRACT FROM AUTHOR]

In recent decades, workshop scheduling has excessively focused on time-related indicators, while ignoring environmental metrics. With the advent of sustainable manufacturing, the energy-aware scheduling problem has been attracting more and more attention from scholars and researchers. In this study, we investigate an energy-aware flexible job shop scheduling problem to reduce the total energy consumption in the workshop. For the considered problem, the energy consumption model is first built to formulate the energy consumption, such as processing energy consumption, idle energy consumption, setup energy consumption and common energy consumption. Then, a mathematical model is established with the criterion to minimize the total energy consumption. Secondly, a modified migrating birds optimization (MMBO) algorithm is proposed to solve the model. In the proposed MMBO, a population initialization scheme is presented to ensure the initial solutions with a certain quality and diversity. Five neighborhood structures are employed to create neighborhood solutions according to the characteristics of the problem. Furthermore, both a local search method and an aging-based re-initialization mechanism are developed to avoid premature convergence. Finally, the experimental results validate that the proposed algorithm is effective for the problem under study. [ABSTRACT FROM AUTHOR]

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances. • Total flow time minimization is considered in no-wait job shop scheduling. • Left timetabling is developed for timetabling subproblem with time O(mn3) in the worst case. • A hybrid group search optimizer is proposed for the sequencing subproblem. • A speed-up method is proposed for evaluating the insertion neighborhood. • The effectiveness of the proposed algorithm is validated by comparisons with other state-of-the-art metaheuristics. [ABSTRACT FROM AUTHOR]

In this paper, a novel improved whale optimization algorithm (IWOA), based on the integrated approach, is presented for solving the flexible job shop scheduling problem (FJSP) with the objective of minimizing makespan. First of all, to make the whale optimization algorithm (WOA) adaptive to the FJSP, the conversion method between the whale individual position vector and the scheduling solution is firstly proposed. Secondly, a resultful initialization scheme with certain quality is obtained using chaotic reverse learning (CRL) strategies. Thirdly, a nonlinear convergence factor (NFC) and an adaptive weight (AW) are introduced to balance the abilities of exploitation and exploration of the algorithm. Furthermore, a variable neighborhood search (VNS) operation is performed on the current optimal individual to enhance the accuracy and effectiveness of the local exploration. Experimental results on various benchmark instances show that the proposed IWOA can obtain competitive results compared to the existing algorithms in a short time. [ABSTRACT FROM AUTHOR]

Under the current environmental pressure, many manufacturing enterprises are urged or forced to adopt effective energy-saving measures. However, environmental metrics, such as energy consumption and CO2 emission, are seldom considered in the traditional production scheduling problems. Recently, the energy-related scheduling problem has been paid increasingly more attention by researchers. In this paper, an energy-efficient job shop scheduling problem (EJSP) is investigated with the objective of minimizing the sum of the energy consumption cost and the completion-time cost. As the classical JSP is well known as a non-deterministic polynomial-time hard (NP-hard) problem, an improved whale optimization algorithm (IWOA) is presented to solve the energy-efficient scheduling problem. The improvement is performed using dispatching rules (DR), a nonlinear convergence factor (NCF), and a mutation operation (MO). The DR is used to enhance the initial solution quality and overcome the drawbacks of the random population. The NCF is adopted to balance the abilities of exploration and exploitation of the algorithm. The MO is employed to reduce the possibility of falling into local optimum to avoid the premature convergence. To validate the effectiveness of the proposed algorithm, extensive simulations have been performed in the experiment section. The computational data demonstrate the promising advantages of the proposed IWOA for the energy-efficient job shop scheduling problem. [ABSTRACT FROM AUTHOR]

• A HMABC algorithm based on load balance was proposed. • The scouter bee mechanism solves the problem of falling into local optimum. • The THR based on machine load balance improves local search ability. • The HMABC is applied successfully into aviation composite materials manufacturing. The manufacturing of composite materials for the aerospace industry represents a cornerstone of future development in this advanced field. In this study, a mathematical model of flexible job-shop scheduling problem (FJSP) was established by extracting the key manufacturing information from an aerospace composite manufacturing workshop. Intelligent algorithms can effectively solve FJSP. However, when applied to a multi-objective FJSP (MOFJSP), they suffer from drawbacks such as blind search and low efficiency. Therefore, this study proposes a new artificial bee colony algorithm and implements it as part of a hybrid method (referred to as the HMABC) to solve MOFJSP. The method involves three steps: (1) A multiple-rule initial population is constructed to minimize randomness and improve quality. (2) A greedy decoding method is used to decode each individual to further narrow the search range to replace the conventional decoding method. (3) By considering the machine load index (which has often been neglected), the concept of machine load rate is proposed, and three heuristic strategies are designed (with the influences ranging from small to high) to diverge the solution in all directions instead of just a direction. The performance of the proposed method is compared with those of existing algorithms using a classical FJSP test example, and the effectiveness and efficiency of HMABC is verified. Finally, the method is applied to an actual aerospace composite manufacturing system to realize the scheduling of actual production activities. [ABSTRACT FROM AUTHOR]

The no-wait job shop where no waiting time is allowed between two successive operations of a job has a strong industrial background, especially in steel-making industry and concrete manufacturing. This study formulates the no-wait job shop problem with a total flow time criterion based on time difference and decomposes the problem into timetabling and sequencing subproblems. Several timetabling methods are designed for the total flow time criterion to generate a sequence timetable. By adopting favourable features of the iterated greedy algorithm, the population-based iterated greedy (PBIG) algorithm for the sequencing subproblem is proposed. The individuals in the population evolve by means of a destruction and construction perturbator and an insertion-based local search. In each iteration, a tournament selection is designed to replace a relatively worse solution. In order to generate starting solutions with a certain quality and diversity, the Nawaz–Enscore–Ham-based heuristics for flow shop scheduling are extended in no-wait job shops. In computational experiments based on well-known benchmark instances, timetabling methods are investigated, and it is shown that the left timetabling is superior to other timetabling methods for the total flow time minimisation. Computational results also show that the proposed algorithm significantly outperforms several state-of-the-art metaheuristics, and it could be applicable to practical production environment. [ABSTRACT FROM AUTHOR]