Combining Reliability and Pareto Optimality—An Approach Using Stochastic Multi-Objective Genetic Algorithms

Genetic Algorithms have been successfully applied to numerous water resources problems, including problems with multiple objectives or uncertainty (noise). GAs tackle multi-objective optimization by following three basic principles — advancing the non-dominated frontier; maintaining diversity in the population (through various techniques like sharing, niching, and crowding); and using an elitist. However finding Pareto-optimal solutions becomes complicated when we add uncertainty to the problem. It was found that the solutions obtained using existing multi-objective solvers, although Pareto optimal were not the most robust or reliable solutions. In single-objective problems noise has typically been dealt with using Monte-Carlo-type sampling and some form of aggregate statistics (e.g., the average of the sample fitness). With multiple objectives the noise can interfere in determining non-domination of individuals, diversity preservation, and elitism (the three basic steps in multi-objective optimization). This paper proposes and tests several approaches to tackling some of these problems. These approaches strike a balance between finding the most optimal and the most reliable solution to the problem, thus giving decision makers and designers a practical and robust optimization tool.