Uncertainty based genetic algorithm with varying population for random fuzzy maximum flow problem

Abstract

AbstractThis paper investigates the uncertain maximum flow of a network whose capacities are random fuzzy variables. We have developed the expected value model (EVM) and the chance‐constrained model (CCM) for maximum flow problem (MFP) under random fuzzy environment and formulated their crisp equivalent models. To solve these models, we have proposed a varying population genetic algorithm with indeterminate crossover (VPGAwIC). In VPGAwIC, selection of a chromosome depends on its lifetime. An improved lifetime allocation strategy (iLAS) has also been proposed to determine the lifetime of the chromosome. The ages of the chromosomes are defined linguistically as Young, Middle, and Old, which follow some uncertainty distributions. The crossover probability is indeterminate, and it depends on the ages of the parents, which is defined by an uncertain rule base. The number of offspring, generated from a population of parents, is determined by the reproduction ratio. The population is updated in 2 ways: (i) All the chromosomes with ages greater than their lifetimes are discarded from the population, and (ii) the offspring are combined with their parents for the next generation. The proposed VPGAwIC is compared with the genetic algorithm developed by Gen, Cheng, and Lin (2008) for maximum flow problem. Wilcoxon signed‐rank test has been performed to show the superiority of the proposed VPGAwIC.