基于极坐标变换的改进NSGA-Ⅱ算法

An Improved NSGA-Ⅱ Algorithm Based on Polar Coordinate Transformation

在实际工程中存在着大量的多目标优化问题,而由于大部分多目标优化问题有无穷多个最优解,且传统的数学方法如梯度下降法和牛顿法,无法求解一些不可微或表达式过于复杂的多目标优化问题。为避免以上局限,NSGA-Ⅱ作为求解多目标优化问题的代表算法被提出,但NSGA-Ⅱ算法仍存在着一些不足,如变异算子功能过于简单,降低了Pareto最优解的多样性。为增加Pareto最优解的多样性,文中设计了一种基于极坐标变换的改进NSGA-Ⅱ算法,该算法可使得Pareto最优解分布更加均匀,并最终通过标准的测试函数验证了算法的有效性。

In engineering practice, there are many multi-objective optimization problems, to most of which exist infinite multiple optimal solutions that are beyond the capability of traditional mathematical methods such as the gradient descent method and the Newton method if they are non-differentiable or the expression is too complex. The NSGA-II, as the representative of solving multi-objective optimization problem algorithms was put forward, which still has some deficiencies such as mutation operator function is too simple, thus reducing the diversity of Pareto opti- mal solutions. In order to increase the diversity of Pareto optimal solutions, this paper designs an improved NSGA-II algorithm based on polar coordinates transform that makes Pareto optimal solutions distribution more uniform. The effectiveness of the algorithm is verified by the standard test functions.