Deep Reinforcement Learning Solves Job-shop Scheduling Problems

To solve the sparse reward problem of job-shop scheduling by deep reinforcement learning,a deep reinforcement learning framework considering sparse reward problem is proposed.The job shop scheduling problem is transformed into Markov decision process,and six state features are designed to improve the state feature representation by using two-way scheduling method,including four state features that distinguish the optimal action and two state features that are related to the learning goal.An extended variant of graph isomorphic network GIN++is used to encode disjunction graphs to improve the performance and generalization ability of the model.Through iterative greedy algorithm,random strategy is generated as the initial strategy,and the action with the maximum information gain is selected to expand it to optimize the exploration ability of Actor-Critic algorithm.Through validation of the trained policy model on multiple public test data sets and comparison with other advanced DRL methods and scheduling rules,the proposed method reduces the minimum average gap by 3.49%,5.31%and 4.16%,respectively,compared with the priority rule-based method,and 5.34%compared with the learning-based method.11.97%and 5.02%,effectively improving the accuracy of DRL to solve the approximate solution of JSSP minimum completion time.

Necessary and Sufficient Conditions for Feasible Neighbourhood Solutions in the Local Search of the Job-Shop Scheduling Problem

The meta-heuristic algorithm with local search is an excellent choice for the job-shop scheduling problem(JSP).However,due to the unique nature of the JSP,local search may generate infeasible neighbourhood solutions.In the existing literature,although some domain knowledge of the JSP can be used to avoid infeasible solutions,the constraint conditions in this domain knowledge are sufficient but not necessary.It may lose many feasible solutions and make the local search inadequate.By analysing the causes of infeasible neighbourhood solutions,this paper further explores the domain knowledge contained in the JSP and proposes the sufficient and necessary constraint conditions to find all feasible neighbourhood solutions,allowing the local search to be carried out thoroughly.With the proposed conditions,a new neighbourhood structure is designed in this paper.Then,a fast calculation method for all feasible neighbourhood solutions is provided,significantly reducing the calculation time compared with ordinary methods.A set of standard benchmark instances is used to evaluate the performance of the proposed neighbourhood structure and calculation method.The experimental results show that the calculation method is effective,and the new neighbourhood structure has more reliability and superiority than the other famous and influential neighbourhood structures,where 90%of the results are the best compared with three other well-known neighbourhood structures.Finally,the result from a tabu search algorithm with the new neighbourhood structure is compared with the current best results,demonstrating the superiority of the proposed neighbourhood structure.

Solving Job-Shop Scheduling Problem Based on Improved Adaptive Particle Swarm Optimization Algorithm

An improved adaptive particle swarm optimization(IAPSO)algorithm is presented for solving the minimum makespan problem of job shop scheduling problem(JSP).Inspired by hormone modulation mechanism,an adaptive hormonal factor(HF),composed of an adaptive local hormonal factor(H l)and an adaptive global hormonal factor(H g),is devised to strengthen the information connection between particles.Using HF,each particle of the swarm can adjust its position self-adaptively to avoid premature phenomena and reach better solution.The computational results validate the effectiveness and stability of the proposed IAPSO,which can not only find optimal or close-to-optimal solutions but also obtain both better and more stability results than the existing particle swarm optimization(PSO)algorithms.

Improved Genetic Algorithm for Job-Shop Scheduling

This paper presents a new genetic algorithm for job-shop scheduling problem. Based on schema theorem and building block hypothesis, a new crossover is proposed. By selecting short, low-order, highly fit schemas for genetic operator, the crossover can maintain a diversity of population without disrupting the characteristics and search the global optimization. Simulation results on famous benchmark problems MT06, MT10 and MT20 coded by Matlab show that our genetic operators are suitable to job-shop scheduling problems and outperform the previous GA-based approaches.

Job-Shop Scheduling问题的一个快速算法

Job-Shop Scheduling问题是优化组合中一个著名的难题,即使规模不大的算例在计算上也是很棘手的。文章给出了一个性能很好的算法,该算法找到了所计算的16个算例中12个算例的最优解,而且每个算例在一台个人计算机(CPU为赛扬633)上所花的计算时间不超过1分钟。

Solving Job-Shop Scheduling Problems by Genetic Algorithms Based on Building Block Hypothesis

In this paper, we propose a new genetic algorithm for job-shop scheduling problems （JSP）. The proposed method uses the operation-based representation, based on schema theorem and building block hypothesis, a new crossover is proposed ： By selecting short, low order highly fit schemas to genetic operator, the crossover can exchange meaningful ordering information of parents effectively and can search the global optimization. Simulation results on MT benchmark problem coded by C ＋ ＋ show that our genetic operators are very powerful and suitable to job-shop scheduling problems and our method outperforms the previous GA-based approaches.

具有模糊加工时间的Flexible Job-Shop Scheduling问题的研究

采用梯形模糊数来表征柔性生产系统中的时间参数,并在此基础上对具有模糊加工时间的柔性作业车间最小化制造跨度调度问题进行了描述。然后给出了基于粒子群优化的柔性作业车间调度模型。最后通过实例验证了模型的有效性。

Energy-efficient Approach to Minimizing the Energy Consumption in An Extended Job-shop Scheduling Problem

The traditional production planning and scheduling problems consider performance indicators like time, cost and quality as optimization objectives in manufacturing processes. However, environmentally-friendly factors like energy consumption of production have not been completely taken into consideration. Against this background, this paper addresses an approach to modify a given schedule generated by a production plarming and scheduling system in a job shop floor, where machine tools can work at different cutting speeds. It can adjust the cutting speeds of the operations while keeping the original assignment and processing sequence of operations of each job fixed in order to obtain energy savings. First, the proposed approach, based on a mixed integer programming mathematical model, changes the total idle time of the given schedule to minimize energy consumption in the job shop floor while accepting the optimal solution of the scheduling objective, makespan. Then, a genetic-simulated annealing algorithm is used to explore the optimal solution due to the fact that the problem is strongly NP-hard. Finally, the effectiveness of the approach is performed small- and large-size instances, respectively. The experimental results show that the approach can save 5%-10% of the average energy consumption while accepting the optimal solution of the makespan in small-size instances. In addition, the average maximum energy saving ratio can reach to 13%. And it can save approximately 1%-4% of the average energy consumption and approximately 2.4% of the average maximum energy while accepting the near-optimal solution of the makespan in large-size instances. The proposed research provides an interesting point to explore an energy-aware schedule optimization for a traditional production planning and scheduling problem.

A bi-objective model for job-shop scheduling problem to minimize both energy consumption and makespan

The issue of reducing energy consumption for the job-shop scheduling problem in machining systems is addressed, whose dual objectives are to minimize both the energy consumption and the makespan. First, the bi- objective model for the job-shop scheduling problem is proposed. The objective function value of the model represents synthesized optimization of energy consumption and makespan. Then, a heuristic algorithm is developed to locate the optimal or near optimal solutions of the model based on the Tabu search mechanism. Finally, the experimental case is presented to demonstrate the effectiveness of the proposed model and the algorithm.

Modified bottleneck-based heuristic for large-scale job-shop scheduling problems with a single bottleneck

A modified bottleneck-based （MB） heuristic for large-scale job-shop scheduling problems with a welldefined bottleneck is suggested, which is simpler but more tailored than the shifting bottleneck （SB） procedure. In this algorithm, the bottleneck is first scheduled optimally while the non-bottleneck machines are subordinated around the solutions of the bottleneck schedule by some effective dispatching rules. Computational results indicate that the MB heuristic can achieve a better tradeoff between solution quality and computational time compared to SB procedure for medium-size problems. Furthermore, it can obtain a good solution in a short time for large-scale jobshop scheduling problems.

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 accotmt 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.

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.

A Layered Energy-EfficientMulti-Node Scheduling Mechanism for Large-Scale WSN

In recent years, target tracking has been considered one of the most important applications of wireless sensornetwork (WSN). Optimizing target tracking performance and prolonging network lifetime are two equally criticalobjectives in this scenario. The existing mechanisms still have weaknesses in balancing the two demands. Theproposed heuristic multi-node collaborative scheduling mechanism (HMNCS) comprises cluster head (CH)election, pre-selection, and task set selectionmechanisms, where the latter two kinds of selections forma two-layerselection mechanism. The CH election innovatively introduces the movement trend of the target and establishesa scoring mechanism to determine the optimal CH, which can delay the CH rotation and thus reduce energyconsumption. The pre-selection mechanism adaptively filters out suitable nodes as the candidate task set to applyfor tracking tasks, which can reduce the application consumption and the overhead of the following task setselection. Finally, the task node selection is mathematically transformed into an optimization problem and thegenetic algorithm is adopted to form a final task set in the task set selection mechanism. Simulation results showthat HMNCS outperforms other compared mechanisms in the tracking accuracy and the network lifetime.

A Novel Predictive Model for Edge Computing Resource Scheduling Based on Deep Neural Network

Currently,applications accessing remote computing resources through cloud data centers is the main mode of operation,but this mode of operation greatly increases communication latency and reduces overall quality of service(QoS)and quality of experience(QoE).Edge computing technology extends cloud service functionality to the edge of the mobile network,closer to the task execution end,and can effectivelymitigate the communication latency problem.However,the massive and heterogeneous nature of servers in edge computing systems brings new challenges to task scheduling and resource management,and the booming development of artificial neural networks provides us withmore powerfulmethods to alleviate this limitation.Therefore,in this paper,we proposed a time series forecasting model incorporating Conv1D,LSTM and GRU for edge computing device resource scheduling,trained and tested the forecasting model using a small self-built dataset,and achieved competitive experimental results.

Performance Prediction Based Workload Scheduling in Co-Located Cluster

Cloud service providers generally co-locate online services and batch jobs onto the same computer cluster,where the resources can be pooled in order to maximize data center resource utilization.Due to resource competition between batch jobs and online services,co-location frequently impairs the performance of online services.This study presents a quality of service(QoS)prediction-based schedulingmodel(QPSM)for co-locatedworkloads.The performance prediction of QPSM consists of two parts:the prediction of an online service’s QoS anomaly based on XGBoost and the prediction of the completion time of an offline batch job based on randomforest.On-line service QoS anomaly prediction is used to evaluate the influence of batch jobmix on on-line service performance,and batch job completion time prediction is utilized to reduce the total waiting time of batch jobs.When the same number of batch jobs are scheduled in experiments using typical test sets such as CloudSuite,the scheduling time required by QPSM is reduced by about 6 h on average compared with the first-come,first-served strategy and by about 11 h compared with the random scheduling strategy.Compared with the non-co-located situation,QPSM can improve CPU resource utilization by 12.15% and memory resource utilization by 5.7% on average.Experiments show that the QPSM scheduling strategy proposed in this study can effectively guarantee the quality of online services and further improve cluster resource utilization.

Improved STNModels and Heuristic Rules for Cooperative Scheduling in Automated Container Terminals

Improving the cooperative scheduling efficiency of equipment is the key for automated container terminals to copewith the development trend of large-scale ships. In order to improve the solution efficiency of the existing spacetimenetwork (STN) model for the cooperative scheduling problem of yard cranes (YCs) and automated guidedvehicles (AGVs) and extend its application scenarios, two improved STN models are proposed. The flow balanceconstraints in the original model are decomposed, and the trajectory constraints of YCs and AGVs are added toacquire the model STN_A. The coupling constraint in STN_A is updated, and buffer constraints are added toSTN_A so that themodel STN_B is built.As the size of the problem increases, the solution speed of CPLEX becomesthe bottleneck. So a heuristic method containing three groups of heuristic rules is designed to obtain a near-optimalsolution quickly. Experimental results showthat the computation time of STN_A is shortened by 49.47% on averageand the gap is reduced by 1.69% on average compared with the original model. The gap between the solution ofthe heuristic rules and the solution of CPLEX is less than 3.50%, and the solution time of the heuristic rules is onaverage 99.85% less than the solution time of CPLEX. Compared with STN_A, the computation time for solvingSTN_B increases by 58.93% on average.

MCWOA Scheduler:Modified Chimp-Whale Optimization Algorithm for Task Scheduling in Cloud Computing

Cloud computing provides a diverse and adaptable resource pool over the internet,allowing users to tap into various resources as needed.It has been seen as a robust solution to relevant challenges.A significant delay can hamper the performance of IoT-enabled cloud platforms.However,efficient task scheduling can lower the cloud infrastructure’s energy consumption,thus maximizing the service provider’s revenue by decreasing user job processing times.The proposed Modified Chimp-Whale Optimization Algorithm called Modified Chimp-Whale Optimization Algorithm(MCWOA),combines elements of the Chimp Optimization Algorithm(COA)and the Whale Optimization Algorithm(WOA).To enhance MCWOA’s identification precision,the Sobol sequence is used in the population initialization phase,ensuring an even distribution of the population across the solution space.Moreover,the traditional MCWOA’s local search capabilities are augmented by incorporating the whale optimization algorithm’s bubble-net hunting and random search mechanisms into MCWOA’s position-updating process.This study demonstrates the effectiveness of the proposed approach using a two-story rigid frame and a simply supported beam model.Simulated outcomes reveal that the new method outperforms the original MCWOA,especially in multi-damage detection scenarios.MCWOA excels in avoiding false positives and enhancing computational speed,making it an optimal choice for structural damage detection.The efficiency of the proposed MCWOA is assessed against metrics such as energy usage,computational expense,task duration,and delay.The simulated data indicates that the new MCWOA outpaces other methods across all metrics.The study also references the Whale Optimization Algorithm(WOA),Chimp Algorithm(CA),Ant Lion Optimizer(ALO),Genetic Algorithm(GA)and Grey Wolf Optimizer(GWO).

A Distributionally Robust Optimization Scheduling Model for Regional Integrated Energy Systems Considering Hot Dry Rock Co-Generation

Hot dry rock(HDR)is rich in reserve,widely distributed,green,low-carbon,and has broad development potential and prospects.In this paper,a distributionally robust optimization(DRO)scheduling model for a regionally integrated energy system(RIES)considering HDR co-generation is proposed.First,the HDR-enhanced geothermal system(HDR-EGS)is introduced into the RIES.HDR-EGS realizes the thermoelectric decoupling of combined heat and power(CHP)through coordinated operation with the regional power grid and the regional heat grid,which enhances the system wind power(WP)feed-in space.Secondly,peak-hour loads are shifted using price demand response guidance in the context of time-of-day pricing.Finally,the optimization objective is established to minimize the total cost in the RIES scheduling cycle and construct a DRO scheduling model for RIES with HDR-EGS.By simulating a real small-scale RIES,the results show that HDR-EGS can effectively promote WP consumption and reduce the operating cost of the system.

Research on Flexible Job Shop Scheduling Based on Improved Two-Layer Optimization Algorithm

To improve the productivity,the resource utilization and reduce the production cost of flexible job shops,this paper designs an improved two-layer optimization algorithm for the dual-resource scheduling optimization problem of flexible job shop considering workpiece batching.Firstly,a mathematical model is established to minimize the maximum completion time.Secondly,an improved two-layer optimization algorithm is designed:the outer layer algorithm uses an improved PSO(Particle Swarm Optimization)to solve the workpiece batching problem,and the inner layer algorithm uses an improved GA(Genetic Algorithm)to solve the dual-resource scheduling problem.Then,a rescheduling method is designed to solve the task disturbance problem,represented by machine failures,occurring in the workshop production process.Finally,the superiority and effectiveness of the improved two-layer optimization algorithm are verified by two typical cases.The case results show that the improved two-layer optimization algorithm increases the average productivity by 7.44% compared to the ordinary two-layer optimization algorithm.By setting the different numbers of AGVs(Automated Guided Vehicles)and analyzing the impact on the production cycle of the whole order,this paper uses two indicators,the maximum completion time decreasing rate and the average AGV load time,to obtain the optimal number of AGVs,which saves the cost of production while ensuring the production efficiency.This research combines the solved problem with the real production process,which improves the productivity and reduces the production cost of the flexible job shop,and provides new ideas for the subsequent research.

Age of Information Based User Scheduling and Data Assignment in Multi-User Mobile Edge Computing Networks:An Online Algorithm

This paper investigates the age of information(AoI)-based multi-user mobile edge computing(MEC)network with partial offloading mode.The weighted sum AoI(WSA)is first analyzed and derived,and then a WSA minimization problem is formulated by jointly optimizing the user scheduling and data assignment.Due to the non-analytic expression of the WSA w.r.t.the optimization variables and the unknowability of future network information,the problem cannot be solved with known solution methods.Therefore,an online Joint Partial Offloading and User Scheduling Optimization(JPOUSO)algorithm is proposed by transforming the original problem into a single-slot data assignment subproblem and a single-slot user scheduling sub-problem and solving the two sub-problems separately.We analyze the computational complexity of the presented JPO-USO algorithm,which is of O(N),with N being the number of users.Simulation results show that the proposed JPO-USO algorithm is able to achieve better AoI performance compared with various baseline methods.It is shown that both the user’s data assignment and the user’s AoI should be jointly taken into account to decrease the system WSA when scheduling users.