Multi-objective Optimization Methods Based on the Micro Genetic Algorithm and Applications
|Course||Mechanical design theory and methods|
|Keywords||Micro genetic algorithms Multiple-population parallel structure Aproximation model management Multi-objective optimization Engineering optimization|
Many engineering optimization problems involve multiple objectives. Most of these problems have a nonconvex feasible objective space and decision variable space. The two feasible spaces usually have a nonlinear mapping which is expressed by complex computational model. Many multi-objective optimization approaches have lots of difficulties in solving this kind of problems. Genetic algorithms seem to be particularly suited for solving multi-objective optimization problems for their natural ability of finding multiple optimal solutions in one single simulation run. With the wider applications of the multi-objective genetic algorithms in complicated engineering optimization problems, the improvement of the efficiency is needed. In this paper, the primary goal is to improve the efficiency of the multi-objective optimization approaches.Firstly, a micro multi-objective genetic algorithm based on the micro genetic algorithm is suggested to solve the multi-objective optimization problems. An external elite archive is used to store Pareto-optimal solutions found in the evolutionary process. A non-dominated sorting is employed to classify the combinational population of the evolutionary population and the external elite population into several different non-dominated levels. Once the evolutionary population converges, an exploratory operator will be used to explore more non-dominated solutions, and a restart strategy will be subsequently adopted. Simulation results for several difficult test functions indicate that for all test functions the present method has a better spread of Pareto-optimal solutions, better convergence near the globally Pareto-optimal set and higher efficiency compared to non-dominated sorting genetic algorithmⅡ.Secondly, the high efficient micro multi-objective genetic algorithm is successfully applied in some complicated engineering problems, including the ten-bar truss structural optimization for minimizing mass and displacement in z direction, the structural optimization of a composite laminated plate for maximizing stiffness in thickness direction and minimizing mass, and the passively vehicle suspension multi-objective optimization for minimizing the standard deviations of the vertical vehicle body acceleration, the tyre radial force and the relative displacement between the wheel and vehicle body, which are the performance indices of discomfort, road holding and working space. Software based on the micro multi-objective genetic algorithm for engineering multi-objective optimization problems is developed, whose interface is friendly and convenient.Thirdly, the multiple-population parallel structure is applied to the micro multi-objective genetic algorithm for using parallel implementations to improve efficiency. Genetic algorithms have a parallel nature, so they are easily implemented efficiently on parallel computers. Multiple-population parallel genetic algorithms include of several subpopulations that exchange individuals occasionally, which keep the diversity of each population and avoid the mature convergence. The higher efficiency and better performance of the parallel micro multi-objective genetic algorithm are demonstrated by several difficult test functions and the applications in the structural optimization of a composite laminated plate and the optimization of variable binder force in sheet metal forming.Finally, a novel multi-objective optimization method is suggested based on an approximation model management technique. It is a sequential approximation multi-objective optimization strategy, in which a multi-objective optimization with approximation models subject to design variable moving limits is iterated until convergence. In each optimization iteration, the approximation models are constructed by the response surface approximations with the samples which are obtained from the design of experiments, and a Pareto optimal frontier predicted by the approximations is identified by a multi-objective genetic algorithm. According to the prediction of the approximation models, an approximation model management technique is employed to determine the design variable moving limits for the next iteration. At the end of each iteration, some uniform distributed points chosen from the predictive Pareto optimal frontier are verified by the real models and the obtained real Pareto frontier is stored in an external archive. The efficiency of the present method is demonstrated by four different test functions and the applications in the crashworthiness design optimization of thin-walled sections of vehicle body and the optimization of variable binder force in a shoe plate of a car front floor forming.