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Abstract—The cooling system is one of the most important systems in a plastic injection mould. It affects the quality and productivity of the molded part. In this paper, we extend our previous research on the automatic plastic injection cooling system layout design to multiple inlet and outlet systems, and propose an evolutionary approach with ad hoc operators to concurrently optimize the topological connection and geometric position of a cooling system. A mixed encoding scheme is developed to encode a candidate solution, which is represented in the form of a variant-length chromosome. Ad hoc evolutionary operators and parameters adapting to the characteristics of cooling system design are devised. An experimental system is implemented to verify the feasibility of the approach, and the results of case study illustrate the validity of this approach. It can be expected this research will well facilitate the automation of plastic injection mould cooling system design. Keywords- plastic injection mould, layout design automation, Genetic algorithm (GA), Degree of freedom (DOF)37727
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I. INTRODUCTION The performance of cooling system is essential to the quality and productivity of a molded part. Generally, the process of cooling system design can be distinguished into three phases: preliminary design, layout design, and detail design. In the preliminary design phase, basic cooling elements are specified. The layout design phase both addresses the functionality and maufacturability of a cooling system. Some design details are completed in the detail design phase. In our previous research [1,2], we have developed a feature-based technique to generate the preliminary design automatically. Recently, we have extended our research into the automation of the layout design phase, a graph-based technique has been developed to capture all the feasible designs using a graph structure[3,4], and a configuration space method was developed to capture all feasible geometric design within a given topology[5,6]. However, the above research mainly focuses on single inlet/outlet cooling system, and the graph-based method may sometimes results in a design that is not optimal, the configuration space method does not allow changes in the topology. In this research, these limitations are overcome by a genetic algorithm (GA). A major issue in the layout design phase is to connect the inpidual cooling elements specified in the preliminary design phase to form cooling circuits. Each cooling circuit is composed by a simple path, and a cooling system consists of one or more cooling circuits. Another concern in the layout design phase is to find an appropriate position for cooling system. As many different mould sub-systems need to be packed into mould insert, from large quantities of candidate designs, finding an optimal one is a difficult task. An automatic and efficient optimization algorithm to both deal with the topological connections and geometrical position is necessary. GA is a stochastic search method based on biological evolution models, and is successfully applied to address all kinds of optimization problems in many fields. GA has been used in plastic injection mould cooling system design. For example, Lam et al.[7] use GA to optimize the channel size, position, inlet temperature, coolant flow rate and certain process parameters. The GA is interfaced to MOLDFLOW[8] to evaluate candidate designs, and it aims at minimizing the standard deviation of the temperature distribution in the mould cavity. An important issue in the use of genetic algorithm is the encoding of candidate solutions in the form of chromosomes. According to the type that the allele of a chromosome takes, there are four kinds of encoding methods: binary encoding, real number encoding, order-based encoding and the general data structure encoding[9].The binary encoding is the most classic method used by GA researchers because of its simplicity and traceability. Real-number encoding was introduced especially to deal with real parameter problems, and it would be faster than binary encoding in computation and more consistent from the basis of run-to-run. At the same time, its performance can be enhanced by special operators to achieve high accuracy. The order-based encoding [10] is particular useful for those problems where a particular sequence is required to search, i.e. combinatorial optimization problems. In solving complex design problems, directly using the general data structure encoding is often much more successful, for example taking the form of tree or graph [11] as chromosome structure. Another issue in the use of genetic algorithm is the design of problem-oriented operators and parameters. In this paper, an ad hoc chromosome is devised to concurrently optimize the topological connection and geometric position of cooling system. Topological Fig.1 Chromosome structure Number Drilling Ci Separator Integer Bool Bool C2 C1Topology segment … Cn d2 d1 d … Geometry segment Real Preliminary design Layout design Fig.2 From preliminary design to layout design connections is a permutation of cooling channels, it is suitable to use order-based encoding method, while the position of cooling system in mould insert is represented by the degree of freedom(DOF) of a cooling system, and it is a continuous value, it is better to use real-number encoding method. Therefore, a mixed encoding scheme is taken, which uses order-based encode for topology part and real-number encode for geometry part. Ad hoc GA operators adapting to the characteristics of cooling system design are developed. II. ENCODING SCHEME The chromosome structure is designed as shown in Fig.1. There are two parts in the chromosome structure: topology segment and geometry segment. Topology segment and geometry segment represent the topology information and geometry information of a cooling system respectively. The allele in topology segment includes three genes: Number, Drilling and Separator. Number is an integrate number denoting the channel number in preliminary design representation graph; The other two genes are bool number denoting the attribute of this channel, Drilling represents the drilling direction of this channel, and Separator represents if this channel is an end channel. If this channel is an end channel, it means this channel and its next channel are not in the same cooling segment. The genes in geometry segment is encoded by real number, which represents the DOF values of the cooling system determined by topology segment. For different candidate layout design, its topology may be different, and its DOF number is determined by the topology, so the DOF number may also be different. Therefore, this chromosome is of a variable length. III. GA OPERATORS The basic operations of evolution consist of crossover and mutation. Crossover effectuates the recombination of chromosomes, and mutation increases the persity of offspring chromosomes. Because the chromosome structure in this work is very complicated, for different kinds of genes, we design different crossover and mutation methods. There are four kinds of information in a chromosome: Channel number, Channel manufacturing direction, Cooling segment separator and Cooling system DOF. Therefore, there are eight operators: Crossover z Number-oriented crossover z Direction-oriented crossover z Separator-oriented crossover z DOF-oriented crossover Mutation z Number-oriented mutation z Direction-oriented mutation z Separator-oriented mutation z DOF-oriented mutation These operators can be selected inpidually or compositionally during the process of evolution according to the preset crossover rates and mutation rates. Special care has been taken to ensure that the offspring generated by these operators represents a valid cooling system design that can be manufactured by conventional machining method.