A three-level particle swarm optimization with variable neighbourhood search algorithm for the production scheduling problem with mould maintenance

Abstract

To improve the reliability of production systems in the plastics industry, researchers are now taking mould maintenance into consideration, besides machine maintenance, in the production scheduling problem. Different strategies and approaches have been proposed to solve the production scheduling with mould maintenance (PS-MM) problem. However, it remains a challenge to provide a satisfactory solution. In this research, a new hybrid metaheuristic algorithm (TLPSO-VNS algorithm) is proposed, which is a combination of the three-level particle swarm optimization (TLPSO) algorithm devised in this study and variable neighbourhood search (VNS). Differing from the joint scheduling strategies used in existing research, this study divides the integrated problem into three sub-problems and solves them through three interrelated PSOs named TLPSO. Then, the solutions obtained by TLPSO are enhanced by VNS. The key characteristics of TLPSO and VNS are employed simultaneously to achieve superior solutions in solving the addressed optimization problem. In the proposed hybrid algorithm, the TLPSO performs a global search whereas the VNS has a local search role. These two techniques complement each other to enhance the search diversification and intensification. Numerical experiments on a variety of simulated scenarios show the efficiency and effectiveness of the proposed algorithm by comparing it with other algorithms.

Introduction

Because of the special merits of plastics such as high strength, low price, light weight, and user-friendliness, plastics materials find extensive utilization in many industries and daily life [1]. Moreover, the plastics industry greatly contributes to the economy of many countries, such as the United States, through providing employment to a large number of people, and is regarded as the third largest manufacturing industry in the country [2]. The main process of converting plastics into products is by injection moulding, which needs both an injection machine and an injection mould. Since consumer demand for plastic products is reflected by the overall growth of plastics sales [2], more methods are being explored to improve the resource efficiency of the production process under new visions for the future, for example, the “smart factory” [3]. Furthermore, to realize production objectives and avoid production bottlenecks, production scheduling is planned in advance. A good production scheduling can ensure the efficient use of labour resources and guarantee a high machine utilization rate [4]. Many good algorithms are proposed for the scheduling problem [[5], [6], [7], [8]]. In most research studies on production scheduling, it is postulated that machines are always available throughout the whole production planning stage. However, in actual situations, this assumption may not be reasonable, because failure may occur at any time, making some machines unavailable for job processing [9]. So, machine maintenance planning is essential, and can enhance the reliability of the system. To maximize the system productivity, maintenance planning and production scheduling must be considered together, and be given the same importance level [10]. More and more scholars are paying attention to production scheduling with the machine maintenance problem, and different models which integrate production scheduling with machine maintenance planning have been built to optimize productivity by harmonizing both activities. However, only the machine maintenance is considered in traditional production scheduling with the resource maintenance problem and research on production scheduling with the mould maintenance problem is very limited. The injection mould is also a significant component in the plastics industry and the breakdowns caused by factors related to mould are even more than breakdowns caused by factors related to machine [11]. The plastics manufacturer needs to consider the condition of the mould to guarantee a good production efficiency. So the integrated problem with mould maintenance consideration should be given more attention.

Recently, a model [11] was built to integrate production scheduling with mould maintenance. Time-dependent deteriorating maintenance schemes for the machine and mould were used, and a joint scheduling strategy was proposed. This strategy decided production scheduling, machine maintenance, and mould maintenance simultaneously to minimize the overall makespan. The genetic algorithm (GA) approach was used to solve this problem. However, the maintenance planning found may not be the most appropriate one for the production scheduling, when production scheduling and resource maintenance planning are decided concurrently, since the local search ability of the genetic algorithm (GA) is limited. The mismatch between production scheduling and resource maintenance is underestimated, which may result in the low production efficiency. In addition, more efficient algorithms need to be found to improve the quality of the solutions.

To overcome the shortcomings of previous research and improve the overall production efficiency, this study proposes a problem decomposition mechanism to deal with the production scheduling with the mould maintenance (PS-MM) problem, and presents an effective and efficient hybrid metaheuristic algorithm: the TLPSO-VNS algorithm, which innovatively combines three-level particle swarm optimization (TLPSO) and variable neighbourhood search (VNS). Firstly, this integrated problem is divided into a basic production scheduling problem, a machine maintenance problem and a mould maintenance problem. To minimize the overall makespan, the production scheduling problem is considered first. The corresponding machine maintenance planning is decided after the production scheduling is determined. Once the production scheduling and machine maintenance are confirmed, the corresponding mould maintenance is determined. Every sub-problem is solved by one single particle swarm optimization (PSO) algorithm and these three PSOs are interrelated. Once good solutions are obtained by the three-level PSO (TLPSO), variable neighbourhood search (VNS) is applied to these solutions to conduct the local search. Seven types of neighbourhoods are designed, and they are changed systematically. The best solution is chosen as the final solution when all the processes finish. The proposed TLPSO-VNS algorithm is robust and can find high-quality solutions by effectively exchanging search intensification and diversification. To our knowledge, this algorithm is the first algorithm to hybridize TLPSO with VNS to solve the integrated problem, building on the advantages of these two individual metaheuristic components and overcoming the inherent limitations.

The reminder of this paper is organized as follows: Section 2 is a review of the literature on this topic, which provides an understanding of the previous research in this area, as well as providing a rationale for the choice of the topic in the present study. Section 3 restates the production scheduling with mould maintenance (PS-MM) problem. Section 4 proposes the TLPSO-VNS algorithm. Section 5 presents the computational results acquired and shows the superiority of the TLPSO-VNS algorithm. Section 6 provides the conclusions and suggestions for further research.