INTERACTIVE ROBUST CONE CONTRACTION METHOD FOR MULTIPLE OBJECTIVE OPTIMIZATION PROBLEMS

We introduce a new interactive procedure for multiple objective optimization problems. The identification of the most preferred solution is achieved by means of a systematic dialogue with the decision maker (DM) during which (s) he specifies pairwise comparisons of nondominated solutions from a current sample. We represent this preference information by a compatible form of the achievement scalarizing function, i.e., we are searching for weights of objectives which ensure that the reference solutions are compared by the function in the same way as by the DM. Directions of the isoquants of all compatible achievement scalarizing functions create a cone in the evaluation space, with the origin in a reference point. In successive iterations, each new pairwise comparison of solutions contracts the cone which is zooming on a subregion of nondominated points of greatest interest for the DM. The procedure ends when at least one satisfactory solution is selected or when the DM comes to conclusion that there is no such solution for the current problem setting.