基于Nash-Pareto策略的两种改进算法及其应用

针对多目标、多设计变量的优化问题,提出了两种优化的新算法:一种是将多目标问题转化为单目标时,对目标权重的确定提出了新的途径;另一种是直接对多目标问题进行优化,并对Pareto遗传优化技术作了改进,以得到均匀分布的Pareto最优解集.两种新算法都是建立在Nash的系统分解与Pareto遗传算法的基础上,因此称这类算法为Nash-Pareto策略.借助于这类算法,文中以跨声速压气机双圆弧类叶型的气动优化为例,给出了气动优化的全过程.数值优化的实验表明所给出的改进算法是可行的、有效的.

Two improved algorithms based on Nash-Pareto strategy and their applications

Two new algorithms are proposed in the present paper to solve the optimization problems of multi-objectives and multi-design variables.One of these algorithms translates multi-objective into single objective,and develops a new way to determine the objective weights;the other algorithm optimizes multi-objective directly and improves Pareto genetic optimization algorithm in order to obtain optimal solution set of uniform distribution on a Pareto frontier.These two algorithms are based on Nash system decomposition and Pareto genetic algorithm.Therefore,the algorithms of such type are named Nash-Pareto strategy.By using these algorithms,the aerodynamic design optimization of transonic compressor double circular arc profile is computed to show the whole process of optimization.The simulation of numerical optimization experiment illustrates that the improved algorithm is feasible and effective.