A PSO-based approach to cell formation problems with alternative process routings

Group technology (GT) has been extensively applied to cellular manufacturing system (CMS) design for decades due to many benefits such as decreased number of part movements among cells and increased machine utilisation in cells. This paper considers cell formation problems with alternative process routings and proposes a discrete particle swarm optimisation (PSO) approach to minimise the number of exceptional parts outside machine cells. The approach contains two main steps: machine partition and part-routing assignment. Through inheritance and random search, the proposed algorithm can effectively partition machines into different cells with consideration of multiple part process routings. The computational results are compared with those obtained by using simulated annealing (SA)-based and tabu search (TS)-based algorithms. Experimental results demonstrate that the proposed algorithm can find equal or fewer exceptional elements than existing algorithms for most of the test problems selected from the literature. Moreover, the proposed algorithm is further tailed to incorporate various production factors in order to extend its applicability. Four sample cases are tested and the results suggest that the algorithm is capable of solving more practical cell formation problems.     

Complete and fractional cell formation using Kohonen self-organizing map networks in a cellular manufacturing system

The primary objective of group technology (GT) is to enhance the productivity in batch manufacturing environment. The GT cell formation and fractional cell formation are done by using Kohonen self-organizing map (KSOM) networks. The effectiveness of the cell formation is measured with number of exceptional elements, bottleneck parts and grouping efficiency and the effectiveness of the fractional cell formation is measured by number of exceptional elements and the number of machines in the reminder cell. This method is applied to the known benchmarked problems found in the literature and it is found to be equal or best when compared to the other algorithms in terms of minimizing the number of the exceptional elements. The relative merits of using this method with respect to other known algorithms/heuristics in terms of computational speed and consistency are presented.     

AN ASSIGNMENT METHOD FOR THE PART-MACHINE CELL FORMATION PROBLEM IN THE PRESENCE OF MULTIPLE PROCESS ROUTES

This paper considers the part-machine cell formation decision of the generalized Group Technology (GT) problem in which multiple process routes can be generated for each part. The existing p-median model and similarity coefficient algorithm can solve only small-sized or well-structured cases. An assignment method for the cell formation problem is suggested. This method uses an assignment model which is a simple linear programming. Numerical examples show that the assignment method provides good separable cell formation even for large-sized and ill-structured problems.     

GT cell formation for minimizing the intercell parts flow

A methodology is proposed to design a GT cell by considering the intercell parts flow in GT cellular manufacturing systems. The problem of GT cell formation is described in a graph using the quantities to be produced in the specified time period and the process routes for producing the products. The objective of this paper is to minimize the total number of parts produced in more than one cell. The problem, formulated as a quadratic assignment problem (QAP), is solved using both Lagrangean relaxation technique and the optimality conditions of quadratic program. Furthermore, in order to obtain the giobal optimal solution rather than the local optimal solution, a branch-and-bound algorithm is employed. Finally, numerical examples are used to show the effectiveness of the solution techniques and GT cell formation procedure. Moreover, a computer simulation is presented, showing the effectiveness of cellular manufacturing systems     

GT efficacy: a performance measure for cell formation with sequence data

Cell formation in cell manufacturing design is a crucial step for improving productivity. As input data for the cell formation problem, a part-machine incidence matrix is given in binary format or in ordinal format. The solutions for effective cell formation have to be compared using performance measures. Grouping efficacy is used as a standard measure for evaluating solutions based on a binary part-machine matrix, which does not consider ordinal data. However, the representative measures, called standard measures, for the ordinal part-machine matrix are absent. The existing measures designed for ordinal data produce conflicting results and can lead to subjective decisions. In this paper, a new objective measure called group technology (GT) efficacy is proposed for ordinal data, reflecting on both intercellular movement and compactness within cells simultaneously. The advantage of GT efficacy is demonstrated by comparing it with a few previously-proposed measures.     

Fractional cell formation in group technology

Group Technology (GT) aims at improving productivity in batch manufacturing. Here components are divided into families and machines into cells such that every component in a part family visits maximum number of machines in the assigned cell with an objective of minimizing inter-cell movement. In situations where too many inter-cell moves exist, fractional cell formation using remainder cells can be used. Here, machines are grouped into GT cells and a remainder cell, which functions like a job shop. Component families are formed such that the components visit the assigned cell and the remainder cell and do not visit other cells. The fractional cell formation problem to minimise inter-cell moves is formulated as a linear integer programming problem. Here, movement between machine cells and remainder cells is not counted as inter-cell moves but movement of components among GT cells is considered as inter-cell movement. The fractional cell formation problem is solved using Simulated Annealing. A heuristic algorithm is developed to solve large sized GT matrices. These have applied to a variety of matrices from GT literature and tested on randomly generated matrices. Computational experiences with the algorithms are presented     

A general search algorithm for cell formation in group technology

Group Technology (GT) is a manufacturing approach, which organizes and uses the information about an item's similarity (parts and/or machines) to enhance efficiency and effectiveness of batch manufacturing systems. The application of group technology to manufacturing requires the identification of part families and formation of associated machine-cells. One approach is the Similarity Coefficient Method (SCM), an effective clustering technique for forming machine cells. SCM involves a hierarchical machine grouping process in accordance with computed ‘similarity coefficients’. While SCM is capable of incorporating manufacturing data into the machine-part grouping process, it is very sensitive to the data to be clustered (Chan and Milner 1982). It has been argued that for SCM to be meaningful, all machines must process approximately the same numbers of parts (Chan and Milner 1982).We present a new approach, based on artificial intelligence principles, to overcome some of these problems by incorporating an evaluation function into the grouping process. Our goal is to provide a method that is both practical and flexible in its use for the process of cell formation. Our method uses the similarity matrix to generate the feasible machine groups. Then an evaluation function is applied to select a machine-cell arrangement through an iterative process. The approach features a graph-based representation (N-tuple) to represent the problem and illustrate the solution strategies. Also, we develop an algorithm to search for the most promising machine groups from the graph. Compared with Single Linkage Clustering and Average Linkage Clustering approaches, our approach attains comparable or better results     

Design and scheduling of hybridmulti-cell flexible manufacturing systems

The objective of this paper is to minimize machine duplication by increasing its utilization, minimize intercell moves, simplify the scheduling problem and increase the flexibility of the manufacturing system. An integrated approach of design and scheduling alternative hybrid multi-cell flexible manufacturing systems (MCFMSs) in four steps will be presented in this paper. The first step is the implementation of branch and bound techniques which provide tools to design group technology (GT) cells. The second step is balancing the inter-cell workload of GT cells which leads to a hybrid MCFMS with better utilization of the machines. The problem of the exception machines and their utilization and workload balance will be solved within the MCFMScentre. Thus the performance of GT cells can be improved by transferring workloads from a congested (bottleneck) machine in one cell to an alternative one, a less congested (exception) machine in another cell within a group of GT cells forming a MCFMS centre. The third step is the group scheduling; a proposed heuristic method will be used for the scheduling of a family of parts with the objective of minimizing the maximum completion time of each part. The problem of scheduling under MCFMS can be reduced by considering the scheduling of each family of parts. Finally, the flexibility of the system will be enhanced by selecting appropriate machine tools and flexible material handling equipments. This approach is both effective and efficient-it has generated a hybrid MCFMS centre which includes several alternatives, for some benchmark problems in much shorter time than algorithms previously reported in the literature. In addition, the method is conceptually simple and easy to implement.     

A genetic scheduling methodology for virtual cellular manufacturing systems: an industrial application

Effective solutions to the cell formation and the production scheduling problems are vital in the design of virtual cellular manufacturing systems (VCMSs). This paper presents a new mathematical model and a scheduling algorithm based on the techniques of genetic algorithms for solving such problems. The objectives are: (1) to minimize the total materials and components travelling distance incurred in manufacturing the products, and (2) to minimize the sum of the tardiness of all products. The proposed algorithm differs from the canonical genetic algorithms in that the populations of candidate solutions consist of individuals of different age groups, and that each individual's birth and survival rates are governed by predefined aging patterns. The condition governing the birth and survival rates is developed to ensure a stable search process. In addition, Markov Chain analysis is used to investigate the convergence properties of the genetic search process theoretically. The results obtained indicate that if the individual representing the best candidate solution obtained is maintained throughout the search process, the genetic search process converges to the global optimal solution exponentially.

The proposed methodology is applied to design the manufacturing system of a company in China producing component parts for internal combustion engines. The performance of the proposed age-based genetic algorithm is compared with that of the conventional genetic algorithm based on this industrial case. The results show that the methodology proposed in this paper provides a simple, effective and efficient method for solving the manufacturing cell formation and production scheduling problems for VCMSs.     

Modified Hamiltonian chain: A graph theoretic approach to group technology

Graph theory can be effectively applied to the group technology configuration problem (GTCP). Earlier attempts were made to use graph theoretic algorithms, e.g. minimal spanning tree (MST), tree search, and branch & bound to solve the group technology (GT) problem. The proposed algorithm is based on modified Hamiltonian chain (MHC) and consists of two stages. Stage I forms the graph from the machine part incidence matrix. Stage II generates a modified Hamiltonian chain which is a subgraph of the main graph developed in Stage I, and it gives machine sequence and part sequence directly. Dummy edges are considered in MHC for better accessibility in order to arrive at a block diagonal solution to the problem. This paper presents a simple approach by designing a MHC in the graph theoretic method to solve the group technology configuration problem. Results obtained from testing the method are compared with the other well-known methods and found to be satisfactory.     

Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization

Multilevel redundancy allocation optimization problems (MRAOPs) occur frequently when attempting to maximize the system reliability of a hierarchical system, and almost all complex engineering systems are hierarchical. Despite their practical significance, limited research has been done concerning the solving of simple MRAOPs. These problems are not only NP hard but also involve hierarchical design variables. Genetic algorithms (GAs) have been applied in solving MRAOPs, since they are computationally efficient in solving such problems, unlike exact methods, but their applications has been confined to single-objective formulation of MRAOPs. This paper proposes a multi-objective formulation of MRAOPs and a methodology for solving such problems. In this methodology, a hierarchical GA framework for multi-objective optimization is proposed by introducing hierarchical genotype encoding for design variables. In addition, we implement the proposed approach by integrating the hierarchical genotype encoding scheme with two popular multi-objective genetic algorithms (MOGAs)—the strength Pareto evolutionary genetic algorithm (SPEA2) and the non-dominated sorting genetic algorithm (NSGA-II). In the provided numerical examples, the proposed multi-objective hierarchical approach is applied to solve two hierarchical MRAOPs, a 4- and a 3-level problems. The proposed method is compared with a single-objective optimization method that uses a hierarchical genetic algorithm (HGA), also applied to solve the 3- and 4-level problems. The results show that a multi-objective hierarchical GA (MOHGA) that includes elitism and mechanism for diversity preserving performed better than a single-objective GA that only uses elitism, when solving large-scale MRAOPs. Additionally, the experimental results show that the proposed method with NSGA-II outperformed the proposed method with SPEA2 in finding useful Pareto optimal solution sets.     

A vector analytic VECAN method for solving the machine-part grouping problem in GT

A different approach for grouping machine-part in GT is proposed and named the Vector Analytic (VECAN) method. This method consists of two parts and is applicable to solve a standard binary part-machine incidence matrix. The first part deals with vectorial analysis of machines and grouping them as per the heuristic proposed. The second part is concerned with the method of efficiently diagonalizing them once the groups are identified. The effectiveness of the proposed method has been tested with 10 published problems from the literature. A threshold value for the formation of groups has been identified and its method of use has been suggested.     

Integrated use of fuzzy c-means and fuzzy KNN for GT part family and machine cell formation

This paper presents a new approach for GT part family and machine cell formation. It involves the integrated use of two fuzzy clustering algorithms: fuzzy c-means and fuzzy k-nearest neighbours. It is shown that the proposed approach performs better than using fuzzy c-means alone or FACT (Kamal and Burke) in terms of some commonly used measures such as grouping efficacy, grouping index, number of voids, number of exceptional elements, and number of bottleneck machines. The approach is developed a result of our quest for a better clustering algorithm to process non-binary data and to produce a non-binary classification in the domain of GT applications. These features are deemed important to handle imprecise data and to provide a higher degree of flexibility in the operation stage.     

A new approach for solving the P-median problem in group technology

One of the weaknesses of the P-median formulation of the cell configuration problem in group technology (GT) is that the number of cells required has to be specified in advance. Therefore, the most natural clustering of the input matrix might not be obtained. This paper suggests an approach for overcoming this weakness by using a new measure of similarity coefficient. Unlike most of the existing measures of similarity coefficient, the proposed measure can take both positive and negative values and therefore identifies both similarity and dissimilarity between machines. The proposed approach was tested on several problems taken from the literature. The results of this computational study demonstrate the superiority of the proposed method.     

Tabu search‐based approach to multi‐objective machine‐part cell formation

The machine‐part cell formation with respect to multiple objectives has been an attractive search topic since 1990 and many methodologies have been applied to consider simultaneously more than one objective. However, the majority of these works unify the various objectives into a single objective. The final result of such an approach is a compromise solution, whose non‐dominance is not guaranteed. A Pareto‐optimality‐based multi‐objective tabu search (MOTS) algorithm is presented for the machine‐part grouping problems with multiple objectives: it minimizes the total cost, which includes intra‐ and inter‐cell transportation cost and machine investment cost, minimizing the intra‐cell loading unbalance and minimizing the inter‐cell loading unbalance. A new approach is developed to maintain the archive storing non‐dominated solutions produced by the tabu search. The comparisons and analysis show that the proposed algorithm has considerable promise in multi‐objective cell design.     

A transiently chaotic neural network approach to the design of cellular manufacturing

The design of Cellular Manufacturing Systems (CMS) has attained the significant attention of academicians and practitioners over the last three decades. Minimizing intercellular movements while maximizing utilization of machines are the main objectives of interest in designing CMS and are considered in present research. In this paper, the drawbacks of former neural networks-based approaches to cell formation are discussed. The standard version of cell formation problem is formulated and a 'Transiently Chaotic Neural Network' (TCNN) with supplementary procedures is introduced as a powerful rival. A simplified network is constructed. After developing the related equations the approach is tested using the proposed algorithm with 18 problems selected from literature. The results are compared with various other approaches including ART1, Extended-ART1, Ortho-Synapse Hopfield Neural Network (OSHN), etc. The main advantages of our proposed method are: (1) the ability to avoid the local optima trap, (2) the ability to solve problems of different sizes with the same set of values for parameters, and (3) the less computation time. The results also indicate considerable improvement in grouping efficiency through the proposed approach.     

Agent-based dynamic part family formation for cellular manufacturing applications

One of the main critique on cellular manufacturing and its algorithms is their inability to handle dynamics events, especially dynamic changes in part spectrum. Unfortunately, there are not many efforts in the literature to overcome this problem. Agent oriented computing provides a marvellous opportunity to handle dynamic problems and to provide effective solutions, if carefully and intelligently implemented. In this paper, we have proposed a novel agent-based clustering algorithm for part family formation in cellular manufacturing by considering dynamic demand changes. However, it is not easy to directly compare the performance of the proposed algorithm with the literature results as there is no benchmark for dynamic cell formation problems. We attempt to compare the performance of the present algorithm on static test problems by dynamically introducing parts in these data-sets to our algorithm. Many results have been presented on these static data-sets by utilising several heuristics, meta-heuristics and optimisation-based algorithms. Although the proposed algorithm is not an optimisation-based algorithm and its operation is directed to handle dynamic changes in the problem domain through negotiation, we have shown that it has ability to provide very good results which are comparable to the best known solutions.     

A 3D Lagrangian gradient smoothing method framework with an adaptable gradient smoothing domain-constructing algorithm for simulating large deformation free surface flows

A novel smoothing particle hydrodynamics (SPH)-like Lagrangian meshfree method, named as Lagrangian gradient smoothing method (L-GSM), has been proposed to avoid the “tensile instability” issue in SPH simulation by replacing the SPH particle-summation gradient approximation technique with a local grid-based GSM gradient smoothing operator. The L-GSM model has been proven effective and efficient when applied to a wide range of large deformation problems for fluids and flowing solids in two-dimensional case. In this study, a three-dimensional (3D) L-GSM numerical framework is proposed for simulating large deformation problems with the existence of free surfaces through developing a widely adaptable 3D gradient smoothing domain (GSD) constructing algorithm. It includes three key novel ingredients: (i) the localized GSD based on an efficient distance-oriented particle-searching algorithm enabling both easy implementation and efficient computation; (ii) a novel algorithm for constructing 3D GSD to guarantee the effectiveness of the 3D GSM gradient operator adaptable to any extreme cases; (iii) a robust normalized 3D GSM gradient operator formulation that can restore the accuracy of gradient approximation even on boundary interface. The effectiveness of the proposed 3D GSD-constructing algorithm is first verified under various distribution conditions of particles. The accuracy of the proposed adaptable 3D GSM gradient algorithm is then examined through conducting a series of numerical experiments with different spacing ratios. Finally, the 3D L-GSM numerical framework is applied to solve a practical problem of free surface flows with large deformation: collapse of a soil column. The results reveal that the present adaptable 3D L-GSM numerical framework can effectively handle the large deformation problems, like flowing solids, with a constantly changing arbitrary free surface profile.     

Visual hierarchical clustering of supply chain using growing hierarchical self-organising map algorithm

The study identifies a need for efficient and robust visual clustering approach that can potentially deal with complex supply chain clustering problems. Based on the underlying philosophy of group technology, a growing hierarchical self-organising map algorithm (GHSOM) is proposed to identify a lower two-dimension visual clustering map that can effectively address supply chain clustering problems. The proposed approach provides optimal solutions by decomposing a large-sized supply chain problem into independent, small, manageable problems. It facilitates simple decision-making by exploring similar clusters that are represented by the neighbouring branches in the GHSOM map structure. Unlike other approaches in literature, the proposed approach can further attain good topological ordered representations of the various work order families, to be processed by clusters of supply units along with information on hierarchical sub-cell formation as identifiable from the visually navigable map. The proposed approach has been successfully applied on 16 benchmarked problems. The performance of GHSOM based on grouping efficacy measure outperformed the best results in literature.     

Maintaining Complex Formations and Avoiding Obstacles for Multi-Agents

This paper researches some problems in complex formation for multi-agents, in which two matrices are proposed to record the formation. The pattern matrix is used to describe the pattern of the formation; meanwhile, the location matrix is used to record the location of each agent. Thus, all desired positions of each agent will be obtained by geometrical relationship on the basis of two matrices above. In addition a self-adaptation flocking algorithm is proposed to control all agents to form a desired formation and avoid obstacles. The main idea is as follows: agents will form a desired formation through the method of formation control when far away from obstacles; otherwise, agents will freely fly to pass through the area of obstacles. In the simulation, three scenarios are designed to verify the effectiveness of our method. The results show that our method also can be applied in three dimensions. All agents will form a stable formation and keep the same velocity at last.