A decomposition-based approach to flexible flow shop scheduling under machine breakdown

Manufacturing systems in real-world production are generally dynamic and often subject to a wide range of uncertainties. Recently, research on production scheduling under uncertainty has attracted substantial attention. Although some methods have been developed to address this problem, scheduling under uncertainty remains inherently difficult to solve by any single approach. This article considers makespan optimisation of a flexible flow shop (FFS) scheduling problem under machine breakdown. It proposes a novel decomposition-based approach to decompose an FFS scheduling problem into several cluster scheduling problems which can be solved more easily by different approaches. A neighbouring K-means clustering algorithm is developed to first group the machines of an FFS into an appropriate number of machine clusters, based on a proposed machine allocation algorithm and weighted cluster validity indices. Two optimal back propagation networks, corresponding to the scenarios of simultaneous and non-simultaneous job arrivals, are then selectively adopted to assign either the shortest processing time (SPT) or the genetic algorithm (GA) to each machine cluster to solve cluster scheduling problems. If two neighbouring machine clusters are allocated with the same approach, they are subsequently merged. After machine grouping and approach assignment, an overall schedule is generated by integrating the solutions to the sub-problems. Computation results reveal that the proposed approach is superior to SPT and GA alone for FFS scheduling under machine breakdown.     

A hybrid genetic-immune algorithm with improved lifespan and elite antigen for flow-shop scheduling problems

In this paper, a hybrid genetic-immune algorithm (HGIA) is proposed to reduce the premature convergence problem in a genetic algorithm (GA) in solving permutation flow-shop scheduling problems. A co-evolutionary strategy is proposed for efficient combination of GA and an artificial immune system (AIS). First, the GA is adopted to generate antigens with better fitness, and then the population in the last generation is transformed into antibodies in AIS. A new formula for calculating the lifespan of each antibody is employed during the evolution processes. In addition, a new mechanism including T-cell and B-cell generation procedures is applied to produce different types of antibodies which will be merged together. The antibodies with longer lifespan will survive and enter the next generation. This co-evolutionary strategy is very effective since chromosomes and antibodies will be transformed and evolved dynamically. The intensive experimental results show the effectiveness of the HGIA approach. The hybrid algorithm can be further extended to solve different combinatorial problems.     

Minimisation of total tardiness for identical parallel machine scheduling using genetic algorithm

In recent years research on parallel machine scheduling has received an increased attention. This paper considers minimisation of total tardiness for scheduling of n jobs on a set of m parallel machines. A spread-sheet-based genetic algorithm (GA) approach is proposed for the problem. The proposed approach is a domain-independent general purpose approach, which has been effectively used to solve this class of problem. The performance of GA is compared with branch and bound and particle swarm optimisation approaches. Two set of problems having 20 and 25 jobs with number of parallel machines equal to 2, 4, 6, 8 and 10 are solved with the proposed approach. Each combination of number of jobs and machines consists of 125 benchmark problems; thus a total for 2250 problems are solved. The results obtained by the proposed approach are comparable with two earlier approaches. It is also demonstrated that a simple GA can be used to produce results that are comparable with problem-specific approach. The proposed approach can also be used to optimise any objective function without changing the basic GA routine.     

Optimal generator maintenance scheduling using a modified discrete PSO

A modified discrete particle swarm optimisation (MDPSO) algorithm to generate optimal preventive maintenance schedule of generating units for economical and reliable operation of a power system, while satisfying system load demand and crew constraints, is presented. Discrete particle swarm optimisation (DPSO) is known to effectively solve large-scale multi-objective optimisation problems and has been widely applied in power system. The MDPSO proposed for the generator maintenance scheduling optimisation problem generates optimal and feasible solutions and overcomes the limitations of the conventional methods, such as extensive computational effort, which increases exponentially as the size of the problem increases. The efficacy of the proposed algorithm is illustrated and compared with the genetic algorithm (GA) and DPSO in two case studies ? a 21-unit test system and a 49-unit system feeding the Nigerian national grid. The MDPSO algorithm is found to generate schedules with comparatively higher system reliability indices than those obtained with GA and DPSO.     

A block transportation scheduling system considering a minimisation of travel distance without loading of and interference between multiple transporters

Material transportation scheduling problems concerning scheduling optimisation have been extensively investigated by researchers in such fields as industrial engineering and management science. Various algorithms have been proposed to solve such problems. However, the majority of these algorithms cannot be applied to a block transportation problem when a shipyard that uses a transporter, a large vehicle employed for moving weight, is considered. In this study, a hybrid optimisation algorithm is proposed for solving a block transportation problem when multiple transporters are used. With regards to the transporters, a minimisation of the travel distance without loading of and interference between the transporters is considered. A block transportation scheduling system is then developed based on the proposed algorithm. The developed system is applied to an actual block transportation scheduling problem of a shipyard. From the attained results, we demonstrate that the proposed algorithm has the ability to effectively solve the block transportation scheduling problems of a shipyard.     

GA-based adaptive setup planning toward process planning and scheduling integration

Setup planning of a part for more than one available machine is a typical combinatorial optimisation problem under certain constraints. It has significant impact not only on the whole process planning but also on scheduling, as well as on the integration of process planning and scheduling. Targeting the potential adaptability of process plans associated with setups, a cross-machine setup planning approach using genetic algorithms (GA) for machines with different configurations is presented in this paper. First, based on tool accessibility analysis of different machine configurations, partially sequenced machining features can be grouped into certain setups; then by responding to the requirements from a scheduling system, optimal or near-optimal setup plans are selected for certain criteria, such as cost, makespan and/or machine utilisation. GA is adopted for the combinatorial optimisation, which includes gene pool generation based on tool accessibility examination, setup plan encoding and fitness evaluation, and optimal setup plan selection through GA operations. The proposed approach is implemented in a GA toolbox, and tested using a sample part. The results demonstrate that the proposed approach is applicable to machines with varying configurations, and adaptive to different setup requirements from a scheduling system due to machine availability changes. It is expected that this approach can contribute to process planning and scheduling integration when a process plan is combined with setups for alternative machines during adaptive setup planning.     

Scheduling job shop associated with multiple routings with genetic and ant colony heuristics

The general job shop problem is one of the well known machine scheduling problems, in which the operation sequence of jobs are fixed that correspond to their optimal process plans and/or resource availability. Scheduling and sequencing problems, in general, are very difficult to solve to optimality and are well known as combinatorial optimisation problems. The existence of multiple job routings makes such problems more cumbersome and complicated. This paper addresses a job shop scheduling problem associated with multiple job routings, which belongs to the class of NP hard problems. To solve such NP-hard problems, metaheuristics have emerged as a promising alternative to the traditional mathematical approaches. Two metaheuristic approaches, a genetic algorithm and an ant colony algorithm are proposed for the optimal allocation of operations to the machines for minimum makespan time criterion. ILOG Solver, a scheduler package, is used to evaluate the performance of the proposed algorithms. The comparison reveals that both the algorithms are capable of providing solutions better than the solution obtained with ILOG Solver.     

含不一致任务重量的同型熔炼炉批调度优化

为求解含不一致任务重量的同型熔炼炉批调度问题,建立了最小化最大任务完工时间优化模型,设计了一种混合粒子群算法（HPSO）。算法使用随机生成的任务序列作为粒子,采用批首次匹配（BFF）规则对任务序列分批,最长加工时间（LPT）规则将批分配到批处理机,并提出了一种最小完工时间差（MCD）规则对LPT调度结果进行优化;为避免早熟,算法引入交叉和变异操作搜索最优解。通过仿真实验与SA、GA算法对比,实验结果表明算法具有良好的性能。     

Minimising makespan on a single batch processing machine with dynamic job arrivals and non-identical job sizes

Batch scheduling is a prevalent policy in many industries such as burn-in operations in semiconductor manufacturing and heat treatment operations in metalworking. In this paper, we consider the problem of minimising makespan on a single batch processing machine in the presence of dynamic job arrivals and non-identical job sizes. The problem under study is NP-hard. Consequently, we develop a number of efficient construction heuristics. The performance of the proposed heuristics is evaluated by comparing their results to two lower bounds, and other solution approaches published in the literature, namely the first-fit longest processing time-earliest release time (FFLPT-ERT) heuristic, hybrid genetic algorithm (HGA), joint genetic algorithm and dynamic programming (GA+DP) approach and ant colony optimisation (ACO) algorithm. The computational experiments demonstrate the superiority of the proposed heuristics with respect to solution quality, especially for the problems with small size jobs. Moreover, the computational costs of the proposed heuristics are very low.     

A knowledge-guided fruit fly optimization algorithm for dual resource constrained flexible job-shop scheduling problem

Different from the classical job shop scheduling, the dual-resource constrained flexible job-shop scheduling problem (DRCFJSP) should deal with job sequence, machine assignment and worker assignment all together. In this paper, a knowledge-guided fruit fly optimisation algorithm (KGFOA) with a new encoding scheme is proposed to solve the DRCFJSP with makespan minimisation criterion. In the KGFOA, two types of permutation-based search operators are used to perform the smell-based search for job sequence and resource (machine and worker) assignment, respectively. To enhance the search capability, a knowledge-guided search stage is incorporated into the KGFOA with two new search operators particularly designed for adjusting the operation sequence and the resource assignment, respectively. Due to the combination of the knowledge-guided search and the smell-based search, global exploration and local exploitation can be balanced. Besides, the effect of parameter setting of the KGFOA is investigated and numerical tests are carried out using two sets of instances. The comparative results show that the KGFOA is more effective than the existing algorithms in solving the DRCFJSP.     

A robust optimization approach for integrated steel production and batch delivery scheduling with uncertain rolling times and deterioration effect

Efficient collaboration between various sub-processes of steel production is of considerable significance, which directly affects a product’s production cycle and energy consumption. However, current collaborative optimisation models and methods in steel production are still limited: (1) Most of the current collaborative manufacturing problems in steel production focus on obtaining joint schedule between steel-making and continuous casting (SCC), and the works considering continuous casting and hot rolling (CCHR) are very few. (2) The processing time is assumed as a constant in most of the existing SCC scheduling models. However, the rolling time of a product in hot rolling operation is actually uncertain and deteriorating. (3) Exact algorithms cannot be applied to solve the complicated collaborative optimisation problems because of their high complexities. To address these problems, we propose an integrated CCHR and batch delivery scheduling model where interval rolling time and linear deterioration effect are considered. With the concept of min–max regret value, we formulate the collaborative optimisation problem as a robust optimisation problem. Instead of using the exact algorithm, we develop an Improved Variable Neighborhood Search (IVNS) algorithm incorporated a novel population update mechanism and neighbourhood structures to solve the robust optimisation problem. Moreover, we develop an exact algorithm that combines CPLEX solver and two dynamic programming algorithms to obtain the maximum regret value of a given rolling sequence. The results of computational experiments show the excellent performance of the proposed algorithms.

Abbreviations: IVNS: improved variable neighbourhood search; TOPSIS: technique for order of preference by similarity to ideal solution; PUM-TOPSIS: population update mechanism based on TOPSIS; DP: dynamic programming; NSs-PUC: neighbourhood structures based on the parameterised uniform crossover; SNRT: shortest normal rolling time; SNRT-DP: DP algorithm based on SNRT rule; BRKGA: biased random-key genetic algorithm; SCC: steelmaking and continuous casting; MINP: mixed integer nonlinear programme; CCHR: continuous casting and hot rolling; PSO: particle swarm optimisation; GA: genetic algorithm; VNS-HS: variable neighbourhood search and harmony search; HPSO?+?GA: hybrid PSO and GA; SA: simulated annealing; B&B: branch-and-bound; TPSO: two-phase soft optimisation; TSAUN: tabued simulated annealing with united-scenario neighbourhood; VNS: variable neighbourhood search; ABC: artificial bee colony; PRVNS: population-based reduced variable neighbourhood search; NS1: neighbourhood structure 1; NS2: neighbourhood structure 2; DE: differential evolution; WSR: Wilcoxon signed-rank test; ENS: exchange neighbourhood structure; IVNS-ENS: IVNS with ENS; RPI: relative percentage increase; ARPI: average RPI; SD: standard deviation.     

Real-coded genetic algorithm and fuzzy logic approach for real-time tuning of proportional-integral?derivative controller in automatic voltage regulator system

Optimal tuning of proportional?integral?derivative (PID) controller parameters is necessary for the satisfactory operation of automatic voltage regulator (AVR) system. This study presents a combined genetic algorithm (GA) and fuzzy logic approach to determine the optimal PID controller parameters in AVR system. The problem of obtaining the optimal PID controller parameters is formulated as an optimisation problem and a real-coded genetic algorithm (RGA) is applied to solve the optimisation problem. In the proposed RGA, the optimisation variables are represented as floating point numbers in the genetic population. Further, for effective genetic operation, the crossover and mutation operators which can deal directly with the floating point numbers are used. The proposed approach has resulted in PID controller with good transient response. The optimal PID gains obtained by the proposed GA for various operating conditions are used to develop the rule base of the Sugeno fuzzy system. The developed fuzzy system can give the PID parameters on-line for different operating conditions. The suitability of the proposed approach for PID controller tuning has been demonstrated through computer simulations in an AVR system.     

Hybrid algorithm based on improved extended shifting bottleneck procedure and GA for assembly job shop scheduling problem

With the makespan as the optimisation goal, we propose a hybrid solving method that combines improved extended shifting bottleneck procedure (i-ESB) and genetic algorithm (GA) for the assembly job shop scheduling problem (AJSSP). Hybrid genetic algorithm (HGA) uses a GA based on operation constraint chain coding to achieve global search and a local search based on an i-ESB. In the design of i-ESB, an extended disjunctive graph model (EDG) corresponding to AJSSP is presented. The calculation method of the operation head and tail length based on EDG is studied, as well as the searching method of key operations. The Schrage algorithm with disturbance is used to solve the single-machine scheduling subproblem. The selection criterion for bottleneck machines is increased. A greedy bottleneck machine re-optimisation process is designed. The effectiveness and superiority of the proposed algorithm are verified by testing and analysing the relevant examples in the literature.     

多机器人存取系统中的机器人群无冲突调度方法

多机器人存取系统由大量自寻址机器人构成,机器人群体运动过程会频繁发生冲突并引发大量启停,给能耗带来损失并影响机器人寿命。针对该问题,借鉴无等待作业车间调度,基于主动等待提出了机器人群无冲突调度方法。建立了机器人群无冲突调度数学模型并基于模拟退火算法优化任务顺序,进一步建立机器人群调度评估方法。实验结果表明,所提方法与传统方法相比,能够在不弱化运作效率的基础上大幅减少机器人群的启停次数,在节能和延长机器人寿命方面具有显著优势。     

Costing-based coordination between mt-iPSS customer and providers for job shop production using game theory

The industrial product-service system for Computer Numerical Control machine tool (mt-iPSS) has drawn much interest. Under the new paradigm of functional result-oriented mt-iPSS, mt-iPSS customer (i.e. owner of the workshop) pays for time or results of mt-iPSS providers. The present problem for mt-iPSS customer is how to timely identify the optimal machine tools, sequence and cutting parameters of operation to finish the jobs while mt-iPSS providers try to maximise their benefit in a non-cooperative game structure. In this paper, a Stackelberg game model is put forward to solve the coordination problem based on the costing of different job shop scheduling solutions under the result-oriented mt-iPSS paradigm. Then, to solve the established bi-level programming model of the Stackelberg game, a solution procedure based on hierarchical particle swarm optimisation is proposed. Finally, a case from a printing machinery enterprise is analysed to validate the proposed model. This research is expected to improve the quality and effectiveness of coordination for scheduling and process planning decision between mt-iPSS customer and multi-providers.     

基于文化基因算法的开放车间调度问题研究

针对开放车间调度问题,运用了文化基因算法进行优化求解。在文化基因算法的框架中,既有种群中的全局搜索,又包含针对问题自身特点的局部搜索,为解决开放车间调度问题提供了一种新的算法。按照文化基因算法的思想和特点,将爬山法作为局部搜索策略加入到全局搜索策略所用到的遗传算法中,通过对开放车间调度问题的邻域结构进行研究,加入爬山搜索法进行优化求解。基于40个标准算例,通过与下界值的比较,验证了所提算法在解决具有较大搜索空间的调度问题时,其拥有更出色的算法性能。     

Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method

This paper investigates an integrated bi-objective optimisation problem with non-resumable jobs for production scheduling and preventive maintenance in a two-stage hybrid flow shop with one machine on the first stage and m identical parallel machines on the second stage. Sequence-dependent set-up times and preventive maintenance (PM) on the first stage machine are considered. The scheduling objectives are to minimise the unavailability of the first stage machine and to minimise the makespan simultaneously. To solve this integrated problem, three decisions have to be made: determine the processing sequence of jobs on the first stage machine, determine whether or not to perform PM activity just after each job, and specify the processing machine of each job on the second stage. Due to the complexity of the problem, a multi-objective tabu search (MOTS) method is adapted with the implementation details. The method generates non-dominated solutions with several parallel tabu lists and Pareto dominance concept. The performance of the method is compared with that of a well-known multi-objective genetic algorithm, in terms of standard multi-objective metrics. Computational results show that the proposed MOTS yields a better approximation.     

A discrete artificial bee colony algorithm for single machine scheduling problems

This paper presents a discrete artificial bee colony algorithm for a single machine earliness–tardiness scheduling problem. The objective of single machine earliness–tardiness scheduling problems is to find a job sequence that minimises the total sum of earliness–tardiness penalties. Artificial bee colony (ABC) algorithm is a swarm-based meta-heuristic, which mimics the foraging behaviour of honey bee swarms. In this study, several modifications to the original ABC algorithm are proposed for adapting the algorithm to efficiently solve combinatorial optimisation problems like single machine scheduling. In proposed study, instead of using a single search operator to generate neighbour solutions, random selection from an operator pool is employed. Moreover, novel crossover operators are presented and employed with several parent sets with different characteristics to enhance both exploration and exploitation behaviour of the proposed algorithm. The performance of the presented meta-heuristic is evaluated on several benchmark problems in detail and compared with the state-of-the-art algorithms. Computational results indicate that the algorithm can produce better solutions in terms of solution quality, robustness and computational time when compared to other algorithms.     

An exact penalty function method for optimising QAP formulation in facility layout problem

A quadratic assignment problem (QAP), which is a combinatorial optimisation problem, is developed to model the problem of locating facilities with material flows between them. The aim of solving the QAP formulation for a facility layout problem (FLP) is to increase a system’s operating efficiency by reducing material handling costs, which can be measured by interdepartmental distances and flows. The QAP-formulated FLP can be viewed as a discrete optimisation problem, where the quadratic objective function is optimised with respect to discrete decision variables subject to linear equality constraints. The conventional approach for solving this discrete optimisation problem is to use the linearisation of the quadratic objective function whereby additional discrete variables and constraints are introduced. The adoption of the linearisation process can result in a significantly increased number of variables and constraints; solving the resulting problem can therefore be challenging. In this paper, a new approach is introduced to solve this discrete optimisation problem. First, the discrete optimisation problem is transformed into an equivalent nonlinear optimisation problem involving only continuous decision variables by introducing quadratic inequality constraints. The number of variables, however, remains the same as the original problem. Then, an exact penalty function method is applied to convert this transformed continuous optimisation problem into an unconstrained continuous optimisation problem. An improved backtracking search algorithm is then developed to solve the unconstrained optimisation problem. Numerical computation results demonstrate the effectiveness of the proposed new approach.     

Hybrid simulated annealing with memory: an evolution-based diversification approach

This study presents an efficient metaheuristic approach for combinatorial optimisation and scheduling problems. The hybrid algorithm proposed in this paper integrates different features of several well-known heuristics. The core component of the proposed algorithm is a simulated annealing module. This component utilises three types of memories, one long-term memory and two short-term memories. The main characteristics of the proposed metaheuristic are the use of positive (reinforcement) and negative (inhibitory) memories as well as an evolution-based diversification approach. Job shop scheduling is selected to evaluate the performance of the proposed method. Given the benchmark problem, an extended version of the proposed method is also developed and presented. The extended version has two distinct features, specifically designed for the job shop scheduling problem, that enhance the performance of the search. The first feature is a local search that partially explores alternative solutions on a critical path of any current solution. The second feature is a mechanism to resolve possible deadlocks that may occur during the search as a result of shortage in acceptable solutions. For the case of job shop scheduling, the computational results and comparison with other techniques demonstrate the superior performance of the proposed methods in the majority of cases.