Mathematical Problems in Engineering

Volume 2016, Article ID 3763512, 13 pages

http://dx.doi.org/10.1155/2016/3763512

## An Extended Genetic Algorithm for Distributed Integration of Fuzzy Process Planning and Scheduling

School of Information, Zhejiang University of Finance and Economics, No. 18 Xueyuan Street, Xiasha, Hangzhou 310018, China

Received 23 July 2015; Accepted 14 March 2016

Academic Editor: David Bigaud

Copyright © 2016 Shuai Zhang 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

The distributed integration of process planning and scheduling (DIPPS) aims to simultaneously arrange the two most important manufacturing stages, process planning and scheduling, in a distributed manufacturing environment. Meanwhile, considering its advantage corresponding to actual situation, the triangle fuzzy number (TFN) is adopted in DIPPS to represent the machine processing and transportation time. In order to solve this problem and obtain the optimal or near-optimal solution, an extended genetic algorithm (EGA) with innovative three-class encoding method, improved crossover, and mutation strategies is proposed. Furthermore, a local enhancement strategy featuring machine replacement and order exchange is also added to strengthen the local search capability on the basic process of genetic algorithm. Through the verification of experiment, EGA achieves satisfactory results all in a very short period of time and demonstrates its powerful performance in dealing with the distributed integration of fuzzy process planning and scheduling (DIFPPS).

#### 1. Introduction

Nowadays in manufacturing fields, there are desperate needs for not only the integration of process planning and scheduling but also distributed manufacturing. On the one hand, although the conventional job shop scheduling problem (JSSP) is still a hotspot in the studies of manufacturing researchers and has great potential to make progress, its separation from process planning inevitably obstructs the improvement of manufacturing efficiency and disables it in tackling complicated manufacturing environment [1]; on the other hand, the distribution feature of resources such as raw materials, manpower, and technologies propels the enterprise to operate in a more decentralized way and has gradually drawn the attention of many researchers [2–4].

Besides these two concerns, there is also an urge to represent the processing time in manufacturing with fuzzy values. For instance, fuzzy job shop scheduling problem has become the main topic of production scheduling [5]. Due to the unpredictable conditions in realistic manufacturing and the different proficiency among manual workers, the processing time in manufacturing is variable in a certain range. However, in the traditional research, it is fixed to a precise value to facilitate the calculation. To a certain extent, the fixed value loses the flexibility and definitely cannot accord with the practice.

Under these circumstances, the distributed integration of processing planning and scheduling (DIPPS) is proposed first. For one thing, the DIPPS is on the basis of the integrated processing planning and scheduling (IPPS) which overcomes the deficiency of JSSP in integration; for another, it features distribution manufacturing to conform to the realistic manufacturing environment. In addition, considering the necessity of the fuzzy feature in the manufacturing and the distribution feature in the DIPPS, the fuzzy processing time and fuzzy transportation time are both introduced to replace the traditional fixed values and become an integral part of the whole model.

On the basis of the several enhanced parts, the distributed integration of fuzzy process planning and scheduling (DIFPPS) is thus formulated. In order to solve this problem effectively, we construct an upgraded genetic algorithm (EGA) with local enhancement strategy. The EGA has three-class chromosome to fully encode the complex information of DIFPPS, and it gets improved in both crossover and mutation strategies to reinforce the global exploration capability. Also, the local enhancement strategy is equipped in EGA to strengthen its local exploration capability by replacing the processing machines with more efficient ones and exchanging the processing order of some specific operations.

The rest of the paper is arranged as follows: in Section 2, we review the related work addressing IPPS and fuzzy processing time in manufacturing; in Section 3, the DIFPPS model is proposed, and the creative EGA is constructed to deal with it; in Section 4, a two-part experiment with a case study and several comparisons is conducted to demonstrate the capability of EGA in solving DIFPPS; in Section 5, we draw our conclusion.

#### 2. Related Work

In this paper, we mostly focus on formulating and solving the distributed IPPS model with fuzzy processing and fuzzy transportation time, that is, DIFPPS. In this case, the related work is divided into two parts: one is the related work in dealing with IPPS; and the other is the implementation of fuzzy theories in manufacturing. In these two parts, we mainly discuss the application of GA and its related algorithms.

##### 2.1. IPPS Related Work

By simultaneously arranging the process planning and scheduling, IPPS overcomes the scheduling-only deficiency of traditional JSSP and gradually inspires researchers to find the optimal or near-optimal solution with the assistance of various evolutionary algorithms. Mostly, genetic algorithm (GA) is a popular algorithm in tackling IPPS. For example, Shao et al. [6] adopted a modified GA-based approach by improving the genetic representations and operator schemes to solve IPPS. Li et al. [7] made the algorithm closer to the biological evolution by adding a learning operator to GA to record a certain amount of better solutions in the iterations. Zhang and Wong [8] constructed an object-coding GA with inferior selection and population degeneration mechanisms to strengthen the global exploration capability in dealing with IPPS. In order to further enhance the exploration capability, some other methods are also combined with GA to construct hybrid algorithms. For instance, Li et al. [9] combined GA with a local search strategy, and Yu et al. [10] used an additional particle swarm optimization to select the appropriate machines in the scheduling part. These combinations prevented GA from falling into local optima and have achieved better outcomes in the experiments than GA-only strategies.

Besides the above work that is based on GA, quite a number of researchers also adopted other evolutionary algorithms, such as simulated annealing algorithm [11], imperialist competitive algorithm [12], and ant colony algorithm [13], to deal with IPPS. In the experiment and case studies, they all demonstrated their outstanding performance.

However, despite their competence in solving IPPS, these algorithms still fall short of handling DIPPS due to the more complex information accompanying the distributed manufacturing.

##### 2.2. Fuzzy Processing Time in Manufacturing

The theory of fuzzy sets is first introduced by Zadeh [14] and then gets improved and popular in a variety of areas. In the manufacturing field, Sakawa and Kubota [15, 16] were among those who first proposed the fuzzy job shop scheduling problem (fJSSP) in which the triangular fuzzy number (TFN) is applied to represent the fuzzy processing time and fuzzy due date. In their work, the corresponding genetic algorithms are enhanced and achieved desirable results in solving the fJSSP. After the initial exploration, a number of researchers put their efforts in the fJSSP. Lei [5, 17, 18] tried not only a Pareto archive particle swarm optimization but also a random key scheduling algorithm which used a random key representation and the extended version of the first decoding to figure out an optimal solution for fJSSP. Niu et al. [19] redefined and modified the particle swarm optimization by introducing genetic operators to update the particles and then applied this algorithm to the fJSSP. Hu et al. [20] constructed a modified differential evolution algorithm for fJSSP after proposing the ranking concept among fuzzy numbers and several novel objective functions. Li and Pan [21] combined Tabu search with the particle swarm optimization in order to promote the latter one’s local search.

Moreover, the flexible job shop scheduling problem (FJSSP) which is more complicated than traditional JSSP in allowing an operation to be processed on any of the machines in a corresponding set along different routes is gradually equipped with fuzzy processing time [22]. To tackle the fuzzy flexible job shop scheduling problem (fFJSSP), Lei and Guo [23] proposed a swarm-based neighborhood search algorithm, in which they implemented a novel representation, two swaps, and insertion. Wang et al. [24] used a hybrid artificial bee colony algorithm with variable neighborhood search-based local search to enhance local exploitation in search of the optimal solution. Also, Palacios et al. [25] implemented two new neighborhood structures for the local search and proposed a genetic Tuba search for the fFJSSP. And Xu et al. [22] equipped a novel teaching-learning search mechanism with special local search operators in the solution-exploring procedure.

Furthermore, there are also some work focused on some congeneric NP-hard problems such as flow shop scheduling [26, 27] and the general formulated group shop scheduling [28] with fuzzy processing time. However, rare work has been done to discuss the fuzzy processing time in IPPS or even DIFPPS environment.

#### 3. An EGA for the DIFPPS

##### 3.1. Problem Definition and Representation

On the basis of the definition of IPPS problem, the DIPPS problem discussed in this paper is generalized as follows: given independent jobs and geographically distributed manufacturing cells (MCs), where each possesses machines and owns full capability to process every given job, determine the specific MC, manufacturing plan, and schedule for each job in consideration of the constraints and objective. Specifically, due to the diversity of equipment among different MCs, the optional plans and schedules for the same job are also different among MCs. Meanwhile, jobs are delivered to a central warehouse once they are completely manufactured in certain MCs.

Although there exist a variety of flexibilities in the manufacturing process [29, 30], processing flexibility that indicates the operation replaceability for the same feature in the job and operation flexibility that indicates the machine replaceability for the same operation are the major flexibilities adopted in the DIPPS problem. To represent the flexible plans and schedules for different jobs in each MC, the network that was introduced by Ho and Moodie [31] is applied as an example with two MCs and three jobs.

In a network graph (Figure 1), there are three node types in the network: starting node, intermediate node, and ending node [30]. The starting node and ending node labeled “B” and “C” are dummy nodes that denote the beginning and completion of a job, while the intermediate nodes labeled numbers indicate the specific operations with alternative machines that may be done in the processing procedure. From the beginning to the completion node, the arrows connecting the nodes represent the precedence of operations [31]. Besides, the OR-links joining the arrows indicate the processing flexibility. If the links following a node are connected by an “OR” symbol, we only need to traverse one of them [31]. Thus, a job processing procedure is perfectly illustrated by a network. In Figure 1, six networks exhibit the flexible plans and schedules of three jobs in two MCs, respectively.