Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.

Q-Learning-Assisted Meta-Heuristics for Scheduling Distributed Hybrid Flow Shop Problems

The flow shop scheduling problem is important for the manufacturing industry.Effective flow shop scheduling can bring great benefits to the industry.However,there are few types of research on Distributed Hybrid Flow Shop Problems(DHFSP)by learning assisted meta-heuristics.This work addresses a DHFSP with minimizing the maximum completion time(Makespan).First,a mathematical model is developed for the concerned DHFSP.Second,four Q-learning-assisted meta-heuristics,e.g.,genetic algorithm(GA),artificial bee colony algorithm(ABC),particle swarm optimization(PSO),and differential evolution(DE),are proposed.According to the nature of DHFSP,six local search operations are designed for finding high-quality solutions in local space.Instead of randomselection,Q-learning assists meta-heuristics in choosing the appropriate local search operations during iterations.Finally,based on 60 cases,comprehensive numerical experiments are conducted to assess the effectiveness of the proposed algorithms.The experimental results and discussions prove that using Q-learning to select appropriate local search operations is more effective than the random strategy.To verify the competitiveness of the Q-learning assistedmeta-heuristics,they are compared with the improved iterated greedy algorithm(IIG),which is also for solving DHFSP.The Friedman test is executed on the results by five algorithms.It is concluded that the performance of four Q-learning-assisted meta-heuristics are better than IIG,and the Q-learning-assisted PSO shows the best competitiveness.

An Elite-Class Teaching-Learning-Based Optimization for Reentrant Hybrid Flow Shop Scheduling with Bottleneck Stage

Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid flow shop scheduling problem(RHFSP)with a bottleneck stage is considered,and an elite-class teaching-learning-based optimization(ETLBO)algorithm is proposed to minimize maximum completion time.To produce high-quality solutions,teachers are divided into formal ones and substitute ones,and multiple classes are formed.The teacher phase is composed of teacher competition and teacher teaching.The learner phase is replaced with a reinforcement search of the elite class.Adaptive adjustment on teachers and classes is established based on class quality,which is determined by the number of elite solutions in class.Numerous experimental results demonstrate the effectiveness of new strategies,and ETLBO has a significant advantage in solving the considered RHFSP.

A Novel Collaborative Evolutionary Algorithm with Two-Population for Multi-Objective Flexible Job Shop Scheduling

Job shop scheduling(JS)is an important technology for modern manufacturing.Flexible job shop scheduling(FJS)is critical in JS,and it has been widely employed in many industries,including aerospace and energy.FJS enables any machine from a certain set to handle an operation,and this is an NP-hard problem.Furthermore,due to the requirements in real-world cases,multi-objective FJS is increasingly widespread,thus increasing the challenge of solving the FJS problems.As a result,it is necessary to develop a novel method to address this challenge.To achieve this goal,a novel collaborative evolutionary algorithmwith two-population based on Pareto optimality is proposed for FJS,which improves the solutions of FJS by interacting in each generation.In addition,several experimental results have demonstrated that the proposed method is promising and effective for multi-objective FJS,which has discovered some new Pareto solutions in the well-known benchmark problems,and some solutions can dominate the solutions of some other methods.

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

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

Competitive and Cooperative-Based Strength Pareto Evolutionary Algorithm for Green Distributed Heterogeneous Flow Shop Scheduling

This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a competitive and cooperative-based strength Pareto evolutionary algorithm(CCSPEA)which contains the following features:1)An initialization based on three heuristic rules is developed to generate a population with great diversity and convergence.2)A comprehensive metric combining convergence and diversity metrics is used to better represent the heuristic information of a solution.3)A competitive selection is designed which divides the population into a winner and a loser swarms based on the comprehensive metric.4)A cooperative evolutionary schema is proposed for winner and loser swarms to accelerate the convergence of global search.5)Five local search strategies based on problem knowledge are designed to improve convergence.6)Aproblem-based energy-saving strategy is presented to reduce TEC.Finally,to evaluate the performance of CCSPEA,it is compared to four state-of-art and run on 22 instances based on the Taillard benchmark.The numerical experiment results demonstrate that 1)the proposed comprehensive metric can efficiently represent the heuristic information of each solution to help the later step divide the population.2)The global search based on the competitive and cooperative schema can accelerate loser solutions convergence and further improve the winner’s exploration.3)The problembased initialization,local search,and energy-saving strategies can efficiently reduce the makespan and TEC.4)The proposed CCSPEA is superior to the state-of-art for solving DHPFSP.

An improved multi-objective optimization algorithm for solving flexible job shop scheduling problem with variable batches

In order to solve the flexible job shop scheduling problem with variable batches,we propose an improved multiobjective optimization algorithm,which combines the idea of inverse scheduling.First,a flexible job shop problem with the variable batches scheduling model is formulated.Second,we propose a batch optimization algorithm with inverse scheduling in which the batch size is adjusted by the dynamic feedback batch adjusting method.Moreover,in order to increase the diversity of the population,two methods are developed.One is the threshold to control the neighborhood updating,and the other is the dynamic clustering algorithm to update the population.Finally,a group of experiments are carried out.The results show that the improved multi-objective optimization algorithm can ensure the diversity of Pareto solutions effectively,and has effective performance in solving the flexible job shop scheduling problem with variable batches.

Improved multi-objective artificial bee colony algorithm for optimal power flow problem

The artificial bee colony(ABC) algorithm is improved to construct a hybrid multi-objective ABC algorithm, called HMOABC, for resolving optimal power flow(OPF) problem by simultaneously optimizing three conflicting objectives of OPF, instead of transforming multi-objective functions into a single objective function. The main idea of HMOABC is to extend original ABC algorithm to multi-objective and cooperative mode by combining the Pareto dominance and divide-and-conquer approach. HMOABC is then used in the 30-bus IEEE test system for solving the OPF problem considering the cost, loss, and emission impacts. The simulation results show that the HMOABC is superior to other algorithms in terms of optimization accuracy and computation robustness.

Strengthened Dominance Relation NSGA-Ⅲ Algorithm Based on Differential Evolution to Solve Job Shop Scheduling Problem

The job shop scheduling problem is a classical combinatorial optimization challenge frequently encountered in manufacturing systems.It involves determining the optimal execution sequences for a set of jobs on various machines to maximize production efficiency and meet multiple objectives.The Non-dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ)is an effective approach for solving the multi-objective job shop scheduling problem.Nevertheless,it has some limitations in solving scheduling problems,including inadequate global search capability,susceptibility to premature convergence,and challenges in balancing convergence and diversity.To enhance its performance,this paper introduces a strengthened dominance relation NSGA-Ⅲ algorithm based on differential evolution(NSGA-Ⅲ-SD).By incorporating constrained differential evolution and simulated binary crossover genetic operators,this algorithm effectively improves NSGA-Ⅲ’s global search capability while mitigating pre-mature convergence issues.Furthermore,it introduces a reinforced dominance relation to address the trade-off between convergence and diversity in NSGA-Ⅲ.Additionally,effective encoding and decoding methods for discrete job shop scheduling are proposed,which can improve the overall performance of the algorithm without complex computation.To validate the algorithm’s effectiveness,NSGA-Ⅲ-SD is extensively compared with other advanced multi-objective optimization algorithms using 20 job shop scheduling test instances.The experimental results demonstrate that NSGA-Ⅲ-SD achieves better solution quality and diversity,proving its effectiveness in solving the multi-objective job shop scheduling problem.

Job-shop Scheduling with Multi-objectives Based on Genetic Algorithms

The technology of production planning and scheduling is one of the critical technologies that decide whether the automated manufacturing systems can get the expected economy. Job shop scheduling belongs to the special class of NP-hard problems. Most of the algorithms used to optimize this class of problems have an exponential time; that is, the computation time increases exponentially with problem size. In scheduling study, makespan is often considered as the main objective. In this paper, makespan, the due date request of the key jobs, the availability of the key machine, the average wait-time of the jobs, and the similarities between the jobs and so on are taken into account based on the application of mechanical engineering. The job shop scheduling problem with multi-objectives is analyzed and studied by using genetic algorithms based on the mechanics of genetics and natural selection. In this research, the tactics of the coding and decoding and the design of the genetic operators, along with the description of the mathematic model of the multi-objective functions, are presented. Finally an illu-strative example is given to testify the validity of this algorithm.

Sustainable Multi-Objective Multi-Reservoir Optimization Considering Environmental Flow

Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river waters that also require water for their survival. Due to the lack of awareness many times the minimum required quantity and quality of water for river ecosystem is not made available at downstream of storage reservoirs. So, a sustainable approach is required in reservoir operations to maintain the river ecosystem with environmental flow while meeting the other demands. Multi-objective, multi-reservoir operation model developed with Python programming using Fuzzy Linear Programing method incorporating environmental flow requirement of river is presented in this paper. Objective of maximization of irrigation release is considered for first run. In second run maximization of releases for hydropower generation is considered as objective. Further both objectives are fuzzified by incorporating linear membership function and solved to maximize fuzzified objective function simultaneously by maximizing satisfaction level indicator (λ). The optimal reservoir operation policy is presented considering constraints including Irrigation release, Turbine release, Reservoir storage, Environmental flow release and hydrologic continuity. Model applied for multi-reservoir system consists of four reservoirs, i.e., Jayakwadi Stage-I Reservoir (R1), Jayakwadi Stage-II Reservoir (R2), Yeldari Reservoir (R3), Siddheshwar Reservoir (R4) in Godavari River sub-basin from Marathwada region of Maharashtra State, India.

EFFICIENT MULTI-OBJECTIVE EVOLUTIONARY ALGORITHM FOR JOB SHOP SCHEDULING

A new representation method is first presented based on priority roles. According to this method, each entry in the chromosome indicates that in the procedure of the Giffler and Thompson （GT） algorithm, the conflict occurring in the corresponding machine is resolved by the corresponding priority role. Then crowding-measure multi-objective evolutionary algorithm （CMOEA） is designed, in which both archive maintenance and fitness assignment use crowding measure. Finally the comparisons between CMOEA and SPEA in solving 15 scheduling problems demonstrate that CMOEA is suitable to job shop scheduling.

基于广义粗糙集的不确定条件下的Flow Shop调度

在实际生产调度过程中,加工时间的不确定性是普遍存在的,因此引用广义粗糙变量来表示不确定的工件处理时间,定义粗糙加法运算,precision以及ratio,建立了处理时间不确定性的FlowShop调度问题的粗糙规划模型,提出了粗糙遗传调度算法将其应用于调度模型的求解,仿真实验证明了算法的有效性。

调整时间可分离的无等待Flow Shop调度问题

研究了 3台机器调整时间可分离的无等待FlowShop调度问题 ,目标函数为极小化加权完工时间和·基于对问题的分析 ,给出了目标函数的一般表示·对某些特殊情况 ,给出了问题存在多项式最优算法的充分条件·在此条件下 ,将单机调度问题的WSPT规则应用到无等待FlowShop调度问题 ,得到了求解无等待FlowShop问题最优调度的分派规则·通过反例指出了文献中的某些错误·

加工时间依赖开工时间的Flow Shop调度问题

讨论了加工时间依赖开工时间的Flow shop 调度问题。在这类问题中,工件的加工时间是开工时间的简单线性函数,机器间满足某种优势关系。对于这类问题,当目标函数是极小化最大完工时间时,尽管比相应的经典问题复杂,但仍存在多项式算法。如果目标函数是极小化加权完工时间和或极小化最大延误,则经典问题中的结论未必成立。

利用博弈演化算法求解置换Flow shop调度问题

在研究了流程工业中的Flowshop问题的基础上,建立了相应的数学模型,利用基于经济学博弈论的演化博弈算法对经典问题进行了求解,仿真结果证明了算法的有效性。

用混合算法求解Flow shop调度问题

研究了流程工业中的Flowshop调度问题,针对免疫算法的随机性和不确定性,结合分枝定界方法的特点,提出了一种基于免疫算法和分枝定界方法的混合调度算法,仿真结果表明该算法不仅能有效解决调度问题,而且提高了搜索效率。

一类Flow Shop调度问题最优调度区间摄动鲁棒性

调度的鲁棒性是调度应用中的一个重要问题.本文从最优调度不变的角度研究了调度的鲁棒性问题.首先定义了最优调度的区间摄动鲁棒性,即当问题中某些参数在各自的区间上变化时最优调度保持不变的性质.然后对比例FlowShop调度问题(任给一个工件它在各台机器上的加工时间都相同)进行了研究.通过一个引理我们证明了本文的结果,该引理指出了r个参数的大小次序与它们的变化区间的相交关系之间的联系.本文的结果是目标函数为完成时间总和时在加工时间扰动下最优调度具有区间摄动鲁棒性的三个充分必要条件,目标函数为最大拖期时间时及目标函数为拖后工件个数时在加工时间和/或交付期扰动下最优调度具有区间摄动鲁棒性的若干充分条件.这些结果与调度在一个由变化参数构成的超矩形的一些顶点上的最优性有关.文中给出了使用这些结果的例子.

不确定条件下不同交货期窗口的Flow Shop调度

研究了具有不同交货期窗口的Flow Shop的提前/拖期调度问题,并考虑了处理时间的不确定性。采用三角模糊数表示不确定性信息,引入两种模糊运算,建立了问题的模糊规划模型,并采用“中间值最大隶属度”的算法将模糊规划模型转化为清晰的非线性规划模型。针对清晰的数学模型提出了基于遗传算法的优化方法,最小化对所有工件提前/拖期惩罚。最后,大量仿真实验验证了算法的有效性。

模糊交货期Flow Shop调度文化进化算法研究

基于文化算法及文化进化思想设计了的文化进化算法,通过上层文化空间的经验知识指导下层个体进化搜索的方向及步长,通过模拟人类社会文化进化的机制实现文化空间的进化与更新,最后将算法应用到模糊Flow Shop问题的求解,用Matlab编程仿真测试.结果表明,此算法解决生产调度优化问题是可行的,而且其搜索性能优于简单遗传算法及模拟退火算法.