GENETIC ALGORITHM IN UNCERTAIN ENVIRONMENTS FOR SOLVING STOCHASTIC PROGRAMMING PROBLEM
Yasunari Yoshitomi, Hiroko Ikenoue, Toshifumi Takeba, Shigeyuki Tomita · Journal of the Operations Research Society of Japan · 2000
Mamy real problems with uncertainties may often be formulated as Stochastic PrograuimingProblern.In this study, Genetic Algorithm (GA) which has been recently used fbr solving mathematical programming problem is expanded fbr use in uncertain environments,The modified GA is referred as GA in uncertain environments (GAUCE).In the method, the objective function andlor the constraint are fluctuated accerding to the distribution functions of their stochastic variables, Firstly, the individual with highest frequency through all generatiens is neminated as the individual associated with the solution presenting the best expected value of objective function.The individual with highest ftequency is associated with the solution by GAUCE.The proposed method is applied te Stochastic Optimal Assignment Problem, Stochastic Knapsack Problem and newly formulated Stochastic Image Compression Problem.Then, it has been preved that the solution by GAUCE has exeellent agreernent with the solution presenting the best expected value of objective function, in cases of both Stochastic Optimal Assigriment Problem and Stochastic Knapsack Problem.GAUCE is also successfully applied to Stochastic Image Compression Problem where the coeficients of discrete cosine transformatien are treated as stochastic variables.gramming Problem and ordinary GA, iL is natura,l Lhat GA can be exteiided ic Programming Prob]em, through fiuctuating the fitness function or i,he enviing to Lhe stochustic distribution-functiuns for the variables iii t･he fitiiess aa,ch gcncrn,tieTt of GAUCE, the fit,T)ess function or envirenment The OpeiationsReseaich Society of Japan CIA for Solw'ng Stochastib A'ogramming boblem