A tabu search algorithm for unrelated parallel machine scheduling with sequence- and machine-dependent setups: minimizing total tardiness

This study considers the problem of scheduling independent jobs on unrelated parallel machines with machine- and sequence-dependent setup times for the objective of minimizing the total tardiness, i.e., R _m │S _ijk │∑T _j . Since the parallel machines are unrelated, sequence-dependent setup times must depend on machines. To the best of the authors’ knowledge, the simulated annealing and the iterated greedy algorithms are two existing ones for the new class of scheduling problem with an additional constraint of strict due date constraints for some jobs, i.e., deadlines. In this study, we suggest a tabu search algorithm that incorporates various neighborhood generation methods. A computational experiment was done on the instances generated by the method used in the two previous research articles, and the results show that the tabu search algorithm outperforms the simulated annealing algorithm significantly. In particular, it gave optimal solutions for more than 50 % of small-sized test instances. Also, an additional test was done to compare the performances of the tabu search and the existing iterated greedy algorithms, and the result shows that the tabu search algorithm gives quicker solutions than the iterated greedy algorithm although it gives less quality solutions.     

Meta-heuristics to solve single-machine scheduling problem with sequence-dependent setup time and deteriorating jobs

This paper tackles the single-machine scheduling problem in which there are sequence-dependent setup times and deteriorating jobs. In this regard, a mathematical model has been formulated to minimize makespan (C _max). Afterwards, genetic and tabu search algorithms have been developed. Since the population diversity is a very important issue in preventing neighborhood search from trapping in a local optimum, some methods have been applied to genetic algorithm in order to maintain population diversity, and the final results show the effectiveness of these methods. The calibration of genetic algorithm parameters and operators is performed using design of experiments. Finally, several examples are produced to illustrate the proposed approach.     

一类解决Job Shop问题的禁忌搜索算法

针对Job shop问题，设计了一种改进的禁忌搜索算法（MTS算法）。MTS算法从多个初始解开始，将传统禁忌搜索算法由串行搜索结构变为并行搜索结构；采用互换和交叉两种邻域搜索函数，既有利于新邻域的探索又有利于交换信息；基于目标值的禁忌表保证了群体的多样性。实验表明，MTS算法克服了传统禁忌搜索算法的缺陷，具有较高的求解质量和鲁棒性。     

适应性禁忌搜索算法求解带回程的时变速度车辆路径问题

为求解带回程的时变速度车辆路径问题，建立了问题的数学模型并提出适应性禁忌搜索算法求解。适应性禁忌搜索算法为两阶段的启发式方法，改进固定速度下的启发式方法用于生成时变速度下的初始解，然后运用适应性禁忌搜索算法进一步优化，包括邻域生成规则定义，采用Hash表存储搜索过程中的解，检测解的重复状态，定义逃离局部搜索区域规则。对改进的标准问题进行测试，同时与最近邻域搜索算法的结果作比较，结果表明算法是有效的。与固定速度情形相比较，时变速度模型得到的调度方案更加合理。     

A hybrid two-phase encoding particle swarm optimization for total weighted completion time minimization in proportionate flexible flow shop scheduling

A proportionate flow shop (PFS) is a special case of the m machine flow shop problem. In a PFS, a fixed sequence of machines is arranged in s stages (s?>?1) with only a single machine at each stage, and the processing time for each job is the same on all machines. Notably, PFS problems have garnered considerable attention recently. A proportionate flexible flow shop (PFFS) scheduling problem combines the properties of PFS problems and parallel-identical-machine scheduling problems. However, few studies have investigated the PFFS problem. This study presents a hybrid two-phase encoding particle swarm optimization (TPEPSO) algorithm to the PFFS problem with a total weighted completion time objective. In the first phase, a sequence position value representation is designed based on the smallest position value rule to convert continuous position values into job sequences in the discrete PFFS problem. During the second phase, an absolute position value representation combined with a tabu search (TS) is applied starting from the current position of particles that can markedly improve swarm diversity and avoid premature convergence. The hybrid TPEPSO algorithm combines the cooperative and competitive characteristics of TPEPSO and TS. Furthermore, a candidate list strategy is designed for the TS to examine the neighborhood and concentrate on promising moves during each iteration. Experimental results demonstrate the robustness of the proposed hybrid TPEPSO algorithm in terms of solution quality. Moreover, the proposed hybrid TPEPSO algorithm is considerably faster than existing approaches for the same benchmark problems in literature.     

A Tabu Search Algorithm for Single Machine Scheduling with Release Times,Due Dates,and Sequence-Dependent Set-up Times

In this paper, we present a tabu search algorithm that schedules N jobs to a single machine in order to minimise the maximum lateness of the jobs. The release times, due dates, and sequence-dependent set-up times of the jobs are assumed to exist. We modified the original tabu search method to be suitable for the scheduling problem. The proposed tabu search algorithm is composed of two parts: a MATCS (modified apparent tardiness cost with set-ups) rule for finding an efficient initial solution, and the tabu search method to seek a near optimal solution from the initial solution. The experimental results show that the tabu search algorithm obtains much better solutions more quickly than the RHP (rolling horizon procedure) heuristic suggested by Ovacik and Uzsoy.     

A hybrid simulated annealing-tabu search algorithm for the part selection and machine loading problems in flexible manufacturing systems

Part selection and machine loading are two major problems in the production planning phase of the flexible manufacturing systems. The problems have a combinatorial structure and usually, in practice, it is difficult to deal with this kind of problems using a mathematical programming model. In this paper, the above problems are formulated as a mixed-integer programming model which is handled sequentially and solved by a diversification-strategy-added version of the hybrid tabu search/simulated annealing algorithm of Zhang et al. (Comput Oper Res 35:282–294, 2008) presented in 2008. The performance of the algorithm is tested on eight random-generated problems with different sizes. The results are compared with those of the mathematical programming model, the original version of Zhang et al.’s (Comput Oper Res 35:282–294, 2008) algorithm and also a tabu search algorithm developed earlier by the authors.     

Hybrid metaheuristics for unrelated parallel machine scheduling with sequence-dependent setup times

This paper proposes several hybrid metaheuristics for the unrelated parallel-machine scheduling problem with sequence-dependent setup times given the objective of minimizing the weighted number of tardy jobs. The metaheuristics begin with effective initial solution generators to generate initial feasible solutions; then, they improve the initial solutions by an approach, which integrates the principles of the variable neighborhood descent approach and tabu search. Four reduced-size neighborhood structures and two search strategies are proposed in the metaheuristics to enhance their effectiveness and efficiency. Five factors are used to design 32 experimental conditions, and ten test problems are generated for each condition. Computational results show that the proposed hybrid metaheuristics are significantly superior to several basic tabu search heuristics under all the experimental conditions.     

Sequencing of an M machine flow shop with setup, processing and removal times separated

In this research, a flow shop scheduling problem in which setup, processing and removal times are separated, with the objective of minimizing makespan, is considered. A tabu search based heuristic is presented for solving the addressed problem. The proposed heuristic begins with the construction of artificial processing times for each operation; then a modified NEH algorithm is used to generate an initial solution, followed by a designed tabu search procedure applied for further improvement of the solution. The proposed heuristic, as well as the existing one, is evaluated in a large number of randomly generated problems. The results of the experimental investigations of the proposed heuristic algorithm and the existing heuristic in meeting the objective of makespan are also reported. It is found that the solution quality of the proposed tabu search heuristic is better than that of the existing heuristic, but for large size problems more computational efforts are needed; however, the CPU time is still acceptable.     

Solving single-machine total weighted tardiness problems with sequence-dependent setup times by meta-heuristics

Simulated annealing (SA), genetic algorithms (GA), and tabu search (TS) are the three well known meta-heuristics for combinatorial optimization problems. In this paper, single-machine total weighted tardiness problems with sequence-dependent setup times are solved by SA, GA, and TS approaches. A random swap and insertion search is applied in SA, and a mutation operator performed by a greedy local search is used in a GA. Similarly, a swap and an insertion tabu list are adopted in TS. To verify these proposed approaches, computational experiments were conducted on benchmark problem sets. The experimental results show that these approaches find new upper bound values for most benchmark problems within reasonable computational expenses.     

Hybridizing tabu search with ant colony optimization for solving job shop scheduling problems

The manufacturing industry continues to be a prime contributor and it requires an efficient schedule. Scheduling is the allocation of resources to activities over time and it is considered to be a major task done to improve shop-floor productivity. Job shop problem comes under this category and is combinatorial in nature. Research on optimization of the job shop problem is one of the most significant and promising areas of optimization. This paper presents an application of the global optimization technique called tabu search that is combined with the ant colony optimization technique to solve the job shop scheduling problems. The neighborhoods are selected based on the strategies in the ant colony optimization with dynamic tabu length strategies in the tabu search. The inspiring source of ant colony optimization is pheromone trail that has more influence in selecting the appropriate neighbors to improve the solution. The performance of the algorithm is tested using well-known benchmark problems and is also compared with other algorithms in the literature.     

Scheduling jobs under constant period-by-period resource availability to maximize project profit at a due date

In this paper, we propose a lump-sum payment model for the resource-constrained project scheduling problem, which is a generalization of the job shop scheduling problem. The model assumes that the contractor will receive the profit of each job at a predetermined project due date, while taking into account the time value of money. The contractor will then schedule the jobs with the objective of maximizing his total future net profit value at the due date. This proposed problem is nondeterministic polynomial-time (NP)-hard and mathematically formulated in this paper. Several variable neighborhood search (VNS) algorithms are developed by using insertion move and two-swap to generate various neighborhood structures, and making use of the well-known backward–forward scheduling, a proposed future profit priority rule, or a short-term VNS as the local refinement scheme (D-VNS). Forty-eight 20-job instances were generated using ProGen and optimally solved with ILOG CPLEX. The performances of these algorithms are evaluated based on the optimal schedules of the 48 test instances. Our experimental results indicate that the proposed VNS algorithms frequently obtain optimal solutions in a short computational time. For larger size problems, our experimental results also indicate that the D-VNS with forward direction movement outperforms the other VNS algorithms, as well as a genetic algorithm and a tabu search algorithm.     

Realistic variant of just-in-time flowshop scheduling: integration of L p -metric method in PSO-like algorithm

This study strives to schedule a just-in-time hybrid flowshop with sequence-dependent setup times by considering two performance measures, namely makespan and sum of the earliness and tardiness, simultaneously. The paper proposes a mixed integer programming model. However, since the simpler case with a single stage and with a single machine per stage is NP-hard, the utilization of the exact algorithms for the real-life problems is limited. Thus, this paper proposes a novel solving algorithm with a weighted L _p -metric-based framework. Since the particle swarm optimization is originally designed for continuous solution space, in this study, we modify the particle position based on our representation so that a particle position is decoded into a schedule using the largest processing time algorithm, Hadamard product, and swap operator. Furthermore, we apply a variable neighborhood search and a tabu search to improve the solution quality. This hybridization which combines the advantages of the individual components is the key innovative aspect of the approach. We investigate the performance of our algorithm in the comparison with several algorithms and show that it has a good performance.     

A Simple Branch-and-Bound Algorithm for the k-Cut Problem for Applications with k Target Vertices,e.g. VLSI Design

The problems studied here belong to a class called graph partition. They are combinatorial problems which consist of finding a partition of vertices into components in order to optimise a given measure. A variety of applications have been suggested, such as communication cost minimisation in parallel computing systems, clustering problems, VLSI design, and net-work reliability. A 0–1 integer programming is proposed first to define and solve the k-cut problem. Then, an efficient branch-and-bound algorithm is developed to solve this problem. As evidence of the utility of the proposed approach, the extensive computational results on random test problems are presented. In computational experiments on problems with up to 37 vertices, the proposed branch-and-bound algorithm is more efficient when compared to two branch-and-bound algorithms that are the same but without some bounds and dominance rules, and the proposed 0–1 integer programming model. The results show that both the lower and upper bounds are very tight, and the branch-and-bound algorithm performs very well.     

Flexible job shop scheduling with tabu search algorithms

This paper presents a tabu search algorithm that solves the flexible job shop scheduling problem to minimize the makespan time. As a context for solving sequencing and scheduling problems, the flexible job shop model is highly complicated. Alternative operation sequences and sequence-dependent setups are two important factors that frequently appear in various manufacturing environments and in project scheduling. In this paper, we present a model for a flexible job shop scheduling problem while considering those factors simultaneously. The purpose of this paper is to minimize the makespan time and to find the best sequence of operations and the best choice of machine alternatives, simultaneously. The proposed tabu search algorithm is composed of two parts: a procedure that searches for the best sequence of job operations, and a procedure that finds the best choice of machine alternatives. Randomly generated test problems are used to evaluate the performance of the proposed algorithm. Results of the algorithm are compared with the optimal solution using a mathematical model solved by the traditional optimization technique (the branch and bound method). After modeling the scheduling problem, the model is verified and validated. Then the computational results are presented. Computational results indicate that the proposed algorithm can produce optimal solutions in a short computational time for small and medium sized problems. Moreover, it can be applied easily in real factory conditions and for large size problems. The proposed algorithm should thus be useful to both practitioners and researchers.     

The tricriteria flowshop scheduling problem

Multicriteria flowshop scheduling problems have been one of the most attractive subjects in recent years. In the multicriteria flowshop scheduling literature, a very limited number of studies have been performed on problems which include a tardiness criterion. In this paper a multicriteria (tricriteria) two-machine flowshop scheduling problem with a tardiness criterion is tackled. The objective is to minimise a weighted sum of total completion time, total tardiness and makespan. An integer programming model is proposed for the problem which belongs to NP-hard class. The modified NEH (Nawaz, Enscore and Ham) algorithm, a tabu search-based heuristic method, random search and the EDD rule (the earliest due date rule) are used to solve problems with up to 2,500 jobs. A computational analysis is conducted to evaluate the performance of the heuristics. The analysis shows that the heuristics are quite efficient, and the performance of the tabu search based heuristic is the best of all in terms of solution quality.     

机器人制造单元的建模与任务调度策略

机器人资源的合理分配和调度是提高制造单元柔性的关键。本文针对一类机器人制造单元的最小周期调度问题，应用极大代数方法建立了单元系统的调度模型，提出了基于禁忌搜索的启发式调度策略，并给出了初始可行解和搜索邻域的构造方法；最后，通过具体的运算实例，验证了所提出方法具有较高的效率，能够解决较大规模的最小周期调度问题，具有广泛的适用性。     

A block approach to earliness-tardiness scheduling problems

In this paper, we consider a single-machine job scheduling problem where the objective is to minimize the weighted sum of earliness and tardiness (E/T) penalties of jobs. This problem is consistent with the just-in-time (JIT) production. We propose partitioning of permutation into subsequences (blocks) and replacing sets of moves with its representatives, significantly decreasing the size of the searched neighborhood. Some new properties of the problem and compound moves make eliminating “bad” elements and speeding up calculations possible. These properties allow us to propose a new fast local search algorithm based on a tabu search method. Computational experiments are presented and the results show that the algorithm proposed allows us to obtain the best-known results in a short time.     

A tabu search approach to the cell formation problem

The cell formation problem determines the decomposition of the manufacturing cells of a production system in which machines are assigned to these cells to process one or more part families so that each cell is operated independently and the intercellular flows are minimised or the number of parts flow processed within cells is maximised. In this paper, a tabu search heuristic—TSCF—that consists of dynamic tabu tenure with a long-term memory mechanism is presented to solve the cell formation problem. Test problems adopted from the literature and generated randomly are used to evaluate the performance of the proposed algorithm. In addition, two methods for quickly generating the initial solutions are proposed, namely the group-and-assign (GAA) method, and the random approach. Computational results indicate that the GAA method, accompanied by the TSCF algorithm can produce optimal solutions in less than or equal to 0.005 s for all small- and medium-sized problems. The proposed algorithm should thus be useful to both practitioners and researchers.     

一种求解DGPS动态整周模糊度问题的交叉禁忌搜索

利用遗传算法中的交叉因子作为禁忌算法的分散策略,提出了交叉禁忌算法(CTS).分散策略用于开辟新的搜索空间,将所提出的CTS用于DGPS的整周模糊度解算问题中.首先用零空间约束法确定搜索空间,然后用CTS搜索整周模糊度的最优解.用CTS算法对一个实测算例进行解算,当搜索率为6%的时候,搜索可靠率达到了92%;而用传统的禁忌算法解算时,采用相同的搜索率,搜索可靠率只有45%.实验结果表明CTS的性能要优于传统的禁忌算法.