中文摘要：

研究用最近邻分类预测多目标优化问题Pareto支配性的相似性测度方法．在分析决策分量对各目标分量贡献率的基础上定义决策向量的等价子向量，等价子向量由贡献率相同的决策分量所组成．提出基于等价子向量的最小交叉距离加权和相似性测度方法．对每个目标分量，独立评价待测数据与N个已知样本的相似度，每个样本按其相似度值的升序赋予0：N-1之间的序号，按各目标上的序号之和最小准则确定最近邻样本．等价子向量最小交叉距离加权和相似性测度以及多目标最近邻搜索方法在确定决策向量相似性时，经入了决策空间到目标向量空间的映射知识，使决策变量相似性测度更真实地反映目标向量相似性．对典型多目标优化问题的Pareto支配性最近邻分类实验结果表明，提出的方法可显著地提高分类准确性．

英文摘要：

This study investigates the similarity measurement of nearest neighbor classmcaslon ior t-~r~w uumin~l,~~ prediction in multi-objective optimization. The equivalent components of a decision vector are defined by analyzing the contribution rate of each decision component to each objective component. For each objective component, the decision vector is divided into a group of equivalent sub-vectors, each consisting of the equivalent components with the same contribution rate. The distance between two equivalent sub-vectors is computed by minimizing the cross distance among the equivalent components. The similarity of two decision vectors is measured by the weighted sum of the minimized cross distances （WMCDs） corresponding to each equivalent sub-vector, where the weight takes the corresponding contribution rate. For each objective component, after evaluating WMCDs between an observed data and N samples, each sample is assigned a sequential number in [0： N- 1] according to the ascending order of WMCDs. The nearest sample is the one with the minimal sum of the sequential numbers on all objective components. For WMCDs and multi-objective nearest neighbor searching introduce the mapping information from the decision space to the objective space, the similarity measurement in the decision space reflects the similarity in the objective space more seemingly. The experiments on tested problems show that the proposed algorithm remarkably improves the prediction performance of nearest neighbor classifiers.