基于Pareto支配的双目标优化求解非线性双层规划问题

双层规划问题是一类具有双层递阶结构的系统优化问题。采用Pareto支配的双目标优化策略求解非线性双层规划问题。利用K-T条件把双层规划问题等价转化单层规划问题,进而结合约束部分建立可行性度量目标形成双目标规划问题。在基本的差分进化算法框架中融入非负的最小二乘曲线拟合判断候选解的可行性,构造基于动态概率的Pareto支配选择策略挑选下一代个体,解决种群容易陷入局部最优的缺陷。15个标准函数的测试结果对比显示,该算法在求解非线性双层规划问题中具有较好的全局寻优能力、较低的计算复杂度、较强的稳定性和适用性,可以获得全局最优解。

BI-OBJECTIVE OPTIMIZATION FOR SOLVING NONLINEAR BILEVEL PROGRAMMING PROBLEMS BASED ON PARETO DOMINATION

The bilevel programming problem is a kind of system optimization problem with bilevel hierarchical structure.In this paper,bi-objective optimization strategy dominated by Pareto is used to solve the nonlinear bilevel programming problem.We used the K-T condition to convert the bi-level programming problem into a single-level planning problem,and then combined the constraint part to establish a feasible measurement target to form a bi-objective programming problem.In the basic differential evolution algorithm framework,non-negative least squares curve fitting was used to judge the feasibility of the candidate solution.The Pareto domination selection strategy based on dynamic probability preference was constructed to select the next generation of individuals,which solved the defect that the population was easy to fall into local optimum.The comparison of test results of 15 standard functions shows that the proposed algorithm has better global optimization ability,lower computational complexity,stronger stability and applicability in solving nonlinear bilevel programming problems,and it can obtain the global optimal solution.