Total Machine Load Research Articles

An energy-saving distributed flexible job shop scheduling with machine breakdowns

Due to the change of consumption pattern, distributed flexible production is now becoming a major manufacturing mode. The machine breakdown seriously affects the production in workshops. How to efficiently adjust the scheduling scheme after machine breakdowns in distributed flexible job shop is an important concern for enterprises. Meanwhile, energy consumption is attracting more and more attention as environmental issues become increasingly serious. Thus, the energy-saving scheduling on distributed flexible job shop considering machine breakdowns is studied, and a mixed-integer programming model is established to optimize makespan, total energy consumption and machine load difference, simultaneously. Based on the problem characteristics, an improved memetic algorithm is designed. To improve the quality of initial solutions, an initialization strategy incorporating multiple rules is designed. An active decoding method with an adjustment strategy is adopted to fully utilize machine idleness. To expand the search range, the idea of dual-population collaborative optimization is used. Multi-level intelligent mutation operation strategies are introduced to further enhance the quality of solutions. In addition, an adaptive parameter rule is designed to adjust to appropriate search capabilities at different evolutionary stages. To verify the effectiveness of the proposed strategies and algorithm, the memetic algorithm, the artificial bee colony algorithm, the differential evolution algorithm and the estimation of distribution algorithm are chosen as comparison algorithms. The same iteration number and same running time are used as the termination criteria of all algorithms, and 60 instances of different scales are solved. The experimental results demonstrate that the effectiveness of the strategies and algorithm designed in this paper. Notably, our algorithm consistently achieved good results even when the same running time is used as the termination criterion.

An Improved Mayfly Optimization Algorithm for Type-2 Multi-Objective Integrated Process Planning and Scheduling

The type-2 multi-objective integrated process planning and scheduling problem, as an NP-hard problem, is required to deal with both process planning and job shop scheduling, and to generate optimal schedules while planning optimal machining paths for the workpieces. For the type-2 multi-objective integrated process planning and scheduling problem, a mathematical model with the minimization objectives of makespan, total machine load, and critical machine load is developed. A multi-objective mayfly optimization algorithm with decomposition and adaptive neighborhood search is designed to solve this problem. The algorithm uses two forms of encoding, a transformation scheme designed to allow the two codes to switch between each other during evolution, and a hybrid population initialization strategy designed to improve the quality of the initial solution while taking into account diversity. In addition, an adaptive neighborhood search cycle based on the average distance of the Pareto optimal set to the ideal point is designed to improve the algorithm’s merit-seeking ability while maintaining the diversity of the population. The proposed encoding and decoding scheme can better transform the continuous optimization algorithm to apply to the combinatorial optimization problem. Finally, it is experimentally verified that the proposed algorithm achieves better experimental results and can effectively deal with type-2 MOIPPS.

An effective hybrid algorithm for joint scheduling of machines and AGVs in flexible job shop

Flexible job shops motivated by small batches and multiple orders require the collaboration of machines and automated guided vehicles (AGVs) scheduling to boost shop floor flexibility and productivity. The joint scheduling of machines and AGVs can better achieve global optimization. However, joint scheduling requires two NP hard problems to be solved simultaneously. Therefore, this paper employs a multi-AGV flexible job shop scheduling problem (MA-FJSP) with an effective hybrid algorithm. First of all, a model is established with the objectives of minimizing the makespan, the total AGV running time and the total machine load. To solve the MA-FJSP, high-quality initialization methods and improved elite strategies are designed to improve global convergence in the proposed algorithm. In addition, a problem-knowledge-based neighborhood search is integrated to improve its exploitation capability. At last, a series of comparative experimental studies were performed to exam the effectiveness of the improved algorithm. The results demonstrate that the solutions gained by the proposed algorithm perform well in respect of convergence, diversity and distribution.

Multi-Strategy Dynamic Evolution-Based Improved MOEA/D Algorithm for Solving Multi-Objective Fuzzy Flexible Job Shop Scheduling Problem

A scheduling model was developed to optimize the maximum completion time, total machine load, and maximum machine load for the fuzzy flexible job shop problem with uncertain processing times. To solve this problem, a multi-strategy dynamic evolution-based improved multi-objective evolutionary algorithm based on decomposition(IMOEA/D) was proposed. In order to enhance the quality of the non-dominated solution set and improve the algorithm efficiency. The algorithm firstly employs a strategy based on minimum processing time and workload, along with a non-dominated solution prioritization mechanism to generate the initial population. Secondly, three evolutionary strategies are incorporated, and their probabilities are dynamically adjusted with the increase of evolution generations. Finally, a variable neighborhood search method is introduced to improve the search performance of the algorithm. The effectiveness of the proposed algorithm was demonstrated through experimental validation.

Hierarchical Reinforcement Learning for Multi-Objective Real-Time Flexible Scheduling in a Smart Shop Floor

With the development of intelligent manufacturing, machine tools are considered the “mothership” of the equipment manufacturing industry, and the associated processing workshops are becoming more high-end, flexible, intelligent, and green. As the core of manufacturing management in a smart shop floor, research into the multi-objective dynamic flexible job shop scheduling problem (MODFJSP) focuses on optimizing scheduling decisions in real time according to changes in the production environment. In this paper, hierarchical reinforcement learning (HRL) is proposed to solve the MODFJSP considering random job arrival, with a focus on achieving the two practical goals of minimizing penalties for earliness and tardiness and reducing total machine load. A two-layer hierarchical architecture is proposed, namely the combination of a double deep Q-network (DDQN) and a dueling DDQN (DDDQN), and state features, actions, and external and internal rewards are designed. Meanwhile, a personal computer-based interaction feature is designed to integrate subjective decision information into the real-time optimization of HRL to obtain a satisfactory compromise. In addition, the proposed HRL framework is applied to multi-objective real-time flexible scheduling in a smart gear production workshop, and the experimental results show that the proposed HRL algorithm outperforms other reinforcement learning (RL) algorithms, metaheuristics, and heuristics in terms of solution quality and generalization and has the added benefit of real-time characteristics.

A Two-Stage Multi-Objective Genetic Algorithm for a Flexible Job Shop Scheduling Problem with Lot Streaming

The work in this paper is motivated by a recently published article in which the authors developed an efficient two-stage genetic algorithm for a comprehensive model of a flexible job-shop scheduling problem (FJSP). In this paper, we extend the application of the algorithm to solve a lot streaming problem in FJSP while at the same time expanding the model to incorporate multiple objectives. The objective function terms included in our current work are the minimization of the (1) makespan, (2) maximum sublot flowtime, (3) total sublot flow time, (4) maximum job flowtime, (5) total job flow time, (6) maximum sublot finish-time separation, (7) total sublot finish-time separation, (8) maximum machine load, (9) total machine load, and (10) maximum machine load difference. Numerical examples are presented to illustrate the greater need for multi-objective optimization in larger problems, the interaction of the various objective function terms, and their relevance in providing better solution quality. The ability of the two-stage genetic algorithm to jointly optimize all the objective function terms is also investigated. The results show that the algorithm can generate initial solutions that are highly improved in all of the objective function terms. It also outperforms the regular genetic algorithm in convergence speed and final solution quality in solving the multi-objective FJSP lot streaming. We also demonstrate that high-performance parallel computation can further improve the performance of the two-stage genetic algorithm. Nevertheless, the sequential two-stage genetic algorithm with a single CPU outperforms the parallel regular genetic algorithm that uses many CPUs, asserting the superiority of the two-stage genetic algorithm in solving the proposed multi-objective FJSP lot streaming.

An Effective Hybrid Multiobjective Flexible Job Shop Scheduling Problem Based on Improved Genetic Algorithm

Multiobjective Flexible Job Shop Scheduling Problem (MO-FJSP) is a scheduling problem used in manufacturing sectors to use energy efficiently and thriftily. The scheduling problem aims to increase productivity and reduce energy consumption via a mathematical model. With this paper, an effective genetic algorithm is proposed for MO-FJSP based on maximum completion time, total machine load, and bottleneck machine load. The solution method utilizes a hybrid multiobjective genetic algorithm. A combination of global selection and fast selection is used for initialization and obtaining a uniformly distributed initial population. The cross-variance operator is adaptively improved to enhance the searching in the population. Following that an elite retention mechanism is designed to address the possible limitations of the elite strategy in maintaining population diversity. As a result, an improved harmonic search algorithm is introduced to improve the quality of individuals in the elite pool. The proposed hybrid method is implemented in MATLAB R2018a. Tests were conducted using the benchmark Kacem test set, the BR data data set, and with the actual production cases. The algorithm succeeded in achieving 13 nondominated solutions in the initial 20 runs. Moreover, the method obtains the optimal value criterion for the solution accuracy factor. As a whole, results of the evaluation testify that the proposed method can be used to solve the MO-FJSP with high accuracy and fast convergence. The method also provides feasible and effective scheduling solutions for the decision-makers in actual production. Based on the promising results obtained, it is deduced that the method has a wide applicability range particularly in manufacturing sector.

Multi-objective Green Flexible Workshop Scheduling Considering Multi-energy Consumption Factors

In order to solve the energy consumption problem of shop floor caused by machine processing, adjustment, idling and workpiece transportation, the green flexible workshop scheduling problem was studied, and a multi-objective optimization model was established with the maximum completion time, total machine load and total energy consumption as the objectives. The double-layer coding strategy was adopted to encode processes and machines respectively to optimize the scheduling scheme, and then the adaptive hybrid crossover scheme, mutation scheme and improved elite retention strategy were adopted to improve the operation efficiency and population diversity of NSGA-II algorithm. Finally, a case study is used to verify the effectiveness of the algorithm in solving the multi-objective green flexible workshop scheduling problem, which provides a reference for enterprises to achieve green manufacturing.

An Effective Multi-population Grey Wolf Optimizer based on Reinforcement Learning for Flow Shop Scheduling Problem with Multi-machine Collaboration

This paper proposes the Flow Shop Scheduling Problem with Multi-machine Collaboration (FSSP-MC). In FSSP-MC, several machines can operate a single task simultaneously, so it is a coupling problem of resource composition and task sequencing, which is more difficult and has a larger scale solution space than the traditional Flow Shop Scheduling Problem (FSSP), therefore an optimization algorithm with higher efficient and accurate is demanded. However, most existing intelligent algorithms are easily trapped into local optima and have low precision on solving large-scale problems. To this end, an adaptive multi-objective Multi-population Grey Wolf Optimizer (AMPGWO) based on Reinforcement Learning (RL) is developed to address FSSP-MC with the goals of minimizing maximum completion time (makespan) and the total machine load. In AMPGWO, the whole population is divided into three subpopulations, and different search strategies are adopted in different subpopulations to enhance population diversity. Since the numbers of individuals in a subpopulations are pretty crucial for the performance of the algorithm, which needs to be reasonably determined and dynamically adjusted, so RL is applied to adaptively adjust the individual quantity of each subpopulation and strengthen the information exchange among different subpopulations. Finally, 20 instances of FSSP-MC with different sizes are used for three comparative experiments, in which the effectiveness of multi-population and RL mechanisms, effectiveness of mutation mechanism of AMPGWO are verified. Through results analysis, it can be seen that proposed AMPGWO is pretty effective and significantly outperforms its competitors in solving FSSP-MC.

Adaptive genetic algorithm for scheduling problem in flexible workshop with low carbon constraints

Taking the completion time, energy carbon emission and total machine load as independent time factors into consideration, a flexible workshop scheduling model is established to minimise the maximum completion time, energy emissions and the total machine load. The population could be initialised by greedy algorithm and random number method, and this model could be solved by the crossover probability and genetic probability adaptive method. The feasibility and effectiveness of the improved genetic algorithm are verified by testing the data set and comparing several single-objective data and normalised multi-objective data.

Adaptive genetic algorithm for scheduling problem in flexible workshop with low carbon constraints

Taking the completion time, energy carbon emission and total machine load as independent time factors into consideration, a flexible workshop scheduling model is established to minimise the maximum completion time, energy emissions and the total machine load. The population could be initialised by greedy algorithm and random number method, and this model could be solved by the crossover probability and genetic probability adaptive method. The feasibility and effectiveness of the improved genetic algorithm are verified by testing the data set and comparing several single-objective data and normalised multi-objective data.

Scheduling with deterioration effects and maintenance activities under parallel processors

ABSTRACT This article considers unrelated parallel processor scheduling problems with deterioration effects and processor maintenance activities. In this case, deterioration occurs during processing. A maintenance activity on a parallel processor is allowed after a job is processed, and the maintenance time is a fixed constant. After the maintenance work is completed, the processor is restored to the initial state, and job deterioration starts again. The goal of this article is to determine the location of the processor maintenance activity and to find the optimal sequence to minimize the total completion time and total machine load. It is shown in this article that these problems are polynomial-time solvable and the corresponding algorithms are provided.

Low Carbon Multi-Objective Shop Scheduling Based On Genetic and Variable Neighborhood Algorithm

Aiming at the low-carbon scheduling problem of flexible job shop, the carbon emission and key scheduling objectives of machining system are studied. Firstly, the carbon emissions directly generated by machines and indirectly generated by waste treatment are considered in the calculation of carbon emissions, and then a multi-objective optimization model is established with completion time, total machine load and carbon emissions as the objective function; secondly, the hybrid algorithm of genetic variable neighborhood is designed to solve the optimization model, and the completion time, total machine load. Finally, the production example is simulated in Matlab environment. The experimental results show that the multi-objective scheduling model is feasible and effective. According to the production situation of the workshop, the producer can allocate the weight of each objective, and reduce the carbon emissions in the production process on the premise of ensuring the balance of the completion time and equipment utilization.

Parallel machines scheduling based on the impact of deteriorating maintenance

In this paper we study the problem of revising an initial schedule on parallel identical machines after a subset of jobs has finished processing. This is caused by deteriorating and rate-modifying maintenance. During the planning horizon there should be one maintenance activity scheduled on each machine to improve its processing rate. And delaying the starting time of maintenance should increase the time required to perform it. Considering both the total completion times of all jobs and the impact of maintenance in the form of increase in total machine load, we need to determine the job sequence on each machine and the location of maintenance simultaneously. We provide a polynomial time algorithm to the problem and extend the results to the case of unrelated machines.

A Multiple-objective Particle Swarm Optimization for Flexible Job Shop Scheduling Problem

In this paper, a hybrid particle-swarm optimization algorithm is proposed for the flexible job shop scheduling problem with multiple objectives. The optimization objectives are considered to be the production cycle time, total machine load and the maximal single machine load, respectively. A discrete particle swarm combined with variable neighborhood search is proposed to solve the problem based on Maximin fitness. The main benefits of the method are the improvements of both global and local searching ability. Compared to other algorithms on benchmark problems, the simulation results show the effectiveness of the algorithm.

An effective hybrid multi objective evolutionary algorithm for solving real time event in flexible job shop scheduling problem

This paper addresses the multi-objective model for a flexible job shop scheduling problem (FJSSP) to improve the system performance under the condition of machines break down asa real time event. It is important to identify the relevant performance measures to the mentioned problem for examining the system performance. Therefore, minimization of make span and minimization of total machine load variation is considered as two performance measures. Generally, it is very difficult to develop a mathematical model for the real-time situations in FJSSP. Hence, in this paper we divided the research work into two folds: Primarily, a mixed-integer non-linear programming (MINLP) model has been developed to represent the above-mentioned multi-objectives that subjected to constraints without considering machines break down. Secondarily, by incorporating the machines break down as the real-time event the performance of the system is examined. Solving conflicting objectives simultaneously for finding the optimal/near optimal solutions in a reasonable time is a challenge. In this paper, we proposed a new evolutionary based multi-objective teacher learning-based optimization algorithm (MOTLBO) to solve the above-mentioned complex problem. Moreover, to improve the obtained solutions a local search technique has been incorporated in the MOTLBO and comparisons has been made with existing multi-objective particle swarm optimization (MOPSO) and conventional non-dominated sorting genetic algorithm (CNSGA-II). Results found that the proposed multi-objective-based hybrid meta-heuristic algorithm produced high-quality solutions as proved by the tests we performed over a number of randomly generated test problems. Finally, comparisons also made with how the machines break down can affect the proposed systems performance.

Coordination mechanisms for scheduling games with proportional deterioration

We study parallel-machine scheduling games with deteriorating jobs. The processing time of a job increases proportionally with its starting time by a positive deterioration rate. Each job acts selfishly aiming to minimize its completion time while choosing a machine on which it will be processed. Machines are equipped with coordination mechanisms to diminish chaos caused by jobs’ competition. We consider three coordination mechanisms in this paper, namely Smallest Deterioration Rate first, Largest Deterioration Rate first and MAKESPAN policy. Under these mechanisms, we precisely quantify the inefficiency of their Nash Equilibriums by investigating the Price of Anarchy (PoA) and the Price of Stability (PoS), concerning minimization of social costs including the makespan and the total machine load. By using some new methods, we obtain parametrical bounds on the PoA and PoS, and demonstrate that most of these bounds are tight.

On the Multi-objective Optimization Method of the Flexible Job-shop Scheduling Problem Based on Ant Colony Algorithm

Using the multi-objective method is to solve the flexible job-shop scheduling problem (FJSP), this paper optimizes the three objectives of the total processing time, the total machine load and the key machine load, analyzes the relations between the three optimization objectives in detail, and decides to minimize the total machine load and the key machine load during the process route selection and to minimize the total processing time during the process scheduling. According to the characteristics of multi-objective optimization, the author redesigns the update mode and state transition probability formula for local heuristic information of ant in the optimized ant colony algorithm. The simulation experiment proves the effectiveness of the mixed optimization algorithm of ant colony algorithm and particle swarm algorithm.

A robust hybrid approach based on particle swarm optimization and genetic algorithm to minimize the total machine load on unrelated parallel machines

This paper dealt with an unrelated parallel machines scheduling problem with past-sequence-dependent setup times, release dates, deteriorating jobs and learning effects, in which the actual processing time of a job on each machine is given as a function of its starting time, release time and position on the corresponding machine. In addition, the setup time of a job on each machine is proportional to the actual processing times of the already processed jobs on the corresponding machine, i.e., the setup times are past-sequence-dependent (p-s-d). The objective is to determine jointly the jobs assigned to each machine and the order of jobs such that the total machine load is minimized. Since the problem is NP-hard, optimal solution for the instances of realistic size cannot be obtained within a reasonable amount of computational time using exact solution approaches. Hence, an efficient method based on the hybrid particle swarm optimization (PSO) and genetic algorithm (GA), denoted by HPSOGA, is proposed to solve the given problem. In view of the fact that efficiency of the meta-heuristic algorithms is significantly depends on the appropriate design of parameters, the Taguchi method is employed to calibrate and select the optimal levels of parameters. The performance of the proposed method is appraised by comparing its results with GA and PSO with and without local search through computational experiments. The computational results for small sized problems show that the mentioned algorithms are fully effective and viable to generate optimal/near optimal solutions, but when the size of the problem is increased, the HPSOGA obtains better results in comparison with other algorithms.

Unrelated Parallel-Machine Scheduling Problems with General Truncated Job-Dependent Learning Effect

In this paper, we consider scheduling problems with general truncated job-dependent learning effect on unrelated parallel-machine. The objective functions are to minimize total machine load, total completion (waiting) time, total absolute differences in completion (waiting) times respectively. If the number of machines is fixed, these problems can be solved in m On 2 () + time respectively, where m is the number of machines and n is the number of jobs.