Multiobjective Optimization Using the Niched Pareto Genetic Algorithm

Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives (i.e., attributes or criteria) have been combined ad hoc to form a scalar objective function, usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The most recent development in the eld of decision analysis has yielded a rigorous technique for combining attributes multiplicatively (thereby incorporating nonlinearity), and for handling uncertainty in the attribute values. But MultiAttribute Utility Analysis (MAUA) provides only a mapping from a vector-valued objective function to a scalar-valued function, and does not address the diiculty of searching large problem spaces. Genetic algorithms (GAs), on the other hand, are well suited to searching intractably large, poorly understood problem spaces, but have mostly been used to optimize a single objective. The direct combination of MAUA and GAs is a logical next step for multiobjective GA optimization. However, there is an alternative approach. It turns out that the GA is readily modiied to deal with multiple objectives by incorporating the concept of Pareto domination in its selection operator, and applying a niching pressure to spread its population out along the Pareto optimal tradeoo surface. In this report, we discuss the general issues involved in searching large problem spaces while trying to optimize several objectives simultaneously. We explore various combinations of decision analysis techniques , speciically MAUA, and GAs. Finally, we introduce the Niched Pareto GA as an algorithm for nding the Pareto optimal set. We compare and contrast the Niched Pareto GA with MAUA. And we demonstrate the ability of the Niched Pareto GA to nd and maintain a diverse \Pareto optimal population" on two artiicial problems, and an open problem in hydrosystems.