Computational Intelligence and Neuroscience

Volume 2019, Article ID 4787856, 16 pages

https://doi.org/10.1155/2019/4787856

## Solving the Manufacturing Cell Design Problem through Binary Cat Swarm Optimization with Dynamic Mixture Ratios

^{1}Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile^{2}Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso 2390123, Chile^{3}Universidad Diego Portales, Av. Ejército 441, Santiago 8370109, Chile^{4}Universidad de Valparaíso, General Cruz 222, Valparaíso 2603631, Chile

Correspondence should be addressed to Hanns de la Fuente-Mella; lc.vcup@etneufaled.snnah

Received 29 October 2018; Revised 11 January 2019; Accepted 14 January 2019; Published 14 February 2019

Academic Editor: Oscar Castillo

Copyright © 2019 Ricardo Soto 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

In this research, we present a Binary Cat Swarm Optimization for solving the Manufacturing Cell Design Problem (MCDP). This problem divides an industrial production plant into a certain number of cells. Each cell contains machines with similar types of processes or part families. The goal is to identify a cell organization in such a way that the transportation of the different parts between cells is minimized. The organization of these cells is performed through Cat Swarm Optimization, which is a recent swarm metaheuristic technique based on the behavior of cats. In that technique, cats have two modes of behavior: seeking mode and tracing mode, selected from a mixture ratio. For experimental purposes, a version of the Autonomous Search algorithm was developed with dynamic mixture ratios. The experimental results for both normal Binary Cat Swarm Optimization (BCSO) and Autonomous Search BCSO reach all global optimums, both for a set of 90 instances with known optima, and for a set of 35 new instances with 13 known optima.

#### 1. Introduction

Group technology is a manufacturing philosophy in which similar parts are identified and grouped together to take advantage of their similarities in design and production [1] by organizing similar parts into part families, where each part of the family has similar design and manufacturing characteristics. The basic concept of group technology has been practiced for many years around the world, as part of good engineering and scientific management practices [2, 3], which states that similar things should be manufactured in a similar way [4].

The Manufacturing Cell Design Problem (MCDP) is an application of group technology to organize cells containing a set of machines to process a family of parts [5]. In this context, MCDP involves the creation of an optimal design of production plants, in which the main objective is to minimize the movement and exchange of material between these cells, thus generating greater productivity and reducing production costs.

The Manufacturing Cell Design Problem belongs to the complex NP-hard class of problems, and then exploring good search algorithms is always a challenging task from the optimization and now also from the artificial intelligence world [5]. In particular, in this paper, an efficient metaheuristic implementation is proposed to tackle this problem, demonstrating through several benchmark instances its performance (various global optima are reached), which is also valuable from an artificial intelligence and optimization standpoint. Additionally, this algorithm includes an Autonomous Search Component (dynamic mixture ratio), which is currently an important research trend in the optimization and metaheuristic sphere. Metaheuristics are intrinsically complex to be configured in order to reach good results, and Autonomous Search comes to facilitate this task by letting the metaheuristic itself to self-tune its internal configuration without the need of a user expert for reaching good results. To the best of our knowledge, the work done on Autonomous Search in metaheuristics is very recent, and no Autonomous Search work for cat swarm exists.

The research work that has been done to solve the problem of cell formation has followed two complementary lines, which can be organized into two groups: approximate methods and exact methods. Approximate methods are mostly focused on finding an optimal solution in a limited time; however, they do not guarantee a global optimum. Exact methods, on the contrary, aim to fully analyze the search space to ensure a global optimum [6]; however, these algorithms are quite time-consuming and can only solve cases of very limited size. For this reason, many research efforts have focused on the development of heuristics, which find near-optimal solutions within a reasonable period of time.

This research focuses on solving the MCDP through a recent metaheuristic in the vein of Swarm Intelligence (SI) [7] called Binary Cat Swarm Optimization (BCSO) [8]. This algorithm was generated from observations of cat behavior in nature, in which cats either hunt or remain alert. BCSO is based on the CSO algorithm, recently proposed by Chu and Tsai [9]. The difference is that in BCSO, the vector position consists of ones and zeros, instead of real numbers (CSO), and the proposed alternate version makes use of a dynamic mixture ratio.

As aforementioned, reaching good results for problems belonging from the NP class is always a challenging and appealing task from the optimization and artificial intelligence world. In this research, our goal was to provide an intelligent algorithm for solving this problem by additionally integrating self-tuning features, which is a very recent research trend in the optimization and metaheuristic sphere.

#### 2. Theoretical Framework

The formation of manufacturing cells has been researched for many years. One of the first investigations focused on resolving this set of problems was Burbidge’s work in 1963 [4], which proposed the use of an incidence matrix reorganized into a Block Diagonal Form (BDF) [4]. In recent years, many exact and heuristic algorithms have been proposed in the literature to solve MCDP. Such metaheuristic techniques include genetic Algorithm (GA) [10], inspired by biological evolution and its genetic-molecular basis; the Neural Network (NN) [11] that takes the behavior of neurons and the connections of the human brain; and Constraint Programming (CP) [12] where the relationships between the variables are expressed as constraints. For extensive reviews of previous research and other methods of cell formation, see Selim et al. [1].

Among the metaheuristics used for cell formation, there is also the branch of Swarm Intelligence, which was initially introduced by Beni and Wang in 1989 [13]. Inspired by nature, Swarm Intelligence systems are typically formed by a population of simple agents who interact locally with each other and with their environment and who are able to optimize an overall objective through the search for collaboration in a space [14]. Within this branch, the main techniques are Particle Swarm Optimization (PSO) designed and presented by Eberhart et al. [7, 9] in 1995; Ant Colony Optimization (ACO), which is a family of algorithms derived from Dorigo’s 1991 work based on the social behavior of ants [15, 16]; Migrating Birds Optimization (MBO) [17] algorithm based on the alignment of migratory birds during flight; Artificial Fish Swarm Algorithm (AFSA) [18], based on the behavior of fish to find food by themselves or by following other fish; and the discrete Cat Swarm optimization (CSO) Technique presented in 2007 by Chu and Tsai [9], which is based on the behavior of cats. Interestingly, the CSO cat corresponds to a particle in PSO, with a small difference in its algorithms [19, 20]. CSO and PSO were originally developed for continuous value spaces, but there are a number of optimization problems where the values are discrete [21].

#### 3. The Manufacturing Cell Design Problem

The Manufacturing Cell Design Problem (MCDP) divides an industrial production plant into a number of cells. Each cell contains machines with similar process types or part families, determined according to the similarity between parts [4]. A manufacturing cell can be defined as an independent group of functionally different machines, located together, dedicated to the manufacture of a family of similar parts. In addition, a family of parts can be defined as a collection of parts that are similar, either because of their geometric shape and size or because similar processing steps are required to manufacture them [22].

The goal of MCDP is to identify a cell organization in a way that minimizes the transport of different parts between cells, in order to reduce production costs and increase productivity. The idea is to represent the processing requirements of machine parts through an incidence matrix called machine part. This reorganization involves the formulation of two new matrices called machine-cell and part-cell.

A detailed mathematical definition of the formulation of the machine-part clustering problem is defined by the optimization model explained below [6]:(i)*:* number of machines(ii)*:* number of parts(iii): number of cells(iv): machine index ()(v): part index ()(vi): cell index ()(vii): maximum number of machines per cell(viii): machine-to-part binary incidence matrix, where(ix): machine-to-part binary incidence matrix, where(x): machine-to-part binary incidence matrix, where

#### 4. Binary Cat Swarm Optimization

There are about thirty different species of known felines, e.g., lions, tigers, leopards, common housecat, etc. [23]. Although they have different living environments, cats share similar behavioral patterns [24]. For wild cats, the ability to hunt ensures food supply and survival of the species [25]. To hunt their food, wild cats form groups ranging from 2–15 individuals [26]. Domestic cats also show the same ability to hunt and are curious about moving objects [26–28]. Although cats might seem to be resting most of the time, even when awake [29, 30], they are actually in a constant state of alert; without moving, they may be listening or have their eyes open to look around [31]. BCSO [8] was formulated on the basis of all these behaviors and is an optimization algorithm that mimics the natural behavior of cats [9, 32, 33]. The authors identified two main modes of behavior for simulating cats [3, 34–39]:(i)Seeking mode: exploration-oriented mode, where cats are attracted by moving objects and have a high hunting capacity. Cats may seem to spend most of their time resting, but in fact, they are constantly alert when moving slowly.(ii)Tracing mode: exploitation-oriented mode, where cats detect a prey and run after it, spending a lot of energy due to its rapid movements. In this way, the cats follow the best in their group.

In BCSO, these two behaviors are mathematically modeled to solve complex optimization problems. The first decision is to define the number of cats needed for each iteration. Each cat, represented by cat_{k}, where , has its own position consisting of *M* dimensions composed of ones and zeros (1 and 0). In addition, they have speed for each dimension *d*, a flag to indicate whether the cat is in the seeking or tracing mode, and finally a fitness value that is calculated based on the MCDP. The BCSO keeps looking for the best solution until iterations are finalized. In BCSO, each cat_{x} represents a MCDP solution through a machine-cell matrix, where *x* identifies the cat and *d* are the position bits of the cat. In addition, the constraint matrix ensures that each row *i* is covered by at least one column.

Algorithm 1 describes the general BCSO pseudocode where the mixture ratio (MR) is a percentage that determines the number of cats in the seeking mode.