基于PEV准则的不确定随机多目标规划问题求解

为解决独立变量的不确定随机多目标规划问题在传统求解中存在分析不全面等问题,在期望值-方差准则下提出了一种新的求解方法。基于机会理论,引入不确定随机变量,在此基础上提出了不确定随机多目标规划问题;引入不确定随机变量的序关系,利用变量间的序关系把不确定随机多目标规划问题转化成不确定随机单目标规划问题,并通过期望值-方差准则把不确定随机单目标规划问题转化成确定的单目标规划问题进行求解;通过理论推导证明,在新准则下转化后的问题得到的最优解是原不确定随机多目标规划问题的有效解;最后,通过对无人机情报侦察监视任务分配问题的求解,利用改进的萤火虫算法求得有效飞行序列,验证了所提方法的可行性和有效性。

Solving Uncertain Random Multi-objective Programming Problems Based on PEV Principle

Aiming at the shortcomings of the traditional solution method for multiobjective programming with independent uncertain random variables, a new method is proposed to solve the problem under the new criterion. First of all, through the introduction of uncertainty relation between random variables, an effective solution of uncertain stochastic multiobjective programming problem is defined; Then, by using sequence relationship between the variables, the uncertain stochastic multi-objective problem is transformed into single objective stochastic uncertain programming problems. The uncertain stochastic single objective programming problem is converted into a deterministic single objective programming problem via the expected-variance value principle. Then the validity is proved that the optimal solution of the deterministic single objective programming problem is an efficient solution of the original I-URMOP problem; Finally through using the improved firefly algorithm, the ISR task assignment problem of the UAV is solved, and the feasibility of the method is verified.