Surrogate Scalar Functions and Scalarizing Techniques

Abstract

The most common procedure to compute efficient/nondominated solutions in MOP is using a scalarizing technique, which consists in transforming the original multiobjective problem into a single objective problem that may be solved repeatedly with different parameters. The functions employed in scalarizing techniques are called surrogate scalar functions or scalarizing functions. The optimal solution to these functions should be anon dominated solution to the multiobjective problem. These functions temporarily aggregate in a single dimension the p objective functions of the original model and include parameters derived from the elicitation of the DM’s preference information. Surrogate scalar functions should be able to generate nondominated solutions only, obtain any nondominated solution and be independent of dominated solutions. In addition, the computational effort involved in the optimization of surrogate scalar functions should not be too demanding (e.g., increasing too much the dimension of the surrogate problem or resorting to nonlinear scalarizing functions when all original objective functions are linear) and the preference information parameters should have a simple interpretation (i.e., not imposing an excessive cognitive burden on the DM). Surrogate scalar functions should not be understood as “true” analytical representations of the DM’s preferences but rather as an operational means to transitorily aggregate the multiple objective functions and generate nondominated solutions to be proposed to the DM, which expectedly are in accordance with his/her (evolving) preferences.