An efficient memetic algorithm for total weighted tardiness minimization in a single machine with setups

The single machine scheduling problem with sequence-dependent setup times with the objective of minimizing the total weighted tardiness is a challenging problem due to its complexity, and has a huge number of applications in real production environments. In this paper, we propose a memetic algorithm that combines and extends several ideas from the literature, including a crossover operator that respects both the absolute and relative position of the tasks, a replacement strategy that improves the diversity of the population, and an effective but computationally expensive neighborhood structure. We propose a new decomposition of this neighborhood that can be used by a variable neighborhood descent framework, and also some speed-up methods for evaluating the neighbors. In this way we can obtain competitive running times. We conduct an experimental study to analyze the proposed algorithm and prove that it is significantly better than the state-of-the-art in standard benchmarks.     

A discrete differential evolution algorithm for the single machine total weighted tardiness problem with sequence dependent setup times

This paper is concerned with solving the single machine total weighted tardiness problem with sequence dependent setup times by a discrete differential evolution algorithm developed by the authors recently. Its performance is enhanced by employing different population initialization schemes based on some constructive heuristics such as the well-known NEH and the greedy randomized adaptive search procedure (GRASP) as well as some priority rules such as the earliest weighted due date (EWDD) and the apparent tardiness cost with setups (ATCS). Additional performance enhancement is further achieved by the inclusion of a referenced local search (RLS) in the algorithm together with the use of destruction and construction (DC) procedure when obtaining the mutant population. Furthermore, to facilitate the greedy job insertion into a partial solution which will be employed in the NEH, GRASP, DC heuristics as well as in the RLS local search, some newly designed speed-up methods are presented for the insertion move for the first time in the literature. They are novel contributions of this paper to the single machine tardiness related scheduling problems with sequence dependent setup times. To evaluate its performance, the discrete differential evolution algorithm is tested on a set of benchmark instances from the literature. Through the analyses of experimental results, its highly effective performance with substantial margins both in solution quality and CPU time is shown against the best performing algorithms from the literature, in particular, against the very recent newly designed particle swarm and ant colony optimization algorithms of Anghinolfi and Paolucci [A new discrete particle swarm optimization approach for the single machine total weighted tardiness scheduling problem with sequence dependent setup times. European Journal of Operational Research 2007; doi:10.1016/j.ejor.2007.10.044] and Anghinolfi and Paolucci [A new ant colony optimization approach for the single machine total weighted tardiness scheduling problem. http://www.discovery.dist.unige.it/papers/Anghinolfi_Paolucci_ACO.pdf, respectively. Ultimately, 51 out of 120 overall aggregated best known solutions so far in the literature are further improved while other 50 instances are solved equally.     

A variable neighborhood search for minimizing total weighted tardiness with sequence dependent setup times on a single machine

This paper deals with the single machine scheduling problem to minimize the total weighted tardiness in the presence of sequence dependent setup. Firstly, a mathematical model is given to describe the problem formally. Since the problem is NP-hard, a general variable neighborhood search (GVNS) heuristic is proposed to solve it. Initial solution for the GVNS algorithm is obtained by using a constructive heuristic that is widely used in the literature for the problem. The proposed algorithm is tested on 120 benchmark instances. The results show that 37 out of 120 best known solutions in the literature are improved while 64 instances are solved equally. Next, the GVNS algorithm is applied to single machine scheduling problem with sequence dependent setup times to minimize the total tardiness problem without changing any implementation issues and the parameters of the GVNS algorithm. For this problem, 64 test instances are solved varying from small to large sizes. Among these 64 instances, 35 instances are solved to the optimality, 16 instances' best-known results are improved, and 6 instances are solved equally compared to the best-known results. Hence, it can be concluded that the GVNS algorithm is an effective, efficient and a robust algorithm for minimizing tardiness on a single machine in the presence of setup times.     

An ant colony optimization for single-machine tardiness scheduling with sequence-dependent setups

In many real-world production systems, it requires an explicit consideration of sequence-dependent setup times when scheduling jobs. As for the scheduling criterion, the weighted tardiness is always regarded as one of the most important criteria in practical systems. While the importance of the weighted tardiness problem with sequence-dependent setup times has been recognized, the problem has received little attention in the scheduling literature. In this paper, we present an ant colony optimization (ACO) algorithm for such a problem in a single-machine environment. The proposed ACO algorithm has several features, including introducing a new parameter for the initial pheromone trail and adjusting the timing of applying local search, among others. The proposed algorithm is experimented on the benchmark problem instances and shows its advantage over existing algorithms. As a further investigation, the algorithm is applied to the unweighted version of the problem. Experimental results show that it is very competitive with the existing best-performing algorithms.     

A neighborhood for complex job shop scheduling problems with regular objectives

Due to the limited applicability in practice of the classical job shop scheduling problem, many researchers have addressed more complex versions of this problem by including additional process features, such as time lags, setup times, and buffer limitations, and have pursued objectives that are more practically relevant than the makespan, such as total flow time and total weighted tardiness. However, most proposed solution approaches are tailored to the specific scheduling problem studied and are not applicable to more general settings. This article proposes a neighborhood that can be applied for a large class of job shop scheduling problems with regular objectives. Feasible neighbor solutions are generated by extracting a job from a given solution and reinserting it into a neighbor position. This neighbor generation in a sense extends the simple swapping of critical arcs, a mechanism that is widely used in the classical job shop but that is not applicable in more complex job shop problems. The neighborhood is embedded in a tabu search, and its performance is evaluated with an extensive experimental study using three standard job shop scheduling problems: the (classical) job shop, the job shop with sequence-dependent setup times, and the blocking job shop, combined with the following five regular objectives: makespan, total flow time, total squared flow time, total tardiness, and total weighted tardiness. The obtained results support the validity of the approach.     

A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem

In this paper, we study the job shop scheduling problem with the objective of minimizing the total weighted tardiness. We propose a hybrid shifting bottleneck-tabu search (SB-TS) algorithm by replacing the re-optimization step in the shifting bottleneck (SB) algorithm by a tabu search (TS). In terms of the shifting bottleneck heuristic, the proposed tabu search optimizes the total weighted tardiness for partial schedules in which some machines are currently assumed to have infinite capacity. In the context of tabu search, the shifting bottleneck heuristic features a long-term memory which helps to diversify the local search. We exploit this synergy to develop a state-of-the-art algorithm for the job shop total weighted tardiness problem (JS-TWT). The computational effectiveness of the algorithm is demonstrated on standard benchmark instances from the literature.     

带机器人制造单元的作业车间调度仿真

针对带有机器人制造单元的作业车间调度优化问题, 在若干加工机器上可以加工具有特定加工工序的若干工件, 并且搬运机器人可以将工件在装卸载站与各加工机器间进行搬运. 在实际生产过程中, 由于不确定性, 特别是带有存货的加工单元, 要求工件的完工时间在一个时间窗内, 而不是一个特定的时间点. 因此针对此情况的作业车间, 考虑到其在求解问题过程中的复杂性和约束性等特点, 研究了在时间窗约束下, 目标值为最小化工件完成时间提前量和延迟量的总权重. 提出了一种将文化基因算法与邻域搜索技术(变邻域下降搜索)相结合的改进元启发式算法, 在求得最优目标值的同时, 可得到最优值的工件加工序列及机器人搬运序列. 通过实验结果表明, 所提出的算法有效且优于传统文化基因算法与遗传算法.     

A note on single-machine scheduling with general learning effect and past-sequence-dependent setup time

In this paper, we study a scheduling model with the consideration of both the learning effect and the setup time. Under the proposed model, the learning effect is a general function of the processing time of jobs already processed and its scheduled position, and the setup time is past-sequence-dependent. We then derive the optimal sequences for two single-machine problems, which are the makespan and the total completion time. Moreover, we showed that the weighted completion time, the maximum lateness, the maximum tardiness, and the total tardiness problems remain polynomially solvable under agreeable conditions.     

An exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times

This study proposes an exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times. The algorithm is an extension of the authors' previous algorithm for the single-machine scheduling problem without setup times, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. In the first stage of the algorithm, the conjugate subgradient algorithm or the column generation algorithm is applied to a Lagrangian relaxation of the original problem to adjust multipliers. Then, in the second stage, constraints are successively added to the relaxation until the gap between lower and upper bounds becomes zero. The relaxation is solved by dynamic programming and unnecessary dynamic programming states are eliminated to suppress the increase of computation time and memory space. In this study a branching scheme is integrated into the algorithm to manage to solve hard instances. The proposed algorithm is applied to benchmark instances in the literature and almost all of them are optimally solved.     

A study of hybrid evolutionary algorithms for single machine scheduling problem with sequence-dependent setup times

We present a systematic comparison of hybrid evolutionary algorithms (HEAs), which independently use six combinations of three crossover operators and two population updating strategies, for solving the single machine scheduling problem with sequence-dependent setup times. Experiments show the competitive performance of the combination of the linear order crossover operator and the similarity-and-quality based population updating strategy. Applying the selected HEA to solve 120 public benchmark instances of the single machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness widely used in the literature, we achieve highly competitive results compared with the exact algorithm and other state-of-the-art metaheuristic algorithms in the literature. Meanwhile, we apply the selected HEA in its original form to deal with the unweighted 64 public benchmark instances. Our HEA is able to improve the previous best known results for one instance and match the optimal or the best known results for the remaining 63 instances in a reasonable time.     

Algorithms for job scheduling problems with distinct time windows and general earliness/tardiness penalties

This paper addresses the single machine scheduling problem with distinct time windows and sequence-dependent setup times. The objective is to minimize the total weighted earliness and tardiness. The problem involves determining the job execution sequence and the starting time for each job in the sequence. An implicit enumeration algorithm denoted IE and a general variable neighborhood search algorithm denoted GVNS are proposed to determine the job scheduling. IE is an exact algorithm, whereas GVNS is a heuristic algorithm. In order to define the starting times, an O(n²) idle time insertion algorithm (ITIA) is proposed. IE and GVNS use the ITIA algorithm to determine the starting time for each job. However, the IE algorithm is only valid for instances with sequence-independent setup times, and takes advantage of theoretical results generated for this problem. Computational experiments show that the ITIA algorithm is more efficient than the only other equivalent algorithm found in the literature. The IE algorithm allows the optimal solutions of all instances with up to 15 jobs to be determined within a feasible computational time. For larger instances, GVNS produces better-quality solutions requiring less computational time compared with the other algorithm from the literature.     

An adaptive multi-population genetic algorithm to solve the multi-objective group scheduling problem in hybrid flexible flowshop with sequence-dependent setup times

In this paper we consider a multi-objective group scheduling problem in hybrid flexible flowshop with sequence-dependent setup times by minimizing total weighted tardiness and maximum completion time simultaneously. Whereas these kinds of problems are NP-hard, thus we proposed a multi-population genetic algorithm (MPGA) to search Pareto optimal solution for it. This algorithm comprises two stages. First stage applies combined objective of mentioned objectives and second stage uses previous stage’s results as an initial solution. In the second stage sub-population will be generated by re-arrangement of solutions of first stage. To evaluate performance of the proposed MPGA, it is compared with two distinguished benchmarks, multi-objective genetic algorithm (MOGA) and non-dominated sorting genetic algorithm II (NSGA-II), in three sizes of test problems: small, medium and large. The computational results show that this algorithm performs better than them.     

Data-Driven Heuristic Assisted Memetic Algorithm for Efficient Inter-Satellite Link Scheduling in the BeiDou Navigation Satellite System

Inter-satellite link (ISL) scheduling is required by the BeiDou Navigation Satellite System (BDS) to guarantee the system ranging and communication performance. In the BDS, a great number of ISL scheduling instances must be addressed every day, which will certainly spend a lot of time via normal metaheuristics and hardly meet the quick-response requirements that often occur in real-world applications. To address the dual requirements of normal and quick-response ISL schedulings, a data-driven heuristic assisted memetic algorithm (DHMA) is proposed in this paper, which includes a high-performance memetic algorithm (MA) and a data-driven heuristic. In normal situations, the high-performance MA that hybridizes parallelism, competition, and evolution strategies is performed for high-quality ISL scheduling solutions over time. When in quick-response situations, the data-driven heuristic is performed to quickly schedule high-probability ISLs according to a prediction model, which is trained from the high-quality MA solutions. The main idea of the DHMA is to address normal and quick-response schedulings separately, while high-quality normal scheduling data are trained for quick-response use. In addition, this paper also presents an easy-to-understand ISL scheduling model and its NP-completeness. A seven-day experimental study with 10 080 one-minute ISL scheduling instances shows the efficient performance of the DHMA in addressing the ISL scheduling in normal (in 84 hours) and quick-response (in 0.62 hour) situations, which can well meet the dual scheduling requirements in real-world BDS applications.      

A fuzzy-mixed-integer goal programming model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates

This paper presents a new mixed-integer goal programming (MIGP) model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates. Two objectives are considered in the model to minimize the total weighted flow time and the total weighted tardiness simultaneously. Due to the complexity of the above model and uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the parallel-machine scheduling problem with sequence-dependent set-up times under the hypothesis of fuzzy processing time's knowledge and two fuzzy objectives as the MIGP model. In addition, a quite effective and applicable methodology for solving the above fuzzy model are presented. At the end, the effectiveness of the proposed model and the denoted methodology is demonstrated through some test problems.     

A discrete electromagnetism-like mechanism for single machine total weighted tardiness problem with sequence-dependent setup times

Electromagnetism-like mechanism (EM) is a novel meta-heuristic, inspired by the attraction–repulsion mechanism of electromagnetic theory. There are very few applications of EM in scheduling problems. This paper presents a discrete EM (DEM) algorithm for minimizing the total weighted tardiness in a single-machine scheduling problem with sequence-dependent setup times. Unlike other discrete EM algorithms that use a random key method to deal with the discreteness, the proposed DEM algorithm employs a completely different approach, with an attraction–repulsion mechanism involving crossover and mutation operators. The proposed algorithm not only accomplishes the intention of an EM algorithm but also can be applied in other combinatorial optimization problems. To verify the algorithm, it is compared with a discrete differential evolution (DDE) algorithm, which is the best meta-heuristic for the considered problem. Computational experiments show that the performance of the proposed DEM algorithm is better than that of the DDE algorithm in most benchmark problem instances. Specifically, 30 out of 120 aggregated best-known solutions in the literature are further improved by the DEM algorithm, while other another 70 instances are solved to an equivalent degree.     

Notes on “some single-machine scheduling problems with general position-dependent and time-dependent learning effects”

This paper provides a continuation of the idea presented by Yin et al. [Yin et al., Some scheduling problems with general position-dependent and time-dependent learning effects, Inform. Sci. 179 (2009) 2416-2425]. For each of the following three objectives, total weighted completion time, maximum lateness and discounted total weighted completion time, this paper presents an approximation algorithm which is based on the optimal algorithm for the corresponding single-machine scheduling problem and analyzes its worst-case bound. It shows that the single-machine scheduling problems under the proposed model can be solved in polynomial time if the objective is to minimize the total lateness or minimize the sum of earliness penalties. It also shows that the problems of minimizing the total tardiness, discounted total weighted completion time and total weighted earliness penalty are polynomially solvable under some agreeable conditions on the problem parameters.     

多目标和声搜索算法求解序依赖单机调度问题

针对一种具有序依赖设置时间的单机调度问题,建立了目标为总机器设置时间最小、总交货延误时间最短和交货延误率最小的多目标优化模型,提出了一种自适应多目标和声搜索算法,算法中引入了信息熵的概念来评价种群中个体的多样性和拥挤度。实例计算结果表明该算法可行、有效。     

Single-machine scheduling with deteriorating jobs and setup times to minimize the maximum tardiness

In many realistic production situations, a job processed later consumes more time than the same job when it is processed earlier. Production scheduling in such an environment is known as scheduling with deteriorating jobs. However, research on scheduling problems with deteriorating jobs has rarely considered explicit (separable) setup time (cost). In this paper, we consider a single-machine scheduling problem with deteriorating jobs and setup times to minimize the maximum tardiness. We provide a branch-and-bound algorithm to solve this problem. Computational experiments show that the algorithm can solve instances up to 1000 jobs in reasonable time.     

求解异构并行机调度问题的混合多目标教-学优化算法

以异构并行机调度问题为研究对象,考虑了一类以优化总加权完工时间和加权延误总和的调度问题。首先,基于问题描述构建了该问题的混合整数规划模型。其次,提出了混合多目标教-学优化算法。在算法设计中,结合问题的特点设计序列编码方法,并采用分解技术来实现多目标调度问题的求解。此外,该算法通过融合多种交叉算子来定义个体进化过程,并通过与变邻域搜索算法的混合来提升其优化效果。最后,给出了仿真实验与分析,测试结果验证了多目标教-学优化算法求解该调度问题的优越性。     

A dynamic-programming-based exact algorithm for general single-machine scheduling with machine idle time

This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors’ previous algorithm for the problem without machine idle time, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. We first extend our previous algorithm to the problem with machine idle time and next propose several improvements. Then, the proposed algorithm is applied to four types of single-machine scheduling problems: the total weighted earliness-tardiness problem with equal (zero) release dates, that with distinct release dates, the total weighted completion time problem with distinct release dates, and the total weighted tardiness problem with distinct release dates. Computational experiments demonstrate that our algorithm outperforms existing exact algorithms and can solve instances of the first three problems with up to 200 jobs and those of the last problem with up to 80 jobs.