Automatic Algorithm Design for Hybrid Flowshop Scheduling Problems

This paper investigates the multistage hybrid flow shop (HFS) scheduling problems using the new bat algorithm. A HFS is the generalisation of flowshop with multiple machines. HFS is one of the important scheduling problems that represent many industries like iron and steel, chemical, textile and ceramic industries. The HFS scheduling problems have been proved to be NP-hard. A recently developed bat meta-heuristic algorithm is proposed to solve the HFS problems. The proposed algorithm is validated with a well-chosen set of benchmark problems in the literature. Computational results indicate that the proposed bat algorithm is more efficient than the genetic algorithm and particle swarm optimisation.

Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. Furthermore, most scheduling problems which have been discussed in the literature are under the assumption that machines are continuously available. Nevertheless, in most real life industries, a machine can be unavailable for many reasons, such as unanticipated breakdowns, i.e., stochastic unavailability, or due to a scheduled preventive maintenance where the periods of unavailability are known in advance, i.e., deterministic unavailability. This paper deals with the hybrid flow shop scheduling problems in which there are sequence-dependent setup times, commonly known as the SDST, and machines which suffer stochastic breakdown to optimize objectives based on expected makespan. This type of production system is found in industries such as chemical, textile, metallurgical, printed circuit board, and automobile manufacture. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. The genetic algorithm can be used to tackle complex problems and produce a reasonable manufacturing schedule within an acceptable time. This paper describes how we can incorporate simulation into genetic algorithm approach to the scheduling of a SDST hybrid flow shop with machines that suffer stochastic breakdown. An overview of the hybrid flow shops and scheduling under stochastic unavailability of machines are presented. Subsequently, the details of incorporated simulation into genetic algorithm approach are described and implemented. Consequently, the results obtained are analyzed with Taguchi experimental design.

Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. Furthermore, most scheduling problems that have been discussed in the literature are under the assumption that machines are continuously available. Nevertheless, in most real-life industries a machine can be unavailable for many reasons, such as unanticipated breakdowns (stochastic unavailability), or due to scheduled preventive maintenance where the periods of unavailability are known in advance (deterministic unavailability). This paper deals with hybrid flow shop scheduling problems in which there are sequence-dependent setup times (SDSTs), and machines suffer stochastic breakdowns, to optimise objectives based on the expected makespan. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. An immune algorithm (IA) can be used to tackle complex problems and produce a reasonable manufacturing schedule within an acceptable time. In this research, a computational method based on a clonal selection principle and an affinity maturation mechanism of the immune response is used. This paper describes how we can incorporate simulation into an immune algorithm for the scheduling of a SDST hybrid flow shop with machines that suffer stochastic breakdowns. The results obtained are analysed using a Taguchi experimental design.

This paper is survey of hybrid flow shop scheduling problems. An HFS scheduling problem is a classical flow-shop in which parallel machines are available to perform the same operation. Most real world scheduling problems are NP-hard in nature. The hybrid flow shop scheduling problems have received considerable research attention. The several optimization and heuristic solution procedures are available to solve a variety of hybrid flow shop scheduling problems. It discusses and reviews sustainability of several variants of the hybrid flow shop scheduling problem for economical analysis, each in turn considering different assumptions, constraints and objective functions. Sustainability is the long-term maintenance of responsibility, which analysis the economics and encompasses the concept of stewardship. The Hybrid flow shop problem has sustained for several decades with multi – objective constraints. The paper shows some fruitful directions for future research and opportunities in the area of hybrid flow shop.

This paper considers the characteristics of hybrid flow shop with energy saving. First of all, established the model of hybrid flow shop with energy saving problem. Then Lagrangian relaxation was proposed to solve the energy scheduling problem in hybrid flow shop. Lagrangian relaxation algorithm introduced precedence constraints into the objective function, and the original problem was decomposed into a series of parallel machine sub-problems. A dynamic programming algorithm was then designed to solve these sub-problems. The method of updating of multiples was sub-gradient algorithm. Lastly, a two stage heuristic approach was constructed to convert the infeasible solution into a feasible solution. Testing results demonstrated that the proposed method can generate near optimal schedules in an acceptable computational time.

This paper considers the characteristics of a hybrid flow shop with JIT technical constraints. Lagrangian relaxation is presented to solve the Earliness/Tardiness problem in the hybrid flow-shop. By introducing precedence constraints into the objective function, the original problem is decomposed into a series of parallel machine sub-problems and a dynamic programming algorithm is designed to solve these sub-problems. Heuristic approach is further applied to convert the infeasible solution into a feasible solution. Testing results demonstrated that the proposed method can generate near optimal schedules in an acceptable computational time.

Improved cuckoo search algorithm for hybrid flow shop scheduling problems to minimize makespan

This article investigates a hybrid flow shop scheduling problem that consists of a batch processor in the upstream and a discrete processor in the downstream. Limited waiting time between the batch processor and discrete processor is taken into consideration. Such a scheduling problem is commonly seen as bottlenecks in the production of precision parts, back-end process of semiconductor products, and glass and steel industries. A mixed-integer linear programming model is presented to minimize the makespan. Considering the complexity of this problem and the imperative requirement in real-time optimization, we first develop a constructive heuristic together with the worst case analysis by exploiting the key decision structure of the problem. Based on the decision structure, we then develop a learning-based scheduling approach via customized genetic programming to automatically generate effective heuristics for this problem. Lower bounds are also developed to provide a measurement for the performance of proposed algorithms. Numerical results show that our proposed algorithms outperform the existing metaheuristics and are capable of providing high-quality solutions using less computational time. Note to Practitioners —The production system consisting of a batch processor in the upstream and a discrete processor in the downstream is common in practice. The batch processor first handles a group of jobs simultaneously. Then, the jobs are released to a buffer to wait for the process on the discrete processor one by one. However, the waiting time of the jobs in the buffer is often required to be limited according to the production requirements. For example, after being heated in the heat-treatment oven, the aerospace precision parts have to be processed on the machining equipment in limited waiting time to improve the processability in subsequent manufacturing. The semiconductor chips have to be packed in limited waiting time after baking to avoid getting wet. The incongruous production modes between the batch processor and discrete processor, together with the limited waiting time constraint, make such operations always the bottleneck in manufacturing. Efficient heuristics, providing high-quality solutions with low time complexity, are much preferred in practice for most of the complicated scheduling problems, such as the scenarios described earlier. However, the designing process of an effective heuristic is tedious, and the heuristic is usually deeply customized for a certain production scenario. Genetic programming (GP) provides an inspiring approach to automatically generate sophisticated heuristics for complicated scheduling problems through evolutionary learning processes. By customizing a GP-based approach, the designing process of heuristics is automated, and some undetectable knowledge relations can be obtained to enhance the quality of heuristics. Such an approach facilitates to obtain more sophisticated schedules by analyzing valuable knowledge for smart manufacturing. The superiority of the heuristic learned by GP is shown in the computational experiment, and it has great potential to be applied to the practical scheduling.

<p indent="0mm">As a high-performance general-purpose form of parallel solvers, parallel algorithm portfolios (PAPs) have recently shown great performance for solving decision, counting, continuous, and discrete optimization problems. However, the manual construction of PAPs is laborious work, which typically requires substantial domain knowledge and human effort. To address this issue, this paper proposes AutoPAP, an evolutionary intelligence-based method for PAP construction. Overall, AutoPAP follows the (<italic>n</italic>+1) evolutionary framework, i.e., in each generation, <italic>n</italic> candidate algorithms are generated, and the best one among them is retained in the PAP. Considering that the algorithm configuration space is typically very large, this study designs a highly effective mutation operator to improve the practical performance of AutoPAP and further theoretically proves that AutoPAP can achieve (1−1/<italic>e</italic>) approximation. Finally, to validate the effectiveness of AutoPAP, this study uses it to build a PAP, namely, TSP_PAP, for traveling salesman problems (TSPs). The test results show that TSP_PAP significantly outperforms state-of-the-art TSP solvers EAX and LKH in terms of efficiency (runtime) and effectiveness (solution quality). On 128 TSP instances of sizes ranging from 1000 to 30000, compared with LKH and EAX, TSP_PAP can reduce the average runtime by at least 45.71% and lower the average deviation ratio by at least 87.50%, indicating the huge potential of AutoPAP in automatic algorithm design and evolution.

An effective co-evolutionary artificial bee colony algorithm for steelmaking-continuous casting scheduling

This research addresses scheduling problem of n jobs on a Hybrid Flow Shop (HFS) with unrelated parallel machines in each stage. A monolithic mixed integer linear programming (MILP) model is presented to minimize the maximum completion time (makespan). As the research problem is shown to be strongly NP-hard, a Lagrangian relaxation (LR) algorithm is developed to handle the HFS scheduling problem. We design two approaches, simplification of subproblems and dominance rules, to solve the subproblems which are generated in each iteration. For evaluation purposes, numerical experiments with small and large size problems are randomly generated with up to 50 jobs and four stages. The experimental results show that the Lagrangian relaxation approaches outperform the MILP model with respect to CPU time. Furthermore, from the results, it can be conclude that the simplification of subproblems shows slightly better solutions in comparison with dominance rules to solve the subproblems.

In this research, a bi-criteria group scheduling problem is investigated in a hybrid flow shop (HFS) environment, wherein the parallel machines are unrelated. The objective of the problem is to minimize a linear combination of the total weighted completion time being mindful of the producer and the total weighted tardiness being mindful of the customers. The underlying assumption is that the jobs are released into the system in dynamic times. The machine ready times are considered to be dynamic as well. Sequence-dependent setup times are required for changing the process between groups of jobs. The runtimes of jobs are assumed to be decreasing as the workers learn how to process similar jobs. A mixed-integer linear programing model is developed for the problem. However, since the problem is non-deterministic polynomial-time hard (NP-hard), it may not be solved to optimality within a reasonable time. This research comprehensively addresses the question of what type of meta-heuristic algorithm is more appropriate for solving these problems. In particular, local search algorithms are compared to the population-based algorithms with respect to the permutation or non-permutation properties of the optimal solution. Three algorithms based on tabu search as well as three algorithms based on simulated annealing are developed to represent the local search algorithms. Two other algorithms are developed based on genetic algorithm (GA) to exemplify the population-based algorithms. The results of a comprehensive experimental design reveal that GA-based algorithms have greater potential for identifying better quality solutions in HFS scheduling problems compared to the local search algorithms.

In this chapter, we consider some practical scheduling problems under unavailability constraints (breakdown periods, maintenance durations and/or setup times). Such problems can be met in different industrial environments and be associated to numerous real-life applications. This explains why many researchers have become interested in this subject. We aim to present the recent approaches proposed to solve these problems and to discuss their performances. This family of scheduling problems, addressed in this chapter, has been intensively studied (Kacem [8], Lee [17], Schmidt [24]). The studied criteria in this chapter are related to the flowtime minimization (the weighted and unweighted cases). The chapter is organized in two main parts. The first part focuses on the single machine scheduling problem (see Section 2). The second part is devoted to the parallel machine scheduling problem (see Section 3). In each part, we present the main contributions and explain their principles (complexity results, heuristic algorithms and their worstcase performance, existing approximation schemes, exact methods, branch-and-bound algorithms, dynamic programming, integer linear models, lower bounds. . .). Finally, Section 4 concludes the paper.

This paper addresses a real-life production scheduling problem with identical parallel machines, originating from a plant producing Acrylonitrile-Butadiene-Styrene (ABS) plate products. In the considered practical scheduling problem, ABS plate has some specific specifications and each specification has several different levels. Because there is at least one different level of specification between two ABS plate products, it is necessary to make a set-up adjustment on each machine whenever a switch occurs from processing one ABS plate product to another product. As tardiness leads to extra penalty costs and opportunity losses, the objective of minimising total tardiness has become one of the most important tasks for the schedule manager in the plant. The problem can be classified as an identical parallel machine scheduling problem to minimise the total tardiness. A dispatching rule is proposed for this problem and evaluated by comparing it with the current scheduling method and several existing approaches. Moreover, an iterated greedy-based metaheuristic is developed to further improve the initial solution. The experimental results show that the proposed metaheuristic can perform better than an existing tabu search algorithm, and obtain the optimal solution for small-sized problems and significantly improve the initial solutions for large-sized problems.

The research on the theory and method of single machine scheduling is a difficult subject, but it is very important for the companies to improve the production efficiency and effectiveness. The study on single machine scheduling problem has the history of 50 years, but there is still a gap between the classical scheduling theories and practical scheduling problems. According to this characteristic, the problems in practical scheduling area and the various factors need to be concerned are mentioned, and the main methods to solving the single machine scheduling problem and their applications are presented in details. Finally, the directions and suggestions of future work in single machine scheduling problem are summarized.