面向多目标优化的多样性代理辅助进化算法

代理辅助进化算法（SAEA）是目前解决昂贵优化问题的一种有效途径.提出一种基于多样性的代理辅助进化算法（DSAEA）来解决昂贵多目标优化问题.DSAEA采用Kriging模型近似每个目标来代替原目标函数进行评估，加速了进化算法的优化过程.其引入参考向量把问题分解为多个子问题，根据解与参考向量之间的角度大小建立它们的相关性，然后计算出最小相关解集.在此基础上，候选解生成算子和选择算子会趋向于保留多样性的解.另外，训练集A在每次迭代后会进行更新，根据多样性删除价值不大的样本以减少建模时间.实验部分对DSAEA与目前流行的代理辅助进化算法在大规模2目标和3目标优化问题上进行对比实验.每个算法在不同的测试问题上分别独立运行30次，并计算和统计反向迭代距离（IGD）、超体积（HV）和运行时间，最后使用秩和检验分析实验结果.结果表明：DSAEA在多数实验测试问题上表现更好，因此具有有效性和可行性.

Diversity Based Surrogate-assisted Evolutionary Algorithm for Expensive Multi-objective Optimization Problem

The surrogate-assisted evolutionary algorithm (SAEA) is an effective way to solve expensive problems. This study proposed a diversity-based surrogate-assisted evolutionary algorithm (DSAEA) to solve the expensive multi-objective optimization problem. DSAEA approximates each objective with the Kriging model to replace the original objective function evaluation, accelerating the optimization process of the evolutionary algorithm. It decomposes the problem into several subproblems with the reference vectors. The correlation between the solution and the reference vector is established according to the angle between them. Then the minimum correlative solution set is computed. Based on it, the candidate producing operator and the selection operator tend to preserve the solutions of diversity. In addition, as the training set, Archive A is updated after each iteration, deleting the little value samples according to diversity to reduce the modeling time. In the experiment section, large scale 2- and 3-objective comparative experiments for DSAEA and several current popular SAEAs were done. Each algorithm on different test problems ran 30 times independently, and the inverted generational distance (IGD), hypervolume (HV), and running time were calculated and collected. At last, rank sum test was used to analyze the experimental results. The results show that DSAEA performs better on the most experimental test problems, therefore, it is effective and feasible.