Abstract

This paper deals with the specifics of computing (fuzzy) steady state probabilities. We use both exhaustive methods and genetic algorithms to determine required minimum and maximum of the modeling system's fuzzy number outputs. The fuzzy steady state probabilities are determined within a framework which utilizes fuzzy, finite, regular Markov chains; the work is a follow-up to work suggested in the paper by Reilly, Buckley, Zheng and Hernandez and more thoroughly elucidated in the submitted paper by Buckley, Reilly and Zheng (In press). Exhaustive method uses intuitive approach to search the maximum and minimum of the modeling system's parameters. It searches every possible value of input variables by certain steps, and compares the output to get the required results. We have implemented two kinds of exhaustive methods, one is naive method, the other is the improved exhaustive method; Genetic Algorithm (GA) uses guided random searching through the input variables space to get the results. Our GA solutions employing floating-point computations reduce computer memory load and speed up computation (relative to using binary representations). The modeling scheme involves complex constraints which, when translated to linear ones, effect a convex space for the search with expedited genetic mutation and crossover. We also compared the results of these different methods in terms of timing and precision.

Key Words:

Genetic Algorithm, exhaustive methods, fuzzy probability, optimization, queuing theory.