Differential evolution algorithm for hybrid flow-shop scheduling problems

Aiming at the hybrid flow-shop （HFS） scheduling that is a complex NP-hard combinatorial problem with wide engineering background, an effective algorithm based on differential evolution （DE） is proposed. By using a special encoding scheme and combining DE based evolutionary search and local search, the exploration and exploitation abilities are enhanced and well balanced for solving the HFS problems. Simulation results based on some typical problems and comparisons with some existing genetic algorithms demonstrate the proposed algorithm is effective, efficient and robust for solving the HFS problems.

A Cross Entropy-Genetic Algorithm for m-Machines No-Wait Job-ShopScheduling Problem

No-wait job-shop scheduling (NWJSS) problem is one of the classical scheduling problems that exist on many kinds of industry with no-wait constraint, such as metal working, plastic, chemical, and food industries. Several methods have been proposed to solve this problem, both exact (i.e. integer programming) and metaheuristic methods. Cross entropy (CE), as a new metaheuristic, can be an alternative method to solve NWJSS problem. This method has been used in combinatorial optimization, as well as multi-external optimization and rare-event simulation. On these problems, CE implementation results an optimal value with less computational time in average. However, using original CE to solve large scale NWJSS requires high computational time. Considering this shortcoming, this paper proposed a hybrid of cross entropy with genetic algorithm (GA), called CEGA, on m-machines NWJSS. The results are compared with other metaheuritics: Genetic Algorithm-Simulated Annealing (GASA) and hybrid tabu search. The results showed that CEGA providing better or at least equal makespans in comparison with the other two methods.

Combined Timetabling Procedure and Complete Local Search for No-Wait Job Shop Scheduling with Total Tardiness

The strong non-deterministic polynomial-hard( NP-hard)character of job shop scheduling problem( JSSP) has been acknowledged widely and it becomes stronger when attaches the nowait constraint,which widely exists in many production processes,such as chemistry process, metallurgical process. However,compared with the massive research on traditional job shop problem,little attention has been paid on the no-wait constraint.Therefore,in this paper, we have dealt with this problem by decomposing it into two sub-problems, the timetabling and sequencing problems,in traditional frame work. A new efficient combined non-order timetabling method,coordinated with objective of total tardiness,is proposed for the timetabling problems. As for the sequencing one,we have presented a modified complete local search with memory combined by crossover operator and distance counting. The entire algorithm was tested on well-known benchmark problems and compared with several existing algorithms.Computational experiments showed that our proposed algorithm performed both effectively and efficiently.

Pareto-Based Complete Local Search and Combined Timetabling for Multi-objective Job Shop Scheduling Problem with No-Wait Constraint

Job shop scheduling has become the basis and core of advanced manufacturing technology. Various differences exist between academic research and practical production. The majority of previous researches on job shop scheduling problem (JSSP)describe the basic production environment, which have a single objective and limited constraints. However,a practical process of production is characterized by having multiple objectives,no-wait constraint,and limited storage. Thus this research focused on multiobjective,no-wait JSSP. To analyze the problem,it was further divided into two sub-problems, namely, sequencing and timetabling. Hybrid non-order strategy and modified complete local search with memory were used to solve each problem individually. A Pareto-based strategy for performing fitness assessment was presented in this study. Various experiments on benchmark problems proved the feasibility and effectiveness of the proposed algorithm.

MODIFIED BOTTLENECK-BASED PROCEDURE FOR LARGE-SCALE FLOW-SHOP SCHEDULING PROBLEMS WITH BOTTLENECK

A new bottleneck-based heuristic for large-scale flow-shop scheduling problems with a bottleneck is proposed, which is simpler but more tailored than the shifting bottleneck （SB） procedure. In this algorithm, a schedule for the bottleneck machine is first constructed optimally and then the non-bottleneck machines are scheduled around the bottleneck schedule by some effective dispatching rules. Computational results show that the modified bottleneck-based procedure can achieve a tradeoff between solution quality and computational time comparing with SB procedure for medium-size problems. Furthermore it can obtain a good solution in quite short time for large-scale scheduling problems.

Cooperative Game Theory Based Coordinated Scheduling of Two-Machine Flow-Shop and Transportation

A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop(TFS-PTCS problems)with an interstage transporter.The authors assume that there is an initial scheduling order for processing jobs on the machines.The cooperative sequencing game models associated with TFS-PTCS problems are established with jobs as players and the maximal cost savings of a coalition as its value.The properties of cooperative games under two different types of admissible rearrangements are analysed.For TFS-PTCS problems with identical processing time,it is proved that,the corresponding games areσ_(0)-component additive and convex under one admissible rearrangement.The Shapley value gives a core allocation,and is provided in a computable form.Under the other admissible rearrangement,the games neither need to beσ_(0)-component additive nor convex,and an allocation rule of modified Shapley value is designed.The properties of the cooperative games are analysed by a counterexample for general problems.

Makespan Minimization in Two-Machine Flow-Shop Scheduling under No-wait and Deterministic Unavailable Interval Constraints

This paper systematically studies the two machine flow-shop scheduling problems with no-wait and deterministic unavailable interval constraints.To minimize the makespan,three integer programming mathematical models are formulated for two-machine flow-shop with no-wait constraint,two-machine flow-shop with resumable unavailable interval constraint,and two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problems,respectively.The optimal conditions of solv-ing the two-machine flow-shop with no-wait constraint problem by the permutation schedules,the two-machine flow-shop with resumable unavailable interval constraint problem by the Johnson algorithm,and two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problem by the Gilmore and Gomory Algorithm(GGA)are presented,respectively.And the tight worst-case performance bounds of Johnson and GGA algorithms for these problems are also proved to be 2.Several instances are generated to demonstrate the proposed theorems.Based on the experimental results,GGA obtains the optimal solution for the two-machine flow-shop with no-wait constraint problem.Although it cannot reach the optimal solution for the two-machine flow-shop with resumable unavailable interval constraint problem,the optimal gap is 0.18%on average when the number of jobs is 100.Moreover,under some special conditions,it yields the optimal solution for the two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problem.Therefore,GGA is an efficient heuristic to solve these problems.

No-Wait Flowshops to Minimize Total Tardiness with Setup Times

The m-machine no-wait flowshop scheduling problem is addressed where setup times are treated as separate from processing times. The objective is to minimize total tardiness. Different dispatching rules have been investigated and three were found to be superior. Two heuristics, a simulated annealing (SA) and a genetic algorithm (GA), have been proposed by using the best performing dispatching rule as the initial solution for SA, and the three superior dispatching rules as part of the initial population for GA. Moreover, improved versions of SA and GA are proposed using an insertion algorithm. Extensive computational experiments reveal that the improved versions of SA and GA perform about 95% better than SA and GA. The improved version of GA outperforms the improved version of SA by about 3.5%.

Multidirection Update-Based Multiobjective Particle Swarm Optimization for Mixed No-Idle Flow-Shop Scheduling Problem

The Mixed No-Idle Flow-shop Scheduling Problem(MNIFSP)is an extension of flow-shop scheduling,which has practical significance and application prospects in production scheduling.To improve the efficacy of solving the complicated multiobjective MNIFSP,a MultiDirection Update(MDU)based Multiobjective Particle Swarm Optimization(MDU-MoPSO)is proposed in this study.For the biobjective optimization problem of the MNIFSP with minimization of makespan and total processing time,the MDU strategy divides particles into three subgroups according to a hybrid selection mechanism.Each subgroup prefers one convergence direction.Two subgroups are individually close to the two edge areas of the Pareto Front(PF)and serve two objectives,whereas the other one approaches the central area of the PF,preferring the two objectives at the same time.The MDU-MoPSO adopts a job sequence representation method and an exchange sequence-based particle update operation,which can better reflect the characteristics of sequence differences among particles.The MDU-MoPSO updates the particle in multiple directions and interacts in each direction,which speeds up the convergence while maintaining a good distribution performance.The experimental results and comparison of six classical evolutionary algorithms for various benchmark problems demonstrate the effectiveness of the proposed algorithm.

Flow-Shop Scheduling Models with Parameters Represented by Rough Variables

In reality, processing times are often imprecise and this imprecision is critical for the scheduling procedure. This research deals with flow-shop scheduling in rough environment. In this type of scheduling problem, we employ the rough sets to represent the job parameters. The job processing times are assumed to be rough variables, and the problem is to minimize the makespan. Three novel types of rough scheduling models are presented. A rough simulation-based genetic algorithm is designed to solve these models and its effectiveness is well illustrated by numerical experiments.

流水车间排列排序专家系统—PFSCH

流水车间排列排序问题可以简单表示为:n/m/p/Fmax,其含义为,n个不同的工件（J1,J2,…,Jn）要经m台机器（M1,M2…,Mm）加工;加工路线为M1—M2—…—Mm,n个工件在每台机器上的加工顺序都一样;p表示排列排序;目标函数是使最长流程时间Fmax（加工周期）最短.n个工件有n!种不同的加工顺序.现已证明,n/m/p/Fmax（m≥3）问题属于NP难题,找不到多项式时间算法.因此,人们提出了若干个启发式算法,其中最著名的是Campbell等人提出的启发式算法（简称为CDS法）.Dannenbring曾比较过11种不同的启发式算法的效果,指出“快速接近扩展搜索法（RAES法）”的结果最好.但是,RAES法实质上还是一种列举法,它不从问题本身的结构出发,具有很大的盲目性.

Research on Ant Colony Algorithm in Vehicle Operation Adjustment Based on IOT

Automatic solution of vehicle operation adjustment is the important content in realizing vehicle traffic command automation on Internet of Things platform. Based on both the organization realization of Internet of Things platform and the merging vehicle operation adjustment into the Flow-Shop scheduling problem in manufacturing systems,this paper has constructed the optimization model with a two-lane vehicle operation adjustment. With respect to the large model solution space and complex constraints,a better solution algorithm is proposed based on ant colony algorithm for optimal quick solution. The simulation results show that the algorithm is feasible and the approximate optimal solution can be quickly obtained.