一类区间系数非线性优化问题的遗传算法

A Genetic Algorithm for a Class of Nonlinear Optimization Problems with Interval Coefficients

摘要: 本文针对一类带区间系数的非线性优化问题，提出了一种基于均匀搜索的遗传算法。首先，将原问题分解为两个确定的双层规划问题；其次，对两个双层问题的上层变量进行编码，通过求解相应的双层规划获得对个体的评估；最后，为避免近亲繁殖产生相似后代，采用相对距离控制杂交运算；并且引进摆动式正交杂交算子产生后代个体，使后代尽可能均匀产生。数据仿真结果表明，该算法是可行有效的。

Abstract: For a class of nonlinear programming problems with interval coefficients, a genetic algorithm based on a uniformly searching scheme is proposed in this paper. Firstly, the original problem is transformed into two exact bilevel programs. Secondly, the upper level variables are encoded as individuals, and these individuals are evaluated by solving the bilevel programs. Finally, in order to avoid producing similar offspring by inbreeding, a relative distance is adopted to provide a threshold value for crossover. Also, an orthogonal crossover operator with point oscillating is provided to generate offspring as uniformly as possible. The experimental data indicate that this algorithm is feasible and effective.