解非线性规划的多目标遗传算法及其收敛性

给出非线性约束规划问题的一种新解法。它既不需用传统的惩罚函数,又不需区分可行解和不可行解,新方法把带约束的非线性规划问题转化成为两个目标函数优化问题,其中一个是原约束问题的目标函数,另一个是违反约束的度函数,并利用多目标优化中的Pareto优劣关系设计了一种新的选择算子,通过对搜索操作和参数的合理设计给出了一种新型遗传算法,且给出了算法的收敛性证明,最后数据实验表明该算法对带约束的非线性规划问题求解是非常有效的。

Multi-objective Genetic Algorithm for Nonlinear Programming Problem and Its Convergence

A new approach is presented to solve the nonlinear constrained programming problem.h neither uses any penalty function nor distinguishes the feasible solutions and the infeasible solutions.Firstly,the nonlinear constrained programming problem is transformed into a bi-objeetive optimization problem.One objective is the objective function of the original constrained optimization problem,and the other is the scalar constraints violation.Based on the dominating relation of the Pareto,a new choosing operator is first designed,and then by combining the reasonable design of the searching operation and different parameters,a new genetic algorithm is finally proposed.Moreover,the new algorithm is convergent.The numerical experiment shows that the algorithm is effective in dealing with the nonlinear constrained programming problem.