General purpose metrics for solution variety

Abstract

When using optimization in the context of a decision support system, a decision maker would often be more interested in seeing a diverse collection of good solutions rather than the one solution that is in some mathematical sense the optimal solution to an approximate problem with imprecise data. A recent paper (Glover, Lokketagen and Woodruff, 2000) describes a method for generating diverse solutions using scatter search. However, very little research has been done on general purpose methods to characterize solution variety. This paper describes and explains desirable characteristics for general purpose methods for characterizing diversity. Field research serves to demonstrate and compare various methods. We provide some fundamental research concerning methods that are fully general and do not rely on any knowledge of the problem.© 2005 by Kluwer Academic Publishers.