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 birandorn 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 birandont 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. (c) 2007 Elsevier Ltd. All rights reserved.