Birandom variables and birandom programming

The emphasis of this paper is to introduce a novel concept of birandom variable and to exhibit the framework of birandom programming. The so-called birandom variable is a measurable mapping from a probability space to a collection of random variables. Based on this definition, the expected value operator of birandom variable and chance measures of birandom event are further introduced. As a generalized scenario of stochastic programming, a spectrum of birandom programming models are developed to deal with birandom systems. To solve the proposed models, birandom simulations are presented and then a hybrid intelligent algorithm is designed by embedding neural networks into genetic algorithm. Finally, some numerical experiments are provided to illustrate the effectiveness of the algorithm.

[1]  Baoding Liu,et al.  Fuzzy random chance-constrained programming , 2001, IEEE Trans. Fuzzy Syst..

[2]  Baoding Liu,et al.  Random fuzzy dependent-chance programming and its hybrid intelligent algorithm , 2002, Inf. Sci..

[3]  Arnold F. Shapiro,et al.  The merging of neural networks, fuzzy logic, and genetic algorithms , 2002 .

[4]  Mitsuo Gen,et al.  Evolution program for deterministic and stochastic optimizations , 1996 .

[5]  Jitka Dupacová,et al.  Applications of stochastic programming: Achievements and questions , 2002, Eur. J. Oper. Res..

[6]  Baoding Liu,et al.  Uncertain Programming , 1999 .

[7]  Jatinder N. D. Gupta,et al.  Comparative evaluation of genetic algorithm and backpropagation for training neural networks , 2000, Inf. Sci..

[8]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[9]  George B. Dantzig,et al.  Linear Programming Under Uncertainty , 2004, Manag. Sci..

[10]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[11]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[12]  Roger J.-B. Wets.  Challenges in stochastic programming , 1996, Math. Program..

[13]  A. Charnes,et al.  Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints , 1963 .

[14]  Mitsuo Gen,et al.  Genetic algorithms and engineering optimization , 1999 .

[15]  Baoding Liu,et al.  Fuzzy random dependent-chance programming , 2001, IEEE Trans. Fuzzy Syst..

[16]  Mitsuo Gen,et al.  Genetic algorithm approach on multi-criteria minimum spanning tree problem , 1999, Eur. J. Oper. Res..

[17]  John R. Birge.  Models and model value in stochastic programming , 1995, Ann. Oper. Res..

[18]  Yian-Kui Liu,et al.  Expected Value Operator of Random Fuzzy Variable, Random Fuzzy Expected Value Models , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[19]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[20]  Yasunari Yoshitomi,et al.  GENETIC ALGORITHM IN UNCERTAIN ENVIRONMENTS FOR SOLVING STOCHASTIC PROGRAMMING PROBLEM , 2000 .

[21]  Mitsuo Gen,et al.  Fuzzy multiple objective optimal system design by hybrid genetic algorithm , 2003, Appl. Soft Comput..

[22]  Mitsuo Gen,et al.  Network design techniques using adapted genetic algorithms , 2001 .

[23]  Baoding Liu.  Dependent-Chance Programming: A Class of Stochastic Optimization , 1997 .

[24]  Yian-Kui Liu,et al.  Fuzzy Random Variables: A Scalar Expected Value Operator , 2003, Fuzzy Optim. Decis. Mak..