An Attribute Based Similarity Function for VRP Decision Support

Abstract

When solving problems in the real world using optimization tools, the model solved by the tools is often only an approximation of the underlying, real, problem. In these circumstances, a decision maker (DM) should consider a diverse set of good solutions, not just an optimal solution as produced using the model. On the other hand, the same DM will only be interested in seeing a few of the alternative solutions, and not the plethora of solutions often produced by modern search techniques. There is thus a need to distinguish between good solutions using the attributes of solutions. We develop a distance function of the type proposed in the Psychology literature by Tversky (1977) for the class of VRP problems. We base our difference on the underlying structure of solutions.

A DM is often interested in focusing on a set of solutions fulfilling certain conditions that are of specific importance that day, or in general, like avoiding a certain road due to construction that day. This distance measure can also be used to generate solutions containing these specific classes of attributes, as the normal search process might not supply enough of these interesting solutions. We illustrate the use of the functions in a Multiobjective Decision Support System (DSS) setting, where the DM might want to see the presence (or absence) of certain attributes, and show the importance of identifying solutions not on the Pareto front. Our distance measure can use any attributes of the solutions, not just those defined in the optimization model.