Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 685824, 9 pages

http://dx.doi.org/10.1155/2015/685824

## A Novel Assembly Line Scheduling Algorithm Based on CE-PSO

^{1}Key Laboratory of Intelligent Manufacturing and Robotics, School of Mechatronic Engineering and Automation, Shanghai University, Mailbox 232, No. 149 Yanchang Road, Shanghai 200072, China^{2}Shanghai Institute of Radio Equipment, Shanghai 200090, China

Received 24 September 2014; Accepted 5 December 2014

Academic Editor: Trung Nguyen-Thoi

Copyright © 2015 Xiaomei Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With the widespread application of assembly line in enterprises, assembly line scheduling is an important problem in the production since it directly affects the productivity of the whole manufacturing system. The mathematical model of assembly line scheduling problem is put forward and key data are confirmed. A double objective optimization model based on equipment utilization and delivery time loss is built, and optimization solution strategy is described. Based on the idea of solution strategy, assembly line scheduling algorithm based on CE-PSO is proposed to overcome the shortcomings of the standard PSO. Through the simulation experiments of two examples, the validity of the assembly line scheduling algorithm based on CE-PSO is proved.

#### 1. Introduction

With the rapid development of economy and technology, there is a trend of diversification in manufacturing companies [1]. In order to meet this tendency, many advanced manufacturing modes, such as just-in-time (JIT), material requirements planning (MRP), manufacturing resource planning (MRPII), enterprise resource planning (ERP), and computer integrated manufacturing (CIM), are proposed [2]. Computer integrated manufacturing system (CIMS) based on the combination of new production organization principles and concepts is one of new production models [3]. Many examples prove that successful application of CIMS in manufacturing enterprises has brought huge improvement to the production, operation, and management of enterprises [4]. The assembly line scheduling is one of the difficult problems in the application of CIMS [5, 6].

In the actual production process, enterprises may achieve the make-to-order (MTO) thought balancing the flexible production planning and controlling the production management. Since an excellent schedule of assembly line is able to meet the need of market, which is also the requirement of JIT, the assembly line planning and scheduling has become an important means for the enterprise to save resources, reduce costs, increase productivity, and improve the overall operational efficiency [7, 8].

Assembly line scheduling is a nondeterministic polynomial (NP) complete problem. With the development of heuristic algorithm, many advanced algorithms, such as genetic algorithm and ant colony (AC) algorithm, are applied to solve the scheduling problem [9, 10]. The paper [11] defines the production scheduling as a function of technical process and workpiece delivery from the perspective of production tasks and orders. In order to solve the problem of the production line scheduling in the MTO enterprise, the paper [12] establishes a general model of the MTO enterprise scheduling by applying the theory of linear programming MTO enterprises based on the analysis of its scheduling features and the stipulation of the scheduling. The adaptive genetic algorithms for solving scheduling model are proposed. The paper [13] introduces the concept of advanced planning and scheduling in order to study the problem of the production planning and scheduling which exists in discrete manufacturing. Through analyzing and applying the core ideas of the concept which is comparative advantage of constraints theory, the paper builds the advanced scheduling model based on machine capacity by applying the linear programming algorithm. Although there is a great development in the area of the production scheduling, no systematical methods and theories can solve all the assembly line scheduling application problem because of a huge gap between theoretical research and practical application. Particularly with the widespread adoption of JIT in the scheduling problems, the delivery just-in-time becomes increasingly important. In practical application, the scheduling method can respond to the dynamics of the system, but the result of the method is not guaranteed. Some methods of scheduling can theoretically provide optimal scheduling, but these often can only solve the problem of single target due to its computational complexity.

In this paper, a multiobjective optimization function based on equipment utilization and delivery time loss is constructed and a Catfish Effect (CE) Particle Swarm Optimization (PSO) algorithm is applied to solve the assembly line scheduling problem in view of its high solution precision and good robustness [14].

#### 2. Related Work

##### 2.1. PSO Algorithm

The Particle Swarm Optimization (PSO) is an evolutionary computation developed by Zeng and Cui [15]. It simulated the social swarm behavior of bird group in the early time. PSO treats each individual as a particle which has no weight and volume in dimensional search space and the particle flies at a certain speed in the search space. The speed is dynamically adjusted based on the flying experience of individual and group [16].

In the dimensional search space, express a current position of particle .

express the speed; is the current speed of particle .

express the best experiencing position of particle ; namely, has the smallest fitness.

Assume that is the minimized objective function; the best position of particle is calculated as follows [17]:

Assume that the number of particles is in population; all particles have experienced the best position ; then [18]

PSO algorithm basic solving equations are as follows [19].

Speed and position evolution equations are shown as

In (3), and are the acceleration constants, which take the value in . and both are a random number between ; is inertia coefficient between and it has the ability of keeping inertia expansion of particle movement to explore new areas.

PSO was developed and used as a useful computation technique to tackle the optimization problem. However, in PSO algorithm, particles seek the optimal solution by its own memory ability and the information shared among particles. At the beginning of PSO algorithm, the particles have quick convergence speed. When most of the particles have similar state with the passage of time, the convergence speed of the particles becomes slow, which maybe leads to the algorithm into a local optimal solution. This is also called “precocious phenomena” [20].

As the optimization performance of the original PSO algorithm is not ideal, various revised versions of PSO have been studied to overcome “precocious phenomena.” The related work includes modifying the updating formula, introducing new operator into PSO, and developing hybrid PSO algorithm [21]. Currently, chaos PSO algorithm, genetic PSO algorithm, immune PSO algorithm in adaptive, and bee evolutionary PSO algorithm are studied to improve the diversity of particle population and guide directions to research [22, 23]. With the continuous improvement, PSO algorithm has been used in many fields because of its simple concept, easy implementation, few parameters to tune, and excellent optimization ability.

##### 2.2. Catfish Effect PSO

Most of advanced PSO algorithms aim to modify the position coordinates of individual particles, instead of the population. However, Catfish Effect PSO (CE-PSO) algorithm can modify the position coordinates of the population to obtain the noninferior set on behalf of the entire solution space, homogeneous distribution, and immediate Pareto front and improve convergence velocity of PSO algorithm [24].

Catfish Effect (CE) refers to the effect that a strong competitor called catfish has in causing the weak sardines to better themselves. CE mechanism is the fact that the algorithm introduces dynamic and competitive individuals into the population to change social loafing and inspire community [25]. In the framework of CE mechanism, three core elements are as follows.(1)The population has been at a relatively stable level, and the catfish particle needs to be introduced to achieve the population objectives.(2)The catfish particle has high quality and individual competitiveness in the population.(3)The catfish particle can use negative incentives to enhance population vitality.

Different from PSO algorithm, speed evolution equations of CE-PSO algorithm are shown as

In (4), is a threshold value of population diversity and is a function which is used to evaluate the population diversity at the time . If , the diversity of the population is poor and catfish particle is introduced into population; if , CE-PSO algorithm and PSO algorithm have the identical definition.

The effect of CE to PSO algorithm is shown in Figure 1. Compared with PSO algorithm, CE-PSO algorithm monitors the diversity of the population [26]. When the diversity is poor, CE-PSO algorithm introduces the catfish particle with the driving role to encourage population activity and maintain the population diversity [27]. In order to improve the search performance, CE-PSO algorithm can regulate flight mode of sardine particles dynamically according to the convergence of catfish [28].