The Multi-objective Optimization Method Combining Fuzzy Clustering With Cooperative Competition Game For Mechanical Parts

Most of engineering problems and social problems are always very complex, and have many design variables and design objectives under specific or given constraints. The traditional ways of resolution of those problems, both in the domestic and overseas, have always been linear combine all the multiple targets which is relying greatly on people’s knowledge and experience to distribute the weight of each target, at the same time, it need to do large amount of calculation which makes the optimization efficiency very low, and the solution method can solve specific practical problem, but for other special multi-objective optimization problems they are limited. Because of those limitations, those ways’ application scopes have been limited in certain range. All those shortcomings make the traditional multi-objective optimization methods have great limitations in engineering applications.Boundaries between objects are mostly fuzzy, similarly the boundary between design variables of multi-objective problems is also not absolute discriminative. Often objects are both cooperated and conflicted between each other, so are the objects of the multi-objective problems. Multi-objective optimization problems, the fuzzy clustering problems, and cooperative competition game problems all have the nature of the fuzzy boundaries and conflict properties. So the fuzzy clustering and cooperative competition game thoughts can be introduced to solve the problem of multi-objective optimization design, inspiring a new method different from the traditional multi-objective optimization design. Sample experimental design, analysis and testing methods provide the data base for fuzzy clustering and cooperative competition game optimization analysis.This paper is under above technical ideas, using the sample design, analysis and testing method, modeling multi-objective problem and also doing the model analysis, processing, inspection to get the Impact Factor Matrix from the every design variables to each target in the sample experiments. Using the fuzzy clustering thought processing Impact Factor Matrix, can obtain the fuzzy similar matrix which can translate into Transitive Closure Matrix (TCM). Under given confidence coefficient, the TCM can do the clustering of design variables. In this way, the multi-objective problems can be translated into cooperative competition game problems which can be solved under cooperative competition game thoughts. This method has high convergence rate and calculation efficiency. It is also not relying on personal knowledge and experience to determine the target weight (converted into single objective) and can adjust the target of cooperation between degrees conveniently to get the most satisfactory solution under certain conditions. Sample experimental design can handle discrete problems and not absolutely request the objective function is derivable. Fuzzy clustering can make complicate problems modular, simplify the problem, guarantee the quality and at the same time simplify the problem analysis and solving.In order to verify the effectiveness of the method, this paper designed a common mechanical structure, truss, as the multi-objective optimization problem example. Results from this paper have small theoretical errors with the theoretical solution. On the basis of the validity that have already been verified of the method, this paper applied this method to solve the complex optimization design problem of gear reducer, simultaneous considering three co-cooperative and co-competition target, contact ratio, volume, center distance. Optimal designing the gear parameters like multiple gear modulus, tooth number, tooth width coefficient, can effectively improve the common problems of gear reducer like running deviation, spillage and abnormal noise.