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. Introduction Evolutionary and genetic optimization has, over the past few years, ‘evolved’ from being a rare curiosity to a firmly entrenched practice in the circles of engineering and management optimization. These techniques have been applied to many water resources applications, including groundwater remediation design, optimal reservoir system operation, calibrating rainfall-runoff models, remediation policy selection, and solving multiple objective groundwater pollution contaminant problems (e.g., Ritzel et al, 1994; Wang and Zheng, 1997; Wardlaw and Sharif, 1999; Reed et al., 2001). One of the reasons that genetic algorithms have been chosen is that they have been shown to easily handle non-convex, discrete, discontinuous, noisy, and multi-objective problems (Goldberg, 1989) that arise frequently in these applications. In addition, evolutionary algorithms are arguably domain independent, which make them excellent candidates for the simulation/optimization methodology commonly used in this field. Two areas of evolutionary optimization where progress has been in terms of theory and application are multi-objective optimization and noisy or uncertainty based optimization. Evolutionary multi-objective optimization (EMO) methods, which seek to find the most Pareto