中文摘要：

在多目标最优化问题中，如何求解一组均匀散布在前沿界面上的有效解具有重要意义．MOEA／D是最近出现的一种杰出的多目标进化算法，当前沿界面的形状是某种已知的类型时，MOEA／D使用高级分解的方法容易求出均匀散布在前沿界面上的有效解．然而，多目标优化问题的前沿界面的形状通常是未知的．为了使MOEA／D能求出一般多目标优化问题的均匀散布的有效解，利用幂函数对目标进行数学变换，使变换后的多目标优化问题的前沿界面在算法的进化过程中逐渐接近希望得到的形状，提出了一种求解一般的多目标优化问题的MOEA／D算法的权重设计方法，并且讨论了经过数学变换后前沿界面的保距性问题．采用建议的权重设计方法，MOEA／D更容易求出一般的多目标优化问题均匀散布的有效解．数值结果验证了算法的有效性．

英文摘要：

In multi-objective optimization problems, it is very important to find a group of uniformly distributed Pareto optimal solutions on Pareto fronts. MOEA/D is one of the promising evolutionary algorithms for multi-objective optimization at present. When the Pareto front is some known types of shape, the MOEA/D can find uniformly distributed Pareto-optimal solutions by using the advanced decomposition. Nevertheless, it is a nontrivial task for the MOEA/D for a general shape of the Pareto front. In this paper, each objective function is transformed by the power function, which makes the Pareto front of multi-objective optimization close to the desired shape. Furthermore, a kind of weight design method of MOEA/D is proposed to solve general multi-objective optimization problem. This paper also discusses the distance preserving character of Pareto front by mathematics transform. MOEA/D, making use of proposed weight design method, easily finds uniformly distributed Pareto optimal solutions for general multi-objective optimization problem. Numerical results show the effectiveness of MOEA/D with the proposed weight design method.