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.

FLEXIBLE JOB-SHOP SCHEDULING WITH FUZZY GOAL THROUGH IOCDGA

The fuzzy goal flexible job-shop scheduling problem （FGFJSP） is the extension of FJSP. Compared with the convention JSP, it can solve the fuzzy goal problem and meet suit requirements of the key job. The multi-object problem, such as the fuzzy cost, the fuzzy due-date, and the fuzzy makespan, etc, can be solved by FGFJSP. To optimize FGFJSP, an individual optimization and colony diversity genetic algorithm （IOCDGA） is presented to accelerate the convergence speed and to avoid the earliness. In IOCDGA, the colony average distance and the colony entropy are defined after the definition of the encoding model. The colony diversity is expressed by the colony average distance and the colony entropy. The crossover probability and the mutation probability are controlled by the colony diversity. The evolution emphasizes that sigle individual or a few individuals evolve into the best in IOCDGA, but not the all in classical GA. Computational results show that the algorithm is applicable and the number of iterations is less.

INTEGRATED OPERATOR GENETIC ALGORITHM FOR SOLVING MULTI-OBJECTIVE FLEXIBLE JOB-SHOP SCHEDULING

In the flexible job-shop scheduling problem （FJSP）, each operation has to be assigned to a machine from a set of capable machines before alocating the assigned operations on all machines. To solve the multi-objective FJSP, the Grantt graph oriented string representation （GOSR） and the basic manipulation of the genetic algorithm operator are presented. An integrated operator genetic algorithm （IOGA） and its process are described. Comparison between computational results and the latest research shows that the proposed algorithm is effective in reducing the total workload of all machines, the makespan and the critical machine workload.

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。

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.

APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOPSCHEDULING PROBLEM

A new heuristic algorithm is proposed for the problem of finding the minimummakespan in the job-shop scheduling problem. The new algorithm is based on the principles ofparticle swarm optimization (PSO). PSO employs a collaborative population-based search, which isinspired by the social behavior of bird flocking. It combines local search (by self experience) andglobal search (by neighboring experience), possessing high search efficiency. Simulated annealing(SA) employs certain probability to avoid becoming trapped in a local optimum and the search processcan be controlled by the cooling schedule. By reasonably combining these two different searchalgorithms, a general, fast and easily implemented hybrid optimization algorithm, named HPSO, isdeveloped. The effectiveness and efficiency of the proposed PSO-based algorithm are demonstrated byapplying it to some benchmark job-shop scheduling problems and comparing results with otheralgorithms in literature. Comparing results indicate that PSO-based algorithm is a viable andeffective approach for the job-shop scheduling problem.

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.

A Grafted Genetic Algorithm for the Job-Shop Scheduling Problem

The standard genetic algorithm has limitations of a low convergence rate and premature convergence in solving the job-shop scheduling problem.To overcome these limitations,this paper presents a new improved hybrid genetic algorithm on the basis of the idea of graft in botany.Through the introduction of a grafted population and crossover probability matrix,this algorithm accelerates the convergence rate greatly and also increases the ability to fight premature convergence.Finally,the approach is tested on a set of standard instances taken from the literature and compared with other approaches.The computation results validate the effectiveness of the proposed algorithm.

Genetic Algorithm and the Application for Job-Shop Group Scheduling

Genetic algorithm(GA)is a heuristic and random search technique for mimicking na-ture.This paper presents the basic principle and principal character of GA,and the defini-tion and function of the genetic operators.On the basis of these,the paper proposes a newmethod of solving the Job-Shop group scheduling problem by use of GA,and discusses thecoded representation method of the feasible solution and the particular limitation to the ge-netic operators.

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.

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.

Simultaneous scheduling of machines and automated guided vehicles in flexible manufacturing systems using genetic algorithms

The problem of simultaneous scheduling of machines and vehicles in flexible manufacturing system (FMS) was addressed.A spreadsheet based genetic algorithm (GA) approach was presented to solve the problem.A domain independent general purpose GA was used,which was an add-in to the spreadsheet software.An adaptation of the propritary GA software was demonstrated to the problem of minimizing the total completion time or makespan for simultaneous scheduling of machines and vehicles in flexible manufacturing systems.Computational results are presented for a benchmark with 82 test problems,which have been constructed by other researchers.The achieved results are comparable to the previous approaches.The proposed approach can be also applied to other problems or objective functions without changing the GA routine or the spreadsheet model.

Hybrid heuristic algorithm for multi-objective scheduling problem

This research provides academic and practical contributions. From a theoretical standpoint, a hybrid harmony search(HS)algorithm, namely the oppositional global-based HS(OGHS), is proposed for solving the multi-objective flexible job-shop scheduling problems(MOFJSPs) to minimize makespan, total machine workload and critical machine workload. An initialization program embedded in opposition-based learning(OBL) is developed for enabling the individuals to scatter in a well-distributed manner in the initial harmony memory(HM). In addition, the recursive halving technique based on opposite number is employed for shrinking the neighbourhood space in the searching phase of the OGHS. From a practice-related standpoint, a type of dual vector code technique is introduced for allowing the OGHS algorithm to adapt the discrete nature of the MOFJSP. Two practical techniques, namely Pareto optimality and technique for order preference by similarity to an ideal solution(TOPSIS), are implemented for solving the MOFJSP.Furthermore, the algorithm performance is tested by using different strategies, including OBL and recursive halving, and the OGHS is compared with existing algorithms in the latest studies.Experimental results on representative examples validate the performance of the proposed algorithm for solving the MOFJSP.

An Improved Genetic Algorithm for Solving the Mixed⁃Flow Job⁃Shop Scheduling Problem with Combined Processing Constraints

The flexible job-shop scheduling problem(FJSP)with combined processing constraints is a common scheduling problem in mixed-flow production lines.However,traditional methods for classic FJSP cannot be directly applied.Targeting this problem,the process state model of a mixed-flow production line is analyzed.On this basis,a mathematical model of a mixed-flow job-shop scheduling problem with combined processing constraints is established based on the traditional FJSP.Then,an improved genetic algorithm with multi-segment encoding,crossover,and mutation is proposed for the mixed-flow production line problem.Finally,the proposed algorithm is applied to the production workshop of missile structural components at an aerospace institute to verify its feasibility and effectiveness.

Dynamic scheduling and analysis of real time systems with multiprocessors

This research work considers a scenario of cloud computing job-shop scheduling problems. We consider rn realtime jobs with various lengths and n machines with different computational speeds and costs. Each job has a deadline to be met, and the profit of processing a packet of a job differs from other jobs. Moreover, considered deadlines are either hard or soft and a penalty is applied if a deadline is missed where the penalty is considered as an exponential function of time. The scheduling problem has been formulated as a mixed integer non-linear programming problem whose objective is to maximize netprofit. The formulated problem is computationally hard and not solvable in deterministic polynomial time. This research work proposes an algorithm named the Tube-tap algorithm as a solution to this scheduling optimization problem. Extensive simulation shows that the proposed algorithm outperforms existing solutions in terms of maximizing net-profit and preserving deadlines.

Research on Fuzzy Decision of Resources Selection in Job-sh op Scheduling for a One-of-a-Kind and Order-Oriented Production System

In a one-of-a-kind and order-orient ed production corporation, job shop scheduling plays an important role in the prod uction planning system and production process control. Since resource selection in job shop scheduling directly influences the qualities and due dates of produc ts and production cost, it is indispensable to take resource selection into acco unt during job shop scheduling. By analyzing the relative characteristics of res ources, an approach of fuzzy decision is proposed for resource selection. Finall y, issues in the application of the approach are discussed.

求解job-shop调度问题的量子粒子群优化算法

针对粒子群优化算法搜索空间有限、容易出现早熟现象的缺陷,提出将量子粒子群优化算法用于求解作业车间调度问题。求解时,将每个调度按照一定的规则编码为一个矩阵,并以此矩阵作为算法中的粒子;然后根据调度目标确定目标函数,并按照量子粒子群优化算法的进化规则在调度空间内搜索最优解。仿真实例结果证明,该算法具有良好的全局收敛性能和快捷的收敛速度,调度效果优于遗传算法和粒子群优化算法。

An adaptive multi-population genetic algorithm for job-shop scheduling problem

Job-shop scheduling problem （JSP） is a typical NP-hard combinatorial optimization problem and has a broad background for engineering application. Nowadays, the effective approach for JSP is a hot topic in related research area of manufacturing system. However, some JSPs, even for moderate size instances, are very difficult to find an optimal solution within a reasonable time because of the process constraints and the complex large solution space. In this paper, an adaptive multi-population genetic algorithm （AMGA） has been proposed to solve this prob- lem. Firstly, using multi-populations and adaptive cross- over probability can enlarge search scope and improve search performance. Secondly, using adaptive mutation probability and elite replacing mechanism can accelerate convergence speed. The approach is tested for some clas- sical benchmark JSPs taken from the literature and com- pared with some other approaches. The computational results show that the proposed AMGA can produce optimal or near-optimal values on almost all tested benchmark instances. Therefore, we can believe that AMGA can be considered as an effective method for solving JSP.

A decomposition approach to job-shop scheduling problem with discretely controllable processing times

Job-shop scheduling problem with discretely controllable processing times (JSP-DCPT) is modeled based on the disjunctive graph, and the formulation of JSP-DCPT is presented. A three-step decomposition approach is proposed so that JSP-DCPT can be handled by solving a job-shop scheduling problem (JSP) and a series of discrete time-cost tradeoff problems. To simplify the decomposition approach, the time-cost phase plane is introduced to describe tradeoffs of the discrete time-cost tradeoff problem, and an extreme mode-based set dominant theory is elaborated so that an upper bound is determined to cut discrete time-cost tradeoff problems generated by using the proposed decomposition approach. An extreme mode-based set dominant decomposition algorithm (EMSDDA) is then proposed. Experimental simulations for instance JSPDCPT_FT10, which is designed based on a JSP benchmark FT10, demonstrate the effectiveness of the proposed theory and the decomposition approach.