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 problem. Firstly, using multi-populations and adaptive crossover 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 classical benchmark JSPs taken from the literature and compared 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 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.     

An improved method for the hot strip mill production scheduling problem

In most research on the hot strip mill production scheduling problem (HSMPSP) arising in the steel industry, it is accepted that a schedule with lower penalty caused by jumps of width, hardness, and gauge will result in lower roller wear, so it is regarded as a better schedule. However, based on the analysis of production processes, it is realised that rolling each coil also cause roller wear. In order to assessing the roller wear associated with production scheduling more precisely, it is necessary to consider it as another factor besides those jumps, especially when complicated constraints are involved. In this paper, an improved method is proposed to quantify the expected wear of the rollers done by those jumps and rolling processes. Then the HSMPSP whose objective is to maximise the total length of all scheduled coils is formulated as a team orienteering problem with time windows and additional production constraints. A heuristic method combining an improved Ant Colony Extended algorithm with local search procedures dedicated to HSMPSP is developed. Finally, computational results on instances generated based on production data from an integrated steel mill in China indicate that the proposed algorithm is a promising solution specific to HSMPSP.     

Job shop scheduling with a non-regular objective: A comparison of neighbourhood structures based on a sequencing/timing decomposition

Commercial software packages for production management are characterized by a gap between MRP logic, based on a backward scheduling approach, and finite capacity scheduling, usually based on forward scheduling. In order to partially bridge that gap, we need scheduling algorithms able to meet due dates while keeping WIP and inventory costs low. This leads us to consider job shop scheduling problems characterized by non-regular objective functions; such problems are even more difficult than classical job shop scheduling, and suitable heuristics are needed. One possibility is to consider local search strategies based on the decomposition of the overall problem into sequencing and timing sub-problems. For given job sequences, the optimal timing problem can be solved as a node potential problem on a graph. Since solving the timing problem is a relatively time-consuming task, we need to define a suitable neighbourhood structure to explore the space of job sequences; this can be done by generalizing well-known results for the minimum makespan problem. A related issue is if solving timing problems exactly is really necessary, or if an approximate solution is sufficient; hence, we also consider solving the timing problem approximately by a fast heuristic. We compare different neighbourhood structures, by embedding them within a pure local improvement strategy. Computational experiments show that the overall approach performs better than release/dispatch rules, although the performance improvement depends on the problem characteristics, and that the fast heuristic is quite competitive with the optimal timing approach. On the one hand, these results pave the way to the development of better local search algorithms (based e.g. on tabu search); on the other hand, it is worth noting that the heuristic timing approach, unlike the optimal one, can be extended to cope with the complicating features typical of practical scheduling problems.     

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.     

A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems

Evolutionary algorithms cannot effectively handle computationally expensive problems because of the unaffordable computational cost brought by a large number of fitness evaluations. Therefore, surrogates are widely used to assist evolutionary algorithms in solving these problems. This article proposes an improved surrogate-assisted particle swarm optimization (ISAPSO) algorithm, in which a hybrid particle swarm optimization (PSO) is combined with global and local surrogates. The global surrogate is not only used to predict fitness values for reducing computational burden but also regarded as a global searcher to speed up the global search process of PSO by using an efficient global optimization algorithm, while the local one is constructed for a local search in the neighbourhood of the current optimal solution by finding the predicted optimal solution of the local surrogate. Empirical studies on 10 widely used benchmark problems and a real-world structural design optimization problem of a driving axle show that the ISAPSO algorithm is effective and highly competitive.     

Unrelated parallel machine scheduling with setup times and ready times

We consider the problem of scheduling unrelated parallel machines with sequence- and machine-dependent setup times and ready times to minimise total weighted tardiness (TWT). We present a mixed integer programming model that can find optimal solutions for the studied problem. We also propose a heuristic (ATCSR_Rm) and an iterated hybrid metaheuristic (IHM) that can find optimal or nearly optimal solutions for the studied problem within a reasonable time. The proposed IHM begins with effective initial solutions, and then improves the initial solutions iteratively. The IHM integrates the principles of the attraction–repulsion mechanism within electromagnetism-like algorithms with local search. If the search becomes trapped at a local optimum, an elite search procedure is developed to help the search escape. We have compared our proposed IHM with two existing metaheuristics, tabu search (TS) and ant colony optimisation (ACO). Computational results show that the proposed IHM outperforms TS and ACO in terms of TWT for problem instances of all sizes.     

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。     

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.     

A Petri-net-based state-transition model for an optimal operator cyclic walking pattern development in GT cells

An approach for developing the optimal operator scheduling solution for a group technology (GT) production problem is studied. A state-transition model is developed to analyse and gain insight into the operator-machine interaction of the problem. Operator cyclic walking patterns are then denned. A Petri net model has succeeded in determining the optimal cyclic walking pattern. The computational efforts needed for the Petri net model are compared with those for an integer programming model. The results show large savings in computational effort by using the Petri net model. In addition, the extendability of the Petri net model for various system aspects is addressed     

An energy-efficient two-stage hybrid flow shop scheduling problem in a glass production

Energy-efficient scheduling is highly necessary for energy-intensive industries, such as glass, mould or chemical production. Inspired by a real-world glass-ceramics production process, this paper investigates a bi-criteria energy-efficient two-stage hybrid flow shop scheduling problem, in which parallel machines with eligibility are at stage 1 and a batch machine is at stage 2. The performance measures considered are makespan and total energy consumption. Time-of-use (TOU) electricity prices and different states of machines (working, idle and turnoff) are integrated. To tackle this problem, a mixed integer programming (MIP) is formulated, based on which an augmented ε-constraint (AUGMECON) method is adopted to obtain the exact Pareto front. A problem-tailored constructive heuristic method with local search strategy, a bi-objective tabu search algorithm and a bi-objective ant colony optimisation algorithm are developed to deal with medium- and large-scale problems. Extensive computational experiments are conducted, and a real-world case is solved. The results show effectiveness of the proposed methods, in particular the bi-objective tabu search.     

A GRASP algorithm for flexible job-shop scheduling problem with limited resource constraints

A greedy randomised adaptive search procedure (GRASP) is an iterative multi-start metaheuristic for difficult combinatorial optimisation. The GRASP iteration consists of two phases: a construction phase, in which a feasible solution is found and a local search phase, in which a local optimum in the neighbourhood of the constructed solution is sought. In this paper, a GRASP algorithm is presented to solve the flexible job-shop scheduling problem (FJSSP) with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow an appointed process order and each operation must be processed on an appointed machine. These constraints are used to balance between the resource limitation and machine flexibility. The model objectives are the minimisation of makespan, maximum workload and total workload. Representative benchmark problems are solved in order to test the effectiveness and efficiency of the GRASP algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.     

Genetic algorithm with local search for the unrelated parallel machine scheduling problem with sequence-dependent set-up times

In this paper, a genetic algorithm (GA) with local search is proposed for the unrelated parallel machine scheduling problem with the objective of minimising the maximum completion time (makespan). We propose a simple chromosome structure consisting of random key numbers in a hybrid genetic-local search algorithm. Random key numbers are frequently used in GAs but create additional difficulties when hybrid factors are implemented in a local search. The best chromosome of each generation is improved using a local search during the algorithm, but the better job sequence (which might appear during the local search operation) must be adapted to the chromosome that will be used in each successive generation. Determining the genes (and the data in the genes) that would be exchanged is the challenge of using random numbers. We have developed an algorithm that satisfies the adaptation of local search results into the GAs with a minimum relocation operation of the genes’ random key numbers – this is the main contribution of the paper. A new hybrid approach is tested on a set of problems taken from the literature, and the computational results validate the effectiveness of the proposed algorithm.     

A particle swarm optimization algorithm for hybrid flow-shop scheduling with multiprocessor tasks

The multistage hybrid flow-shop scheduling problem with multiprocessor tasks has been found in many practical situations. Due to the essential complexity of the problem, many researchers started to apply metaheuristics to solve the problem. In this paper, we address the problem by using particle swarm optimization (PSO), a novel metaheuristic inspired by the flocking behaviour of birds. The proposed PSO algorithm has several features, such as a new encoding scheme, an implementation of the best velocity equation and neighbourhood topology among several different variants, and an effective incorporation of local search. To verify the PSO algorithm, computational experiments are conducted to make a comparison with two existing genetic algorithms (GAs) and an ant colony system (ACS) algorithm based on the same benchmark problems. The results show that the proposed PSO algorithm outperforms all the existing algorithms for the considered problem.     

ROBOT SCHEDULING IN A CIRCUIT BOARD PRODUCTION LINE:A HYBRID OR/ANN APPROACH

A hybrid method that combines human intelligence, an optimization technique (semi-Markov decision model) and an artificial neural network to solve real-time scheduling problems is proposed. The proposed method consists of three phases: data collection, optimization, and generalization. The testbed of this approach is the robot scheduling problem in a circuit board production line where one overhead robot is used to transport jobs through a line of sequential chemical process tanks. Because chemical processes are involved in this production system, any mistiming or misplacing will result in defective jobs. The proposed hybrid system performs better than the human scheduler from whom the models were formulated, both in terms of productivity and quality.     

A three-stage decomposition approach for energy-aware scheduling with processing-time-dependent product quality

Due to increasing concerns about energy and environmental demands, decision-makers in industrial companies have developed awareness about energy use and energy efficiency when engaging in short-term production scheduling and planning. This paper studied a flow-shop scheduling problem consisting of a series of processing stages and one final quality check stage with the aim of minimising energy consumption. In particular, the product quality in the problem depends on its processing time at each stage, and the energy consumption is related to the processing speed, equipment state and product quality. A novel three-stage decomposition approach is presented to solve the proposed energy-aware scheduling (EAS) problem. The decomposition approach can drastically reduce the search space and provide reliable solutions for the EAS problem. The numerical experiments show that the computational results can achieve an optimality gap of less than 4% when compared to the global optimal solutions. The parameter analysis demonstrates the managerial implications of the proposed problem. For example, increasing the number of alternative processing speeds or relaxing the delivery date will increase energy efficiency. The energy-saving potential is illustrated by comparing the scheduling results using the proposed approach and human experience.     

A heuristic algorithm for master production scheduling problem with controllable processing times and scenario-based demands

Master production scheduling (MPS) is widely used by manufacturing industries in order to handle the production scheduling decisions in the production planning hierarchy. The classical approach to MPS assumes infinite capacity, fixed (i.e. non-controllable) processing times and a single pre-determined scenario for the demand forecasts. However, the deterministic optimisation approaches are sometimes not suitable for addressing the real-world problems with high uncertainty and flexibility. Accordingly, in this paper, we propose a new practical model for designing an optimal MPS for the environments in which processing times may be controllable by allocating resources such as facilities, energy or manpower. Due to the NP-hardness of our model, an efficient heuristic algorithm using local search technique and theory of constraints is developed and analysed. The computational results especially for large-sized test problems show that the average optimality gap of proposed algorithm is four times lower than that of exact solution using GAMS while it consumes also significantly smaller run times. Also, the analysis of computational results confirms that considering the controllable processing times may improve the solution space and help to more efficiently utilise the available resources. According to the model structure and performance of the algorithm, it may be proposed for solving large and complex real-world problems particularly the machining and steel industries.     

Joint optimization of preventive maintenance and flexible flowshop sequence-dependent group scheduling considering multiple setups

This study focuses on a joint optimization problem regarding preventive maintenance (PM) and non-permutation group scheduling for a flexible flowshop manufacturing cell in order to minimize makespan. A mixed-integer linear programming model for the investigated problem is developed, which features the consideration of multiple setups, the relaxation of group technology assumptions, and the integration of group scheduling and PM. Based on the model, a lower bounding technique is presented to evaluate the quality of solutions. Furthermore, a genetic algorithm (GA) is proposed to improve computational efficiency. In the GA, a threshold-oriented PM policy, a hybrid crossover and a group swap mutation operator are applied. Numerical experiments are conducted on 45 test problems with various scales. The results show that the proposed model can remarkably reduce makespan. Comparative experiments reveal that the GA outperforms CPLEX, particle swarm optimization and cuckoo search with respect to effectiveness and efficiency.     

A scatter search approach with dispatching rules for a joint decision of cell formation and parts scheduling in batches

A joint decision of cell formation and parts scheduling is addressed for a cellular manufacturing system where each type of machine and part may have multiple numbers and parts must require processing and transferring in batches. The joint decision problem is not only to assign batches and associated machine groups to cells, but also to sequence the processing of batches on each machine in order to minimise the total tardiness penalty cost. A nonlinear mixed integer programming mathematical model is proposed to formulate the problem. The proposed model, within nonlinear terms and integer variables, is difficult to solve efficiently for real size problems. To solve the model for practical purposes, a scatter search approach with dispatching rules is proposed, which considers two different combination methods and two improvement methods to further expand the conceptual framework and implementation of the scatter search so as to better fit the addressed problem. This scatter search approach interactively uses a combined dispatching rule to solve a scheduling sub-problem corresponding to each integer solution visited in the search process. A computational study is performed on a set of test problems with various dimensions, and computational results demonstrate the effectiveness of the proposed approach.     

On the integer programming formulation of production scheduling optimisation algorithm for the hot rolling processes

This note is concerned with the formulation of scheduling of the hot rolling process (SHRP). Based on the capacitated vehicle routing problem (CVRP), Chen et al. (Chen, A.L., Yang, G.K., and Wu, Z.M., 2008. Production scheduling optimization algorithm for the hot rolling processes. International Journal of Production Research, 46 (7), 1955–1973) proposed a nonlinear integer programming formulation of SHRP. Due to some deficiencies in the formulation, Kim (Kim, B.-I., 2010. Some comments on Chen et al. ‘Production scheduling optimization algorithm for the hot rolling processes’. International Journal of Production Research, 48 (7), 2165–2167) very recently gave some correction to the model. However, even with the correction the model has flaws. The purpose of this note is to give a complete, also based on CVRP, corrected formulation with substantial number of variables reduced.