Mathematical Problems in Engineering

Volume 2018, Article ID 3407646, 14 pages

https://doi.org/10.1155/2018/3407646

## Optimum Assembly Sequence Planning System Using Discrete Artificial Bee Colony Algorithm

^{1}Department of Industrial Design Engineering, Erciyes University, Kayseri 38030, Turkey^{2}Department of Biomedical Engineering, Erciyes University, Kayseri 38030, Turkey^{3}Software’s Functional Management Branch Office, Turkish Air Force, Ankara 06580, Turkey

Correspondence should be addressed to Turgay Batbat; rt.ude.seyicre@tabtabyagrut

Received 20 November 2017; Revised 13 February 2018; Accepted 6 March 2018; Published 12 April 2018

Academic Editor: Abhishek K. Gupta

Copyright © 2018 Özkan Özmen 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

Assembly refers both to the process of combining parts to create a structure and to the product resulting therefrom. The complexity of this process increases with the number of pieces in the assembly. This paper presents the assembly planning system design (APSD) program, a computer program developed based on a matrix-based approach and the discrete artificial bee colony (DABC) algorithm, which determines the optimum assembly sequence among numerous feasible assembly sequences (FAS). Specifically, the assembly sequences of three-dimensional (3D) parts prepared in the computer-aided design (CAD) software AutoCAD are first coded using the matrix-based methodology and the resulting FAS are assessed and the optimum assembly sequence is selected according to the assembly time optimisation criterion using DABC. The results of comparison of the performance of the proposed method with other methods proposed in the literature verify its superiority in finding the sequence with the lowest overall time. Further, examination of the results of application of APSD to assemblies consisting of parts in different numbers and shapes shows that it can select the optimum sequence from among hundreds of FAS.

#### 1. Introduction

With increasing international competition, efficient methods for manufacturing and producing goods at low cost are essential. This is particularly important in the manufacturing sector, where products are designed, assembled, and simulated with the aid of computers before they are produced. Assembly, the process of combining parts to create a structure or the result of this operation, is also the name given to the product. Assembly sequence planning (ASP) is a very complicated procedure which becomes more difficult as the number of parts increases, as this results in more complexities. These complexities in assembly processes necessitate that assembly sequences be well planned and thoroughly scrutinized. Hence, research is actively being conducted in this field with the objective of developing an ideal method for ASP [1–3].

In this paper, assembly planning system design (APSD), a computer program developed based on a previously proposed matrix-based approach and the discrete artificial bee colony (DABC) algorithm, is proposed for automatically generating assembly sequences and determining the optimum sequence without user intervention. The program runs on the computer-aided design (CAD) software AutoCAD using the visual basics for applications (VBA) module and a CAD database. APSD can also work with data from other 3D CAD software programs by first converting it from the 3D CAD data of those software into dwg or ACIS data format. With the capability of counting, identifying, and labelling the components of a 3D model, APSD can automatically determine the relations between parts in terms of contact and translational functions. In the software, these relations are represented in matrix form and used to evaluate assembly sequences for automatic sequence generation and determination of whether connected parts can form a feasible assembly. Then, according to the assembly time criterion, an optimum assembly sequence is selected from the feasible assembly sequences (FAS). DABC algorithm is used for optimisation and compared with the literature to evaluate the performance.

#### 2. Literature Review

Initially, products sequencing planning in assembly lines was performed manually. However, with the development of related software and solid modelling programs, the first solid models of assembly products were developed in CAD programs. Subsequently, by means of various theorems, their assembly sequencing was determined. Finally, the optimum ordering was investigated.

The idea of combining assembly modelling with the 3D model of a product using a feature-based method was first introduced by Eng et al. [4]. Their primary approach involved using disassembly to determine the assembly. More specifically, they used the degree of freedom between two features of connected parts to distinguish kinematic conditions, boundary box control to determine collisions, and user interaction to set the restrictions on precedence relations. In another feature-based study, Zha and Du [5] used STEP standards to show modelling information and to manage and convert that information into assembly data. They proposed an assembly editor that could differentiate all feature connections and generate assembly sequences based on feature identification techniques. However, in their system, information on the location and liaison relations between parts must be detected for the automatic generation of the assembly sequences. This was for the purpose of moving parts along the axes of the Cartesian coordinate system in a CAD environment in order to diagnose the intersections between the parts and generate the assembly sequences. This idea was also utilised by Gottipolu and Ghosh [6] to detect the relational information between parts based on a geometric model of the assembly. In their approach, for every couple, the contact relations and disassembly orientations between parts along the coordinate axes are described in terms of two functions: contact and translational. The feasibility of the assemblies are then examined under two compulsory conditions with the implementation of logical operations: connectivity and precedence constraints. Then, after assessing all the numerous feasible sequences, the optimum sequences are shown as a table of assembly states and assembly tasks in a hierarchical fashion, starting from individual parts in the unassembled state to the completed assembly. This assembly sequence table is also supplied with revised features to use strategic constraints under several quantitative and qualitative criteria for analysis of suitable sequences and to determine the final sequence [7].

Lee and Kumara [8] proposed an approach for analysis and efficient production of the assembly sequencing of a complex assembly design before its schematic design stage. In their approach, every part is disassembled and recorded in a sweeping table. Then, assembly and disassembly sequences are produced using matrices and sweeping tables. Dini and Santochi [9] proposed a method based on a mathematical model of the product obtained by determination of three matrices (interaction, contact, and connection). For each subassembly and product, all the possible assembly sequences are produced and the matrix numbers reduced depending on specified optimisation criteria. Zhang et al. [10] developed a procedure for automatic production of all appropriate assembly sequences for the assembly of the body of a car. Their developed procedure is based on the mathematical model of the car body obtained through its connecting and matching matrices, which represent the precedence constraints between the components and the subassembly. Possible subassemblies are then automatically determined on the basis of whether they satisfy specified mathematical conditions. Ciszak [11] proposed a new concept based on graph theory and heuristic multipurpose optimisation that utilises two kinds of matrices (collision and assembly) to generate assembly sequences. Wu et al. [12] proposed an approach that employs assembly knowledge to ASP problems and presented an appropriate method for articulating geometric information and nongeometric knowledge. In their proposed approach, an assembly connection graph is built based on knowledge in the engineering, design, and manufacturing areas. Complicated and low-performance calculations in the assembly design process are bypassed in their approach, which they demonstrated via an assembly planning example.

Depending on the geometry and number of parts in an assembly, hundreds or even thousands of FAS can exist. Determining the optimum assembly sequence from among these FAS is a major issue. Various researchers are currently actively searching for solutions to this problem using artificial intelligence algorithms. For example, Guo et al. [13] proposed an approach based on the shuffled frog leaping algorithm to optimise the ASP of maintenance activities in radioactive environments. In their proposed approach, the geometrical feasibility of the assembly sequences is tested with the help of interference matrices along six axes. Further, to evaluate the fitness function, assembly directional and gripper changes are made. Experimental results indicated that their proposed method yielded better results than approaches based on classical genetic algorithm and particle swarm optimisation. Motavalli and Islam [14] proposed a multicriteria algorithm to find the best assembly sequence among all FAS based on simulated annealing (SA). Their proposed multicriteria algorithm considers both the assembly time and reorientation to find the optimum sequence. Subsequently, Choi et al. [15] applied genetic algorithm (GA) to the problem and obtained better results than using SA. Further, Karthik and Deb [16] compared GA and an hybrid cuckoo-search genetic algorithm (CS-GA) and found that they resulted in the same assembly time. In addition, Mukred et al. [17] applied the particle swarm algorithm (PSA) and the binary particle swarm algorithm (BPSA) to the same problem and found that PSA produced the optimised solution with the shorter assembly time.

#### 3. Mathematical Model

In this section, our proposed mathematical model is explained from three aspects: minimisation of assembly time, reorientation, and matrix-based assembly sequencing [15, 18]. Minimum assembly time and cost are achieved by considering factors that play a major role, such as the setup time, transfer time, number of tool changes, and proper fixture selection. Therefore, to evaluate the performance of DABC, the following two criteria are discussed: minimisation of assembly time, including setup and actual assembly; minimisation of the number of reorientations to satisfy geometrical constraints, as the parts or subassemblies to be assembled could differ in terms of geometry. When the DABC algorithm is considered in APSD, only assembly time is considered.

##### 3.1. Minimisation of Assembly Time

Assembly time consists of setup time and actual assembly time, which is assumed to be always constant regardless of the sequence. Every component of an assembly demands proper setup. The setup time depends on the geometry of the component itself and the components assembled previously. The following function can be used to predict the setup time for a component:where is component to be assembled, is setup time for product being the first component in the assembly, is contribution to the setup time due to the presence of part when entering part , 1, if component has already assembled, for ; 0, otherwise, for

The total assembly time is the summation of the setup time and actual assembly time:where is the assembly time for component The objective function for minimising the assembly time is as follows:

##### 3.2. Reorientations and Combined Objective Function

There are certain geometric relations between each part in an assemble. Some intermediate assembly may need reorientation in order to get the parts assembled in a particular sequence. The target here is to minimise the number of reorientations. The total number of reorientations necessary during the assembly of a part is a function of the geometry of the part and the subassembly. Reorientation is defined as follows:The total number of reorientations is given byThus, .

A multicriteria utility function is used to describe two combined objective functions ( and ). Thus, the combined objective function (COF) is as follows:where is the combined objective function, is the weight of the individual functions, and is 1 or 2. The weight of the function depends on the strategy followed and expert opinion. In this study, and were used to evaluate the performance of the DABC algorithm. Further, only the function was considered in the APSD program.

##### 3.3. The Matrix-Based ASP Method

The proposed approach for the determination of assembly sequences begins with creation of a CAD assembly model. The assembled parts generated in the CAD medium are sufficient for geometric knowledge but not for assembly planning. The data pertaining to the parts created in the CAD environment are used as input to the assembly planning system. Then, a matrix-based mathematical model is formed and, finally, its assembly sequence is determined by means of Boolean algebra [6, 18]. The theorem is explained below based on the wheel of a shopping cart, as exemplified in Figure 1.