Copyright © IFAC Intelligent Manufacturing Syste ms, Bucharest, Romania, 1995
OPTIMIZATION USING ARTIFICIAL NEURAL NETWORKS
Man-Wook Han and Peter Kopacck Institute for Handling Devices and Robotics. Technical University of Vienna. Austria
Abstract: The optimization of a process is a mostly important research subject There are many approaches optimizing processes, using operation research or artificial neural networks. In this paper, the application of artificial neural networks for the optimizing problems in robotics and manufacturing is investigated. For the investigation purpose the generation of optimal assembly sequences using neural networks is presented. One of the important factors for the automation of assembly processes is the improvement of productivity and flexibility, where costs and time play a substantial role. The optimization of assembly sequences can bring more economical and time saving benefits. Keywords: Neural Networks, Self-Organizing Map, Assembly, Optimization
types and learning algorithms whose application depends on the specific problem. Application fields of ANN include classification, recogmtJon, forecasting, control, optimization and others. Artificial neural networks have been successfully applied especially to control the non-linear and dynamic process. One of the application fields using neural networks is the optimization that we investigate in this paper.
I. INTRODUCTION Many scientists and technicians have tried to solve optimization problems using different techniques. The optimization of a process is a meaningful researching subject. There are many approaches and realizations to optimize process in robotics and manufacturing, such as the optimal trajectory or path generation, optimal assembly sequence generation, optimal manufacturing sequences and so on. There are two terms considering the optimization. One is what can be optimized and other is how.
One of the important factors for the automation of a manufacturing process is the improvement of the productivity and flexibility. The cost and time play an important role. The manufacturing process consists of many individual operations. One of them for the manufacturing process is the assembly. Assembly cost amounts to charges up to 70% of the product cost. The optimization of assembly sequences can bring more economical and time saving effects.
Since mid-80 the artificial neural networks (ANN) are applied in many fields . ANN gain in importance because of its parallelism. adaptability and learning capability. Artificial neural networks are data processing systems that are parallel interconnected networks with simple adaptive processing elements whose working method imitate that of biological nervous systems. Its processing speed is much smaller than that of conventional /lVon Neumann" Computers. The great advantages of artificial neural networks are parallel processing ability, learning ability and adaptability. There are many different net\\'ork
The aim of this work is the investigation of the application of artificial neural networks for the optimization. For the investigation purpose the approach to generate the optimal assembly sequences will be presented in this paper. We have chosen a model product which consists of 8 parts. 357
2. ARTIFICIAL NEURAL NETWORKS There are approaches for the representation of the assembly plan based on directed graph, on AND/OR graphs on establishment conditions and on precedence relationship. (Homem de Mello et al.,1991)
Nowadays artificial neural networks are applied widely in many fields, for the recognition, control and other tasks. The reasons why neural networks are applied for the process are the simplification of the implementation process and the improvement of the reliability. One of the important conditions by application is the existence of data for learning. The modelling of data for neural networks is very important and essential for the practical application. It is difficult to initialise the networks with knowledge and experiences. One of the applying fields using ANN is the optimization of the process. As outputs a set of decisions is expected for the optimization. One of optimi7.ation problems is the traveling salesperson problem (TSP). There are also many approaches to solve this problem, for examples using operation research method and using ANN. Hopficld and Tank (Hopfield and Tank, 1985) have suggested their neural algorithms to solve this problem. Hopfield and Tank represented energy function for the TSP. It could be iteratively solved on the neural networks. Although the energy function is minimized, that means the network reaches stable state, but there is a local minimum problem. For specific problems different energy functions are applied. Based on the Hofpield and Tank's algorithm Hong and Cho (Hong and Cho, 1995) have tried to get the reasonable assembly sequences for robot. They applied an energy function which consists of assembly cost and assembly constraints. Using Simulated annealing networks there are also approaches to optimize the manufacturing process.
A more convenient product representation is an assembly graph of connections. This is an undirected graph, where the nodes are parts of the assembly and the connections represent all contacts between parts. An example of a graph of connections for the assembly in Figure 1. is presented in Figure 2.
Figure I: Eight-part assembly (exploded view)
Kohonen (Kohonen, 1989) has introduced selforganizing feature map (SOM). This network serves for mapping between different dimensions. SOM is a widely applied in robotics. Using SOM there are also many approaches to solve Traveling Salesman Problem (TSP). (Angeniol et aI, 1988) Using Kohonen's self~rganizing map (SOM) there are reasonable solutions of the optimization problem. From this reason we apply SOM to get the optimal assembly sequences. 3. ASSEMBLY Assembly is an important part of the manufacturing process, where a product gets its final form and functionality Assembly is a complicated, time consuming and complex operation. Assembly task is a process joining one part with another part, considering geometrical and mechanical feasibility. Assembly sequence is the order of assembly tasks. What the optimal assembly sequences mean the generation of assembly sequences from the point of following views: ® to minimize the production cost ® to minimize the production time [R> to maximize the product quality
Figure 2: The graph of connections for the example in Figure I All joining possibilities from Figure 2 do not yield stable subasscmblies, so the stability predicate has to be regarded when the assembly tasks are determined from the graph of connections. All combinations of connections from the connection graph do not yield feasible assembly tasks, which have to be geometrically and mechanically feasible . Without regard to the 358
equipment, the assembly sequence can be represented by a directed graph (Figure 3) or by an AND/OR graph (Figure 4).
for the determination of possible assembly operations and their sequences. Each part should be assembled only once. A sequence should be generated to minimize the assembly cost. The number of assembly sequences of this model can be counted as approximately 8!.
The conventional planning of assembly needs analysis to obtain information on its future properties. If they do not satisfy the demands, some changes to the planning assembly have to be made. In human-oriented planning of assembly, analysis is replaced with searching for an optimal solution. If an optimal solution has been found according to the given demands, the assembly planning is finished and results can be represented.
Figure 4 shows the feasible assembly sequences of the model product. In our case the stator is selected as the base part because it is the heaviest and largest part, which should be assembled first. Two clasps are assembled to hold all parts. Based on geometrical feasibility and assembly constraint we can reduce the number of possible assembly sequences to 32. The optiminltion of sequences between levels C and F of the directed graph in Figure 3 should be determined.
[D+ .·.·B · .~· .· .· D .· ..... .· E ·~.·.· ~·.·.·~ 2 4 2 2
Figure 4: Representation of task levels The number under the arrows in the task levels means the number of assembly possibilities between levels. Based on the directed graph possible assembly task sequences between levels C and Fare: 4-5-9-13 4 - 5 - 12 - 13 4-6-9-13 4-6-10-13 4-7-10-13 4-7-11-13 4-8-11-13 4 - 8 - 12 - 13 The assembly task between 4 and 13 is the assembly base component (stator + 2 spools) with rotor and left and right flange. The possible tasks are; - base component + one flange (6, 8) - subassembly of one flanges \\ith rotor (5, 7) In ne:\1level E the assemblies ; - (base component and one of flanges)+ subassembly (9, 11) - (base component and one of flanges) + rotor (10,12) In ne:\1lcvel F other flange will be assembled. (14) In section 2.3 the criterion for the optimal assembly sequences -to minimize assembly cost, which consists of cost of equipment and assembly frequency is already mentioned.
Figure 3: Directed graph of feasible assembly sequence. Numbers means parts and when delimited by a comma, they represent a stable subassembly. Nodes represent stable state partitions and edges feasible assembly tasks. The equipment needed for completion of assembly tasks has to be selected so that according to the optimal assembly sequence the solution yields an optimal assembly system. Miniminltion of assembly costs should be a main criterion for optimization of assembly where assembly costs depend on costs of equipment and assembly frequency. Assembly frequency means time between two finished assemblies and is dependent on time needed for completion of each assembly task and assembly sequence. The assembly task duration depends on the performances of the selected equipment and their spatial relationship. All these parameters should be considered when the optimal solution is searched for.
At first, to generate the optimal sequences. the assembly process of the product is investigated. Assembly task is a process joining one part with another part, considering geometrical and mechanical feasibility. Assembly sequence is the order of assembly tasks. For representation of mechanical assemblies. information about shape of the parts, geometrical relationships. tolerances. attachment of the parts and chemical treatments should be added in the designing phase. This is a basis
In Hong and Cho's work (Hong and Cho, 1995) the to be minimized energy function includes energy for the assembly cost, the precedence constraint, avoidance of plural subassemblics and three other terms. In case of optimal sequences the assembly cost is minimum and other terms become zero.
In this work the generation of assembly sequence \\ill be presented. As we mentioned before tlle selforganizing map is successfully applied to sol\'e the travcling salesman problem. Considering this problem the generation of assembly sequences is investigated. TIle main problem here is the input pattern generation. The transformation of assembly cost and constraints into network inputs plays a important role. We know approximately the assembly operations of whole parts. Because of mechanical and geometrical feasibility some assembly tasks are executed in fixed sequence. Our approach is b.:1sed on assembly part and the assembly task considering the directed graph.
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A consideration using SOM is that the ncurons are distributed in the 2 dimensional space and each neuron represents the each assembly part or the assembly tasks. Two approaches arc considerable. One is that each neuron represents each part. Otllers c.1ch neurons represent each assembly task. A generated neuron chain connecting neurons sho\\'s the assembly sequence. There are some restrictions. Because of geometrical and mechanical fc.1sibility cert.1in parts should be assembled in fixed SC<]uence. Based on tllC approaching \\'ay the number of ncurons is chosen differently. In case that ncuron represents tllC assembly part the number of neurons is chosen as the number of parts. In another case the number of neurons is chosen as the number of assembly tasks. Some approaches showed that se\'eral number of neurons for each part respccti\'ely each task can solve the problems bener than a ncuron for each part respectively each task.
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TIle assembly is an important part of production and amount to charges up to 70% of product cost. The basic consideration is the minimization of the assembly cost. The generation of assembly sequcnces using neural networks is presented.
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Neural networks are applied to solve the optimization problem. Simulated annealing nctworks. Hopfield networks and seif-organizing maps are successfully applied for the optimization problems. especially for the tra\'eling salesl1l.1n problem. In this work the selforganizing map was investigated to find an optimal assembly sequence. The simulation to find an optimal sequence using SOM is not finished completely yet. TIle hybrid nel\\ork approach or the combined application of neural nel\"orks \\ith other Artificial Intelligence (AI)-methods bring more suitable solutions in specific operations.
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