Multi-objective Scheduling Problem Research Articles

A novel approach for multi-objective truck scheduling problems in a cross-docking center

A novel approach for multi-objective truck scheduling problems in a cross-docking center

Algorithm for solving multi-objective hybrid flow shop scheduling problem

Aiming at the multi-objective unrelated parallel machine hybrid flow shop scheduling problem, a multi-objective mathematical model is established with the goal of minimizing the maximum completion time, total machine energy consumption and machine processing cost. An improved multi-objective evolution algorithm based on decomposition (IMOEAD) is proposed. The uniform design table is used to generate the initial weight vector to improve the population diversity. Normal distribution crossover and adaptive Gaussian mutation are used to improve the global and local search capabilities of the algorithm. Individuals are selected in the neighborhood of the weight vector to generate new solutions. The non-dominated rank and crowding distance are used to update the external archive. The inverse generation distance, generation distance and number of non-dominated solutions are used as performance indicators. Through a large number of case simulations, the algorithm is compared with the non-dominated sorting genetic algorithm II and the multi-objective evolution algorithm based on decomposition. The results verify the effectiveness of the algorithm.

A multi-objective optimization scheduling approach of integrated energy system considering the exergy efficiency using the variable step-size approximation method

As an important part of the new power system, it is crucial to consider the efficiency, economy and environment of the integrated energy system simultaneously. In order to improve the efficiency of solving multi-objective optimization scheduling problems for integrated energy systems, a variable step-size approximation method is proposed in this paper. Firstly, a model of integrated energy system is constructed, and the source-side and load-side exergy equations of different energy networks are given, as well as the mathematical expressions of equipment by combining the idea of unification. Secondly, in comparison with the ergodic weights approach, the variable step-size approximation method theoretical minimum reduction percentage of solution time is deduced by mathematical methodology under the m objective functions. Finally, the results from an integrated energy system including a modified New England 30-bus system, a 6-node heat network and a 7-node gas network demonstrate that the multi-objective function proposed compromises the economy, environment and efficiency of integrated energy system compared to the traditional optimization problem. In comparison with the ergodic weights approach, the step size approximation method can save over 97 % of the solution time, and the percentage of average error can be as low as 0 % under the multi-objective functions.

A heuristic method for multi-objective hybrid flow shop scheduling problem with parent-child relationships and space constraints

ABSTRACT In modern ship manufacturing, a ship is divided into hundreds of blocks in the design stage, and the productivity of the block manufacturing process is vital to ship delivery. This paper investigates the production scheduling problem of ship blocks with the parent-child relationship; this relationship is characterised by the fact that sibling jobs at the same BOM layer must be processed on adjacent machines at their assembly stages. We formulate this problem as a multi-objective hybrid flow shop scheduling problem: the first objective is to minimise the total deviation from the target time of the jobs and the second one is to minimise the total processing time. To solve this problem, we propose a heuristic method based on the multi-objective genetic algorithm, in which an adjacent machine priority method is first proposed to generate feasible solutions that satisfy the space constraints. Then, we improve the individual quality in crossover and mutation of the algorithm via tabu search. We verify the performance of our algorithm by test instances generated from real manufacturing data of a shipbuilding company. Results show that the proposed method outperforms the existing algorithms when identifying the Pareto optimal solutions, especially for large-sized problems.

Energy-efficient multi-objective distributed assembly permutation flowshop scheduling by Q-learning based meta-heuristics

This study addresses energy-efficient multi-objective distributed assembly permutation flowshop scheduling problems with minimisation of maximum completion time, mean of earliness and tardiness, and total carbon emission simultaneously. A mathematical model is introduced to describe the concerned problems. Five meta-heuristics are employed and improved, including the artificial bee colony, genetic algorithms, particle swarm optimization, iterated greedy algorithms, and Jaya algorithms. To improve the quality of solutions, five critical path-based neighborhood structures are designed. Q-learning, a value-based reinforcement learning algorithm that learns an optimal strategy by repeatedly interacting with the environment, is embedded into meta-heuristics. The Q-learning guides algorithms intelligently select appropriate neighborhood structures in the iterative process. Then, two machine speed adjustment strategies are developed to further optimize the obtained solutions. Finally, extensive experimental results show that the Jaya algorithm with Q-learning has the best performance for solving the considered problems.

A Self-Learning Hyper-Heuristic Algorithm Based on a Genetic Algorithm: A Case Study on Prefabricated Modular Cabin Unit Logistics Scheduling in a Cruise Ship Manufacturer.

Hyper-heuristic algorithms are known for their flexibility and efficiency, making them suitable for solving engineering optimization problems with complex constraints. This paper introduces a self-learning hyper-heuristic algorithm based on a genetic algorithm (GA-SLHH) designed to tackle the logistics scheduling problem of prefabricated modular cabin units (PMCUs) in cruise ships. This problem can be regarded as a multi-objective fuzzy logistics collaborative scheduling problem. Hyper-heuristic algorithms effectively avoid the extensive evaluation and repair of infeasible solutions during the iterative process, which is a common issue in meta-heuristic algorithms. The GA-SLHH employs a genetic algorithm combined with a self-learning strategy as its high-level strategy (HLS), optimizing low-level heuristics (LLHs) while uncovering potential relationships between adjacent decision-making stages. LLHs utilize classic scheduling rules as solution support. Multiple sets of numerical experiments demonstrate that the GA-SLHH exhibits a stronger comprehensive optimization ability and stability when solving this problem. Finally, the validity of the GA-SLHH in addressing real-world decision-making issues in cruise ship manufacturing companies is validated through practical enterprise cases. The results of a practical enterprise case show that the scheme solved using the proposed GA-SLHH can reduce the transportation time by up to 37%.

A bi-evolutionary cooperative multi-objective algorithm for blocking group flow shop with outsourcing option

In this study, a multi-objective blocking group flow shop scheduling problem with outsourcing option (BGFSP_OO) is addressed, where three objectives, including makespan, total energy consumption (TEC) and outsourcing cost, are considered simultaneously. To solve the BGFSP_OO, a bi-evolutionary cooperative multi-objective algorithm (BECMOA) is proposed. First, a machine switching strategy based on machine idle and blocking time is used in the decoding part to optimize the objective value TEC. Then, an effective heuristic for classifying outsourcing groups is proposed. To balance convergence and diversity abilities, a bi-evolutionary mechanism is proposed. The particle swarm optimization algorithm based on the gravity factor (IPSO) is employed, which exploiting individual performance, can enhance the convergence ability. Cross evolutionary search (CES) strategy is developed which can improve search ability, aiming to ensure diversity of solutions and access to more non-dominated solutions. Finally, the experimental results show that BECMOA is effective in solving BGFSP_OO compared to the state-of-the-art methods.

Energy-saving scheduling strategy for variable-speed flexible job-shop problem considering operation-dependent energy consumption

The rapid growth of industrial production signifies its CO2 footprint and climate impact, highlighting the demand for efficient and energy-saving production scheduling. Generally, a single production job comprises multiple operations on various machines. Existing studies estimate job energy consumption from a broader perspective, often disregarding the detailed scheduling of operations. This simplification may result in inaccurate evaluations of energy consumption and savings, as energy consumption can differ significantly among operations, with each requiring specific levels of energy on various machines. Proposing a new scheduling framework to replace the classical strategy is challenging yet necessary due to these variations. This study aims to investigate the multiobjective flexible job-shop scheduling problem by considering operation-dependent energy consumption and to improve the accuracy and thoroughness of the energy-consumption evaluation framework. First, a core metamodel for energy assessment is established and a mathematical model is introduced to minimize the manufacturing span and total energy consumption. Subsequently, a dynamic diffusion weight adjustment for a multiobjective evolutionary algorithm based on decomposition (MOEA/D-DDWA) is proposed. Operation-dependent energy consumption and processing quality are discussed, and a superior unified energy-saving strategy is designed to facilitate the selection of the processing-speed range, balancing energy consumption and saving. Finally, numerical experiments are conducted based on datasets of various scales, demonstrating that the core metamodel for energy assessment can achieve significant energy savings. Compared with other classical multiobjective optimization algorithms, the MOEA/D-DDWA is more energy efficient.

Multi-objective sustainable flexible job shop scheduling problem: Balancing economic, ecological, and social criteria

Industry 5.0 makes it imperative to reevaluate the manner of using resources in manufacturing systems to ensure sustainability. In this context, scheduling problems are encountering new environmental and human-related challenges, and the concept of sustainable scheduling has gained importance, aiming to balance economic, environmental, and human factors. In this paper, we propose two multi-objective mathematical models to simultaneously address these three factors as objective functions. In the first model, we consider the operator safety while using the Occupational Repetitive Action (OCRA) index to assess ergonomic risks related to task execution. The second model includes workers’ preferences in terms of machines, shifts and task variety. The objective is to improve the general well-being of workers by proposing a schedule that respects as much as possible their preferences. Both models integrate the travel time of workers and products between machines. To solve these NP-hard scheduling problems, we use the Non-dominated Sorting Genetic Algorithms II and III (NSGA-II and NSGA-III), enhanced with a Q-learning strategy for parameter selection and a variable neighborhood search based on reinforcement learning. The obtained results provide a comprehensive analysis of the interactions between these criteria, demonstrating the capability of such approach to achieve a favorable balance between multiple objectives while addressing the new challenges of production scheduling in Industry 5.0 context.

A Pareto-optimality based black widow spider algorithm for energy efficient flexible job shop scheduling problem considering new job insertion

The utilization of flexible job shops is on the rise, driven by the decreasing life cycle of consumer products. In dynamic flexible job shops, the occurrence of disruptive events like machine breakdown, tool wear, and new job arrivals is common, emphasizing the critical need for efficient scheduling to achieve productivity and cost-effectiveness. Additionally with the growing concerns about energy consumption and global warming, the imperative to contemplate workshops with lower energy usage is becoming increasingly significant. Therefore, in this study a multi-objective dynamic flexible job shop scheduling problem (MODFJSP) with insertion of new jobs for optimization objectives: makespan, total energy consumption and schedule instability is addressed. A novel multi-objective black widow spider algorithm (MOBWSA), inspired by the mating behavior of black widow spiders, is proposed. The MOBWSA ensures an optimal balance between minimizing makespan and energy consumption through its superior evolutionary processes of procreation, mutation and cannibalism. Furthermore, a strategic on/off strategy is implemented to enhance energy efficiency. The disruptions in schedule at rescheduling stage are addressed through the proposed sigmoidal weighted instability function. To handle the multi-objective nature of the problem this work incorporates Pareto-optimality approach in combination with novel hybrid crowding distance metric. The optimization is further aided by exploitation of search space through an ensemble of local search operators. Testing and evaluation of the MOBWSA with 30 benchmark problems is conducted, and its performance for multiple metrics is compared with recently published state-of-the-art algorithms. The results establish the effectiveness and efficiency of the proposed algorithm.

Multi-level guided evolution algorithm for solving fuzzy flexible job shop problem

Traditional flexible job shop scheduling problems (FJSP) are mostly limited to deterministic environments. In actual production, some uncertain factors lead to changes in job processing time. When solving multi-objective fuzzy flexible job shop scheduling problems (MOFFJSP), the existing evolutionary algorithms do not fully utilize information transfer between levels during the population evolution process. Therefore, a multi-level guided evolutionary (MLGE) optimization method is proposed to solve MOFFJSP. In the proposed MLGE method, decomposition and dominance techniques are combined to balance the diversity and convergence performance of the algorithm. Meanwhile, the idea of the Jaya algorithm approaching good individuals and distancing poor individuals is introduced. Combined with improved Jaya operator operations, it is used to guide individual evolution, preserving and inheriting solutions that perform well in terms of convergence and diversity. Finally, numerous experiments are carried out to evaluate the effectiveness of MLGE. The results show that MLGE can provide promising results for MOFFJSP. Additionally, it shows how MLGE outperforms other comparison algorithms in terms of convergence and variety of solutions.

Multi-objective fuzzy green scheduling optimization method of special vehicle body-in-white prototype shop considering equipment preventive maintenance

Based on the advantages of non-contact, flexibility, and small heat-affected zone, laser processing technology is widely used in material removal, addition, modification and other manufacturing fields. However, the emission of large amounts of smoke during laser processing of metal materials will result in environmental pollution in the job shop. Additionally, the processing time of laser equipment becomes uncertain as the power decays with prolonged use. Therefore, this paper is mainly focus on a multi-objective flexible job shop fuzzy green scheduling problem to minimize the fuzzy makespan, fuzzy total energy consumption and fuzzy total smoke emission. To solve it, an improved multi-objective particle swarm optimization algorithm has been designed. Firstly, a preventive maintenance strategy is proposed to reduce the makespan and equipment failure frequency by considering periodic power attenuation of laser equipment. Next, different particle updating strategies are employed to enhance particles’ exploration capabilities. Subsequently, five neighborhood structures are introduced to improve the performance of local search. Finally, comparison experiments are conducted with an expanded common benchmark, and a production case study in a special vehicle body-in-white prototype job shop. The results effectively demonstrate the feasibility and effectiveness of the developed model and improved multi-objective particle swarm optimization algorithm.

Approximation schemes for scheduling jobs on identical parallel machines to minimize the maximum lateness and makespan

We consider a multiobjective scheduling problem, with the aim of minimizing the maximum lateness and the makespan on identical machines, when the number of machines is fixed. This paper proposes an exact algorithm (based on a dynamic programming) to generate the complete Pareto Frontier in a pseudo-polynomial time. Moreover, four heuristics have been proposed in order to optimize our algorithm. Then, we present a Polynomial Time Approximation Scheme (PTAS) to generate an approximate Pareto Frontier. In this scheme, we use a simplification technique based on the merging of jobs. Furthermore, we present a Fully Polynomial Time Approximation Scheme (FPTAS) to generate an approximate Pareto Frontier, based on the conversion of the dynamic programming algorithm. The proposed FPTAS is strongly polynomial. Finally, some numerical experiments are provided in order to compare the proposed approaches.

Solving multi-objective green flexible job shop scheduling problem by an improved chimp optimization algorithm

As environmental contamination becomes more and more severe, enterprises need to consider optimizing environmental criteria while optimizing production criteria. In this study, a multi-objective green flexible job shop scheduling problem (MO_GFJSP) is established with two objective functions: the makespan and the carbon emission. To effectively solve the MO_GFJSP, an improved chimp optimization algorithm (IChOA) is designed. The proposed IChOA has four main innovative aspects: 1) the fast non-dominated sorting (FDS) method is introduced to compare the individuals with multiple objectives and strengthen the solution accuracy. 2) a dynamic convergence factor (DCF) is introduced to strengthen the capabilities of exploration and exploitation. 3) the position weight (PW) is used in the individual position updating to enhance the search efficiency. 4) the variable neighborhood search (VNS) is developed to strengthen the capacity to escape the local optimum. By executing abundant experiments using 20 benchmark instances, it was demonstrated that the developed IChOA is efficient to solve the MO_GFJSP and effective for reducing carbon emission in the flexible job shop.

Multi-policy deep reinforcement learning for multi-objective multiplicity flexible job shop scheduling

This study considers the simultaneous minimization of makespan and total tardiness for the multi-objective multiplicity flexible job shop scheduling problem (MOMFJSP). A deep reinforcement learning framework employing a multi-policy proximal policy optimization algorithm (MPPPO) is developed to solve MOMFJSP. The MOMFJSP is treated as a Markov decision process, allowing an intelligent agent to make sequential decisions based on the current production status. This framework involves multiple policy networks with different objective weight vectors. Using MPPPO, these networks are optimized simultaneously to obtain a set of high-quality Pareto-optimal policies. Moreover, a fluid model is introduced to extract state features and devise composite dispatching rules as discrete actions. A multi-policy co-evolution mechanism (MPCEM) is proposed to facilitate collaborative evolution among policy networks, supported by a reward mechanism that considers the objective weights. A training algorithm based on MPPPO is designed for learning across multiple policy networks. The effectiveness and superiority of the proposed method are confirmed through comparisons with composite dispatching rules and other scheduling methods.

Scheduling of Continuous Annealing With a Multi-Objective Differential Evolution Algorithm Based on Deep Reinforcement Learning

This paper studies a multi-objective scheduling problem in a continuous annealing operation of the steel industry, which is to simultaneously determine the production batch sizes for coils and their schedules so as to minimize the cost of setup, earliness, and tardiness. A large batch can reduce the setup costs but lead to a cost increase in earliness and tardiness. Thus, the conflict objectives of minimizing setup cost, earliness, and tardiness can be formulated separately. In this paper, we formulate a multi-objective optimization model for the problem and develop an adaptive multi-objective differential evolutionary based on deep reinforcement learning (AMODE-DRL) for effectively obtaining the Pareto solutions. In the proposed AMODE-RDL, DRL is integrated into the MODE algorithm as a controller, which can adaptively select mutation operators and parameters according to different search domains. Computational results on randomly generated instances and the practical problem instances show that DRL can effectively guide MODE to select mutation operators and parameters. The proposed algorithm can obtain better solutions compared to other powerful multi-objective evolutionary and adaptive MODE algorithms. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Setup usually leads to a decrease in production capacity and an increase in production costs. Similarly, earliness and tardiness costs are also crucial. These costs correspond to production, customer demand, and inventory, which are common objectives in production systems. However, the three objectives are generally conflicting, and it is very hard for practitioners to make appropriate decisions with manual experience. The multi-objective optimization methods can provide different scheduling for practitioners who may choose the suitable one according to current working conditions. Accordingly, the proposed model and algorithm can extend to other fields with similar characteristic problems.

An improved memetic algorithm for multi-objective resource-constrained flexible job shop inverse scheduling problem: An application for machining workshop

Resource-constrained flexible job shop scheduling problems are commonly encountered in some manufacturing industries, and have been widely studied in recent years. However, traditional resource constrained flexible job shop scheduling problem rarely consider the uncertainties in actual manufacturing systems, which may make the original schedule become suboptimal or even unfeasible. Therefore, a resource constrained flexible job shop inverse scheduling problem (RCFJISP) is proposed in this paper, which aims to cope with uncertain events by simultaneously adjusting the machine, worker and process parameters of the original schedule. A multi-objective optimization model is constructed to minimize the makespan, worker cost, machine energy consumption and deviation index. Furthermore, an improved memetic algorithm (IMA) is developed for solving the proposed problem. In IMA, a novel double-layer encoding mechanism is designed to enhance the capacity in exploring new solution’s domains. Three initialization strategies utilizing original scheduling information are designed to improve the quality of initial solutions. An adaptive mutation strategy and a local search mechanism are designed to enhance exploration and exploitation ability of the algorithm. And a crowding operator is proposed to reflect the diversity of the population effectively. In computational experiments, 28 extended benchmarks are constructed, and the effectiveness of the proposed strategy and algorithm is verified by comparing IMA with its 4 variants and other 4 widely used algorithms. Finally, two inverse scheduling problems of a real-world hydraulic cylinder machining workshop under two uncertain situations are studied. The results demonstrate that IMA can effectively solve the actual inverse scheduling problem. With a slight adjustment to the original scheduling, it can reduce the makespan by 11.5%, the worker cost by 8.1% and the machine energy consumption by 27.9% on average.

Enhancing multi-objective evolutionary algorithms with machine learning for scheduling problems: recent advances and survey

Multi-objective scheduling problems in workshops are commonly encountered challenges in the increasingly competitive market economy. These scheduling problems require a trade-off among multiple objectives such as time, energy consumption, and product quality. The importance of each optimization objective typically varies in different time periods or contexts, necessitating decision-makers to devise optimal scheduling plans accordingly. In actual production, decision-makers confront intricate multi-objective scheduling problems that demand balancing clients’ requirements and corporate interests while concurrently striving to reduce production cycles and costs. In solving various problems, multi-objective evolutionary algorithms have attracted the attention of researchers and gradually become one of the mainstream methods to solve these problems. In recent years, research combining multi-objective evolutionary algorithms with machine learning technology has shown great potential, opening up new prospects for improving the performance of multi-objective evolutionary methods. This article comprehensively reviews the latest application progress of machine learning in multi-objective evolutionary algorithms for scheduling problems. We review various machine learning techniques employed for enhancing multi-objective evolutionary algorithms, particularly focusing on different types of reinforcement learning methods. Different categories of scheduling problems addressed using these methods were also discussed, including flow-shop scheduling issues, job-shop scheduling challenges, and more. Finally, we highlighted the challenges faced by the field and outlined future research directions.

Knowledge-transfer based genetic programming algorithm for multi-objective dynamic agile earth observation satellite scheduling problem

The multi-objective dynamic agile earth observation satellite scheduling problem (MO-DAEOSSP) aims to schedule a set of real-time arrival requests and form a reasonable observation plan to satisfy various criteria. According to the requirements in practical applications, the total profit and the average image quality of scheduled requests are taken as optimization goals in this study. Compared to manually designed heuristics and iterative-based methods used in previous research, genetic programming based hyper heuristics (GPHH) can automatically evolve high-quality heuristic rules (HRs) for real-time scheduling without being highly dependent on expert knowledge. In this paper, a knowledge-transfer based multi-objective GPHH framework (KT-MOGP) is proposed, equipped with a heuristic-based simulation considering the idle monitoring, to evolve non-dominated HRs for solving MO-DAEOSSP. The heuristic-based simulation generates feasible schedules and returns fitness values for given HRs, which are the individuals evolved by KT-MOGP. KT-MOGP applies a knowledge transfer mechanism to accelerate convergence. Once a source problem is trained, its non-dominated solutions are extracted and their feature importance is transferred to guide the initialization of another target problem, by which the knowledge generated during the training process can be fully utilized. Experimental results on three sets of instances show that KT-MOGP outperforms the existing GPHH-based method and that the evolved HRs are competitive compared to several classical constructive heuristics and multi-objective evolutionary algorithms. The results also show the effectiveness of the proposed knowledge transfer-based initialization. To the best of our knowledge, this study is the first attempt to consider both multi-objective scenarios and real-time arrival requests.

A multi-objective fuzzy flexible job shop scheduling problem considering the maximization of processing quality

This paper analyzes practical production characteristics, including customer's stringent quality requirements and uncertain processing time in aircraft shaft parts manufacturing. Considering the above characteristics, we propose a multi-objective fuzzy aircraft shaft parts production scheduling problem considering the maximization of production quality. We define this problem as a multi-objective fuzzy flexible job shop scheduling problem (MO-fFJSP) with fuzzy processing time. To address this problem, we developed an improved multi-objective spider monkey optimization (IMOSMO) algorithm. IMOSMO integrates strategies such as genetic operators, variable neighborhood search and Pareto optimization theory on the framework of the conventional Spider Monkey Optimization (SMO) framework and discretize the continuous SMO algorithm to solve MO-fFJSP. To enhance the efficiency of the algorithm, we further adjust the sequence of the local leader learning phase and the global leader learning phase within the proposed IMOSMO framework. We conduct a comparative analysis between the performance of IMOSMO and NSGA-Ⅱ using 28 cases of varying scales. The computational results demonstrate the superiority of our algorithm over NSGA-Ⅱ in terms of both solution diversity and quality. Moreover, the performance of the proposed algorithm upgrades as the problem scale increases.