Fuzzy Random Multi-attribute To The Shortest Path Problem

The shortest path problem of finding the shortest path from a specified source node to the other nodes is a fundamental problem that appears in many practical applications. It generates essential information in transportation, routing, communications applications, and so on.In this paper, we study the multiple attribute shortest path problems with fuzzy random arc length, which has three attribute: distance, transportation time and transportation cost. We formulate three types of the multi-objectives models: expected shortest path model, minmin pessimistic value criterion model and dependent-chance model. When the objectives are in conflict, there is no optimal solution that is optimal solution of all objective functions simultaneously. We get the compromise model that is set up by weighting the objective functions. We solve these compromise models by a hybrid intelligent algorithm integrating fuzzy random simulation, neural network and genetic algorithm. We also generalize some equivalents of fuzzy constraints or stochastic constraints, and find a crisp equivalent of fuzzy random constraints. Finally, the algorithm and the equivalent of fuzzy random constraints are illustrated by some numerical examples, respectively.This paper is organized as follows: In chapter 1 we introduce the shortest path problems, some essential definitions and preliminary theorems; In chapter 2 we generalize some crisp equivalents of fuzzy constrains or stochastic constrains. We also find a crisp equivalent of fuzzy random constrains; In chapter 3 we formulate three types of the shortest path problem models and introduce a hybrid intelligent algorithm; In chapter 4 we present two numerical examples; In chapter 5 we conclude this paper.