非线性规划的遗传算法在多峰函数优化中的应用

Genetic algorithms combined with nonlinear programming for multimodal function optimization

对于函数优化问题,遗传算法具有较强的全局搜索能力,但其局部搜索能力相对较弱,一般只能搜索到问题的次优解,特别是函数具有多个峰值时,遗传算法易陷入局部解,而采用梯度下降方法寻优,非线性规划具有很强的局部搜索能力,但全局搜索能力较弱,所以研究通过结合两种算法的优点,利用遗传算法实施全局搜索和非线性规划实施局部搜索,以得到函数优化问题的全局最优解.通过测试函数证明,结合非线性规划后,遗传算法不仅能解决多峰函数寻优过程中易陷入局部最优的问题,而且具有很高的寻优效率,取得满意的结果.

The genetic algorithm has strong global searching ability, but its local searching ability is weak. Generally, it could only reach the second-best solution of the function optimization problem, not the optimal one. When the function has multiple peaks, the genetic algorithm is easier to fall into the local minimum, and can not find the global minimum. With the gradient descent method, nonlinear programming has strong local searching ability for the function optimization problem. Therefore, this paper takes the advantage of genetic algorithm and nonlinear programming for multimodal optimization. On one hand, it uses genetic algorithm for global optimization, and on the other hand, it employs nonlinear programming for local optimization. The experimental results show that the method can not only solve the problem that the multi-modal function optimization would easily fall into the local minimum, but also have high iterative optimization efficiency, and could obtain satisfactory results.