Algorithm For Job Shop Scheduling Research Articles

A self-learning multi-population evolutionary algorithm for flexible job shop scheduling under time-of-use pricing

Due to the energy crisis and environmental downgrade, manufacturing companies face rising costs. The pressure on manufacturers to reduce costs and increase efficiency is increasing. The flexible job shop scheduling problem considering time-of-use pricing (FJSPTOUP) is studied to minimize the maximum completion time and total electricity cost. A new self-learning multi-population evolutionary algorithm (SLMPEA) is proposed to address the static scheduling problem. A self-learning module is designed to acquire knowledge from elite individuals in subpopulations. The knowledge discovered can guide the evolution of subpopulations. To improve the convergence of the algorithm and maintain the diversity of the population, we present an elite retention and enhancement strategy. Two enhancement operators are developed to elevate the quality of elite individuals, and a selection strategy is designed for the enhancement operators. A time-of-use-based adjustment strategy is proposed to reduce the total electricity costs without increasing the maximum completion time. Experimental results show that the proposed SLMPEA outperforms the comparative algorithms in solving FJSPTOUP.

Deep reinforcement learning-based memetic algorithm for energy-aware flexible job shop scheduling with multi-AGV

The integration of manufacturing and logistics scheduling issues in shop operations has garnered considerable attention. Concurrently, escalating concerns about global warming have propelled the emergence of green manufacturing as a critical challenge. Notably, extant research in this domain lacks an incorporation of green metrics within the framework of manufacturing and logistics-integrated scheduling. Furthermore, the determination of a critical block remains a challenging aspect, with an absence of consideration for a neighborhood structure founded on the critical block. Moreover, prior endeavors have predominantly relied on Q-learning to augment evolutionary algorithms, a strategy criticized for its limited learning capacity. Consequently, this study addresses these gaps by presenting an energy-efficient flexible job Shop scheduling with multi-autonomous guided vehicles (EFJS-AGV). The primary objectives are the simultaneous minimization of makespan and total energy consumption. To tackle this NP-hard problem, a deep Q-network-based memetic algorithm is proposed. The devised algorithm incorporates several distinctive features. Firstly, the strength Pareto evolutionary algorithm (SPEA2) is employed to swiftly explore the objective space, enhancing convergence and diversity. Secondly, four distinct local search operators based on critical paths and blocks are devised to efficiently reduce makespan. Thirdly, deep reinforcement learning is harnessed to understand the interplay between solutions and action selection. This understanding aids the evolutionary algorithm in selecting the most optimal operator. The efficacy of the proposed algorithm is rigorously evaluated through a comparative analysis with five state-of-the-art algorithms. The assessment is conducted on two benchmark datasets encompassing 20 instances. The numerical experimental results affirm the effectiveness of the proposed enhancements and algorithms. Furthermore, the superior performance of the proposed algorithm in addressing the EFJS-AGV substantiates its robustness and applicability.

Grid-based artificial bee colony algorithm for multi-objective job shop scheduling with manual loading and unloading tasks

This paper investigates a multi-objective job shop scheduling problem with manual loading and unloading tasks (MOJSSPLU) aiming to minimize makespan and total workload simultaneously. Taking human factors into consideration achieves a better balance between production efficiency and resource utilization. To address this problem, we first establish a bi-objective mixed-integer linear programming (MILP) model. Afterward, we combine the artificial bee colony algorithm with the grid technique to develop a grid-based artificial bee colony algorithm (GABC) for solving MOJSSPLU. The algorithm uses a decomposition approach with the earliest-shortest dispatching rule to reduce the complexity of MOJSSPLU. A grid coordinate system is constructed to divide the objective space into cells, facilitating individuals’ location and evaluation in the decision space. Moreover, we focus on improving the cooperation between the employed and onlooker bees and design a mathematical formula based on priority weights to generate onlooker bees to maximize information utilization and improve the exploration and exploitation capabilities of the algorithm. To ensure that the most promising individuals are retained and protected from being eliminated during the evolutionary, we propose an elitist non-dominated solutions reservation strategy for improving the diversity of the population. We further propose a dynamic adjustment of the grid-division method that focuses on improving the exploitation capacity of the algorithm in the objective space to enhance the diversity and convergence of the population. To test the performance of the GABC algorithm, we compare it to the MILP approach and other algorithms using modified benchmark instances. Furthermore, we conduct the Friedman and Wilcoxon nonparametric tests to validate the comparison results among the different algorithms. The computational results demonstrate that the algorithm GABC is efficient.

A multi-agent resource bidding algorithm for order acceptance and assembly job shop scheduling

This study uses an agent-based approach with a combinatorial auction mechanism to solve the joint order acceptance and assembly job shop scheduling problem. A set of jobs is offered. Each job has a revenue, ready time, due date, deadline, and consists of a set of operations with precedence relationships. Jobs that deviate from their due dates incur earliness/tardiness penalties. An operation may require several units of capacity per time unit and a resource could have multiple units of capacity. The manufacturer can reject any job to satisfy the capacity constraints and maximise the overall profit. We develop a mathematical model for the problem, then use an agent-based approach to solve it. First, the relaxed problem is decomposed into a set of job-level subproblems. Each job is optimised individually without considering the capacity constraints. Profitable jobs at the individual level submit their optimal schedules as combinatorial bids to an auctioneer to acquire combinations of resource capacity-time units. Then, the auctioneer records the profit upper bound, resolves capacity conflicts to reach a feasible solution, records the profit lower bound, and updates the dual variables. Experimental results show that the proposed methodology can solve large-sized problems in reasonable CPU times.

Mathematical model and adaptive simulated annealing algorithm for mixed-model assembly job-shop scheduling with lot streaming

Mixed-model assembly and lot streaming are two key technologies to improve efficiency and reduce setups in a multi-variety and small-batch discrete manufacturing environment. Yet few studies consider the two technologies in assembly job-shop scheduling problems. Thus, this paper investigates the mixed-model assembly job-shop scheduling problem with lot streaming, which contains two closely coordinated stages with differentiated production lot size: the processing stage with lot streaming and the mixed-model assembly stage with single-piece flow. To tackle this problem, a mathematical model including new constraints i.e. production sequence constraints within/among sublots, sequence-dependent setup constraints between sublots and mixed-model assembly constraints, is developed to establish the temporal and spatial links between the processing and assembly stages. Besides, an adaptive simulated annealing algorithm is proposed. In this algorithm, a sublot sequence rule considering sublot and assembly features is discovered via gene expression programming to promote the performance of initial solutions; a Q-learning-based temperature control mechanism is designed to adaptively adjust the acceptance probability of inferior solutions and accordingly avoid local optima; an adaptive selection mechanism of neighborhood operators is designed to increase the chance of finding potential solutions; an adaptive adjustment mechanism of neighborhood size is put forward to balance computing resources and the coverage of neighborhood space. Experimental results show that both the discovered rule and the adaptive mechanisms are effective, and the developed algorithm is more adapt to fix the studied problem than other state-of-the-art algorithms.

Knowledge-driven two-stage memetic algorithm for energy-efficient flexible job shop scheduling with machine breakdowns

This paper focuses on the multi-objective energy-efficient flexible job shop scheduling problem with machine breakdowns. To mitigate the impact of machine breakdowns, a rescheduling strategy is implemented in the scheduling process. In addition to sequencing the operations, the current problem is to determine the appropriate allocation of the machine and the proper speed of the machine to minimize both makespan and total energy consumption simultaneously. A mixed integer linear programming model is established to describe the considered problem. With the aim of effectively solving this problem, a knowledge-driven two-stage memetic algorithm (KTMA) is proposed. In the first stage, a hybrid initialization strategy that combines three problem-specific heuristics is applied to generate a high-quality initial population. Then, a knowledge-driven variable neighborhood search approach is designed for quickly converging and fully exploiting the solution space of the KTMA. In the second stage, two energy-saving strategies are designed to further reduce the total energy consumption. Extensive experiments carried out to compare the KTMA with some well-known algorithms confirm that the proposed KTMA can efficiently solve this problem.

An Efficient Metaheuristic Algorithm for Job Shop Scheduling in a Dynamic Environment

This paper proposes an Improved Multi-phase Particle Swarm Optimization (IMPPSO) to solve a Dynamic Job Shop Scheduling Problem (DJSSP) known as an non-deterministic polynomial-time hard (NP-hard) problem. A cellular neighbor network, a velocity reinitialization strategy, a randomly select sub-dimension strategy, and a constraint handling function are introduced in the IMPPSO. The IMPPSO is used to solve the Kundakcı and Kulak problem set and is compared with the original Multi-phase Particle Swarm Optimization (MPPSO) and Heuristic Kalman Algorithm (HKA). The results show that the IMPPSO has better global exploration capability and convergence. The IMPPSO has improved fitness for most of the benchmark instances of the Kundakcı and Kulak problem set, with an average improvement rate of 5.16% compared to the Genetic Algorithm-Mixed (GAM) and of 0.74% compared to HKA. The performance of the IMPPSO for solving real-world problems is verified by a case study. The high level of operational efficiency is also evaluated and demonstrated by proposing a simulation model capable of using the decision-making algorithm in a real-world environment.

A decomposition-based multi-objective Jaya algorithm for lot-streaming job shop scheduling with variable sublots and intermingling setting

This study examined the lot-streaming job shop scheduling problem (LSJSP) with variable sublots and intermingling setting, which has rarely been considered in the literature and is beneficial to real industry settings. Upon variable sublots and intermingling setting, a multi-objective mixed-integer linear programming model (MILP) is formulated to achieve a tradeoff between the shortest tardiness and the minimum number of transferred sublots. Considering the NP-hard characteristic of the problem, the MILP model would get restricted in solving medium and large scale instances. Thus building an efficient multi-objective optimization algorithm is desirable. Motivated by the Jaya algorithm and decomposition idea, we propose a new algorithm framework called a decomposition based multi-objective Jaya algorithm (MOJA/D) to achieve a balance between exploration and exploitation. This MOJA/D framework can provide some guidance in algorithm construction for other multi-objective optimization problems. Following the MOJA/D framework, a specific MOJA/D metaheuristic is further designed for coping with the proposed problem. First, a novel forward and backward decoding strategy is designed to implement coevolution among different sub-problems and enhance the population diversity. Second, the Jaya updating mechanism is designed based on problem knowledge to guide the solutions moving towards the best solution and away from the worst solution. Moreover, considering the tradeoff between two conflicting objectives, the problem-specific local search strategies are designed and integrated with the neighborhood based local search strategies to enhance exploitation in the search process. The influence of parameter setting on MOJA/D is investigated by using design of experiments. The statistical results from extensive computational experiments demonstrate the effectiveness of the specific algorithm designs and show that the MOJA/D metaheuristic is superior to the existing algorithms in solving the proposed problem.

Novel Heuristic Algorithm for Flexible Job Shop Scheduling based on the Longest Processing Time Rules to Minimize Makespan

This research examined the scheduling of jobs with multiple stages unto identical parallel machines to minimize the makespan. The work is motivated by a Flexible Manufacturing System case that produces various parts and has multiple machining centers. Early research towards this system proposed a stage-by-stage independent scheduling, resulting in a non-optimal solution. This study aimed to create a better solution for the system by developing a novel heuristic algorithm based on the classical longest processing time algorithm and simultaneously considering processing time for all stages when deciding the job sequencing and job-machine allocation. The algorithm is defined as Modified LPT for Multiple Identical Machine with Multi-process Capability (M-LPT MIMMPC). We performed a numerical experiment to assess the algorithm's performance by incorporating various cases. We concluded that the resulting makespans are always better than LPT's theoretical bound for parallel machine scheduling. In some cases, it successfully gave an optimal value. Although the experiment scope was still limited, the algorithm showed promising performance results.

A hybrid fluid master–apprentice evolutionary algorithm for large-scale multiplicity flexible job-shop scheduling with sequence-dependent set-up time

In this article, a large-scale multiplicity flexible job-shop scheduling problem (FJSP) with sequence-dependent set-up time is studied. In this problem, the large production demand for each type of job yields the large-scale multiplicity manufacturing feature. To address the problem, a hybrid fluid master–apprentice evolutionary algorithm (HFMAE) is presented to minimize the makespan. In the first step, a fluid relaxation initialization method (FRI) and an initialize procedure are proposed to obtain high-quality initial solutions. In the FRI, an online fluid tracking policy is presented to improve the assignment decision and the sequencing decision of operations. In the second step, an improved master–apprentice evolutionary method (IMAE) is presented based on the generated initial solutions. In the IMAE, two neighbourhood structures and three makespan estimation approaches are presented to accelerate the solution space search efficiency. Numerical results show that the proposed HFMAE outperforms the comparison algorithms in solving large-scale multiplicity FJSPs.

A two-stage memetic algorithm for energy-efficient flexible job shop scheduling by means of decreasing the total number of machine restarts

Machine on/off control is an effective way to achieve energy-efficient production scheduling. Turning off machines and restarting them frequently, however, would incur a considerable amount of additional energy and may even cause damage to the machines. In this paper, we propose a mathematical model based on the energy-efficient flexible job shop scheduling problem (EEFJSP), aiming to minimize not just the makespan and total energy consumption but also the total number of machine restarts. Our idea here is that shifting the start time of operations on different machines appropriately can effectively decrease the number of restarts required and the total energy consumption. We present a two-stage memetic algorithm (TMA) to solve the EEFJSP. A variable neighborhood search approach is designed to improve the convergence speed and fully exploit the solution space of the TMA. An operation-block moving operator is developed to further reduce the total energy consumption as well as the total number of machine restarts without affecting the makespan. Extensive computational experiments carried out to compare the TMA with some well-known algorithms confirm that the proposed TMA can easily obtain better Pareto solutions for the EEFJSP.

A hybrid differential evolution algorithm for flexible job shop scheduling with outsourcing operations and job priority constraints

Owing to the increasing complexity of products and the specialization of enterprises, production outsourcing has become a common practice in industrial manufacturing. Moreover, different jobs feature various priorities in actual production. The previous research that aims to minimize the makespan may not be applicable in real scenarios. Therefore, this study investigates a flexible job shop scheduling problem with outsourcing operations and job priority constraints. We propose a sequence-based mathematical model aiming at minimizing weighted overdue days, which considers the outsourcing constraints and different overdue weights of jobs with different priorities. An efficient hybrid self-adaptive differential evolution algorithm with heuristic strategies (HSDE) is proposed to address this problem. In HSDE, a well-designed chromosome encoding and decoding method is presented. To eliminate individuals that do not satisfy the outsourcing constraints, we add a penalty term to improve the objective function. By considering heuristic strategies for initial chromosome generation, the proposed approach is able to achieve a high-quality initial population. Crossover and mutation operators with self-adaptive control of the parameters are established to enlarge the search range and accelerate the convergence speed. Finally, several experiments are conducted to verify the effectiveness of the proposed model and algorithm. Experimental results confirm that the proposed algorithm outperforms other algorithms both in efficiency and accuracy.

Improved Migratory Bird Migration Algorithm for Flexible Job Shop Scheduling

Abstract For flexible job shop scheduling, an improved migratory bird migration algorithm is proposed to minimize the maximum completion time. Firstly, global, local and random selection methods were used to initialize the population, which improved the quality of the initial solution; The structure of migratory bird group was changed by increasing leading birds, and the crossover and mutation operators were introduced to enhance the global optimization ability. And different variable neighborhood search algorithms on critical path were introduced among different bird groups, which improved the local optimization ability of and the diversity of migratory bird groups; The jumping and competition mechanisms were proposed to improve the ability of the algorithm to jump out of the local optimal solution and convergence. Finally, the simulation results of the benchmarks verified the algorithm’s searching ability and stability of the algorithm.

Self-adaptive multi-objective evolutionary algorithm for flexible job shop scheduling with fuzzy processing time

With increasing environmental awareness and energy requirement, sustainable manufacturing has attracted growing attention. Meanwhile, there is a high level of uncertainty in practical processing procedure, particularly in flexible manufacturing systems. This study addresses the multi-objective flexible job shop scheduling problem with fuzzy processing time (MOFFJSP) to minimize the makespan and the total workload simultaneously. A mixed integer liner programming model is presented and a hybrid self-adaptive multi-objective evolutionary algorithm based on decomposition (HPEA) is proposed to handle this problem. HPEA has the following features: (i) two problem-specific initial rules considering triangular fuzzy number are presented for hybrid initialization to generate diverse solutions; (ii) five problem-specific local search methods are incorporated to enhance the exploitation; (iii) an effective solution selection method based on Tchebycheff decomposition strategy is utilized to balance the convergence and diversity; and (iv) a parameter selection strategy is proposed to improve the quality of non-dominated solutions. To verify the effectiveness of HPEA, it is compared against other well-known multi-objective optimization algorithms. The results demonstrate that HPEA outperforms these five state-of-the-art multi-objective optimization algorithms in solving MOFFJSP.

Multi-objective enhanced memetic algorithm for green job shop scheduling with uncertain times

The quest for sustainability has arrived to the manufacturing world, with the emergence of a research field known as green scheduling. Traditional performance objectives now co-exist with energy-saving ones. In this work, we tackle a job shop scheduling problem with the double goal of minimising energy consumption during machine idle time and minimising the project’s makespan. We also consider uncertainty in processing times, modelled with fuzzy numbers. We present a multi-objective optimisation model of the problem and we propose a new enhanced memetic algorithm that combines a multiobjective evolutionary algorithm with three procedures that exploit the problem-specific available knowledge. Experimental results validate the proposed method with respect to hypervolume, ϵ-indicator and empirical attaintment functions.

An improved electromagnetism-like mechanism algorithm for energy-aware many-objective flexible job shop scheduling

An improved electromagnetism-like mechanism algorithm for energy-aware many-objective flexible job shop scheduling

A Q-Learning algorithm for flexible job shop scheduling in a real-world manufacturing scenario

In this work we propose a Reinforcement Learning approach for a real-world flexible job shop scheduling scenario, where a two-armed robot and a human operator share two workstations in order to assemble light switches. The approach returns a schedule of predefined assembly actions, taking into account given constraints specific to the scenario, such as which actions should precede others, which actions should occur together, or which actions should occur separately. In order to avoid collisions, the work area is divided into zones and all these constraints are taken into account by the algorithm in order to propose a schedule that optimizes the time it takes to prepare the customer orders. The approach that is taken is a reinforcement learning approach. There both arms and the operator are considered to be agents, and they learn from experience who should do which job best, taking into account the above mentioned constraints, as well as the estimated timings to execute the tasks. These estimated timings can be online updated, as well as their uncertainty. The experiments show that the proposed algorithm outperforms the currently used algorithm, which is a constraint solver, in terms of computation time and it is more user friendly with respect to expressing constraints. It also allows to take into account the uncertainty on the execution times of the tasks, and to add slack at critical timeslots, without unnecessarily increasing the makespan. Moreover, the algorithm allows to recompute an updated solution dynamically and efficiently when it turns out an action cannot be performed within the proposed time due to unexpected events. While we show the benefits in a scenario with a two-armed robot collaborating with a human for assembling light switches, the approach is relevant for many assembly tasks in the manufacturing industry where machines and human operators work together.

A Dynamic Adaptive Firefly Algorithm for Flexible Job Shop Scheduling

An NP-hard problem like Flexible Job Shop Scheduling (FJSP) tends to be more complex and requires more computational effort to optimize the objectives with contradictory measures. This paper aims to address the FJSP problem with combined and contradictory objectives, like minimization of make-span, maximum workload, and total workload. This paper proposes ‘Hybrid Adaptive Firefly Algorithm’ (HAdFA), a new enhanced version of the classic Firefly Algorithm (FA) embedded with adaptive parameters to optimize the multi objectives concurrently. The proposed algorithm has adopted two adaptive strategies, i.e., an adaptive randomization parameter (α) and an effective heterogeneous update rule for fireflies. The adaptations proposed by this paper can help the optimization process to strike a balance between diversification and intensification. Further, an enhanced local search algorithm, Simulated Annealing (SA), is hybridized with Adaptive FA to explore the local solution space more efficiently. This paper has also attempted to solve FJSP by a rarely used integrated approach where assignment and sequencing are done simultaneously. Empirical simulations on benchmark instances demonstrate the efficacy of our proposed algorithms, thus providing a competitive edge over other nature-inspired algorithms to solve FJSP.

A bi-objective branch-and-bound algorithm for the unit-time job shop scheduling : A mixed graph coloring approach

A bi-objective branch-and-bound and an ∊-constraint algorithms are proposed for the unit-time job shop scheduling problem. These two objectives are the minimization of the makespan and the total completion time. We model this problem as a bi-objective mixed graph coloring using both the chromatic number and the sum of path-endpoints coloring (i.e. sum of the colors assigned to the endpoints of maximal paths) to determine the optimal set of the non-dominated solutions. A new lower bound is also constructed for the sum of path-endpoints coloring which is used alongside an existing lower bound from the literature on two bounding procedures.Computational experiments on benchmark data sets show that the proposed lower bound improves considerably upon the known lower bound from the literature. Besides, our algorithms are found to find an optimal set of non-dominated solutions for most of the tested benchmarks within a reasonable amount of CPU time. In addition, two interesting performance metrics are introduced to compare and assess the effectiveness and the efficiency of our algorithms.

Quantum algorithms for process parallel flexible job shop scheduling

Flexible Job Shop Scheduling is one of the most difficult optimization problems known. In addition, modern production planning and control strategies require continuous and process-parallel optimization of machine allocation and processing sequences. Therefore, this paper presents a new method for process parallel Flexible Job Shop Scheduling using the concept of quantum computing based optimization. A scientific benchmark and the application to a realistic use-case demonstrates the good performance and practicability of this new approach. A managerial insight shows how the approach for process parallel flexible job shop scheduling can be integrated in existing production planning and control IT-infrastructure.