Finding maximum flow with random and genetic search

Abstract

Solving a maximum flow problem requires finding the greatest balanced flow from a source to a sink in a weighted directional graph. In balanced flow, each node's total input and total output are equal. This paper compares one random and two genetic approaches to finding such solutions. The representation of candidate solutions guarantees balanced flow in all products of mutation and crossover. The method of solution uses a stochastic search (random or genetic) to insure that no link is over capacity, no node has excess output, and each allocation is an integer. Then it achieves balance through a fast deterministic search to remove excess input. This method solved a sample problem in about one-ninth as many generations as a genetic search using penalty functions.<>