Some Problems On Stochastic Multi-Objective Optimization

Stochastic multi-objective optimization is a kind of uncertain multi-objective optimization, some or all of the parameters of the stochastic multi-objective optimization model are random variables.This gives great difficulties to decision-maker.In order to solve stochastic multi-objective optimization problem,we need to study theory of stochastic multi-objective optimization problem.By means of deterministic multi-objective optimization theory and thought,we analyze and discuss efficient solutions of stochastic multi-objective optimization.We define the standard deviation efficient solution,With the help of definition of the standard deviation efficient solution, the relationships between expect class efficient solution and variance class efficient solution are added. At the same time,stochastic multi-objective optimization theory develop methodically and systematically.We define the a incredibly efficient solution and a joint incredibly efficient solution.Meanwhile,a problem of stochastic linear multi-objective optimization has been considered when right hand side vector follow uniform distribution and cauchy distribution.An equivalent deterministic model of stochastic linear multi-objective optimization is given. An equivalent deterministic model of stochastic linear multi-objective optimization with joint constraint is also given In the case of uncertain information,decision-maker accurately grasp the key of stochastic multi-objective optimization problem.So stochastic multi-objective optimization has a great progress in the practical application.