Abstract: In order to improve the convergence and diversity of cellular genetic algorithm in solving multi-objective problems, a 3D（three-dimensional） cellular genetic algorithm is proposed, which introduces a 3D topology, based on multi-objective genetic algorithm. Some multi-objective benchmarking problems are selected to assess the performance of the algorithm which is compared with other well-known multi-objective genetic algorithms. The results indicate that the improved algorithm achieves better results on the convergence and diversity. Then, the improved algorithm and several other algorithms are used to solve the machine tool spindle design optimization problem. The improved algorithm outperforms the others. The comparison shows that the improved algorithm is effective in solving this problem.

Key words: 3D cellular topology, multi-objective, cellular genetic algorithm, machine tool spindle, optimization design

摘要： 为了进一步提高元胞遗传算法在求解多目标优化问题时的收敛性和分布性。在多目标元胞遗传算法的基础上，引入了三维空间元胞，提出了三维元胞多目标遗传算法。采用多目标基准测试函数对该算法进行了测试，并将其与目前比较流行的几种多目标遗传算法进行对比。结果表明，此种算法在收敛性和分布性上取得了更好的效果。采用以上这几种算法分别对机床主轴多目标优化问题进行了求解，相比其他几种算法，改进的多目标元胞遗传算法得到了更优的结果，说明了改进的算法在求解此问题时行之有效。

关键词: 三维元胞结构, 多目标, 元胞遗传算法, 机床主轴, 优化设计