Interactive Multiple Criteria Decision Making for Large-Scale Multi-Objective Optimization Problems

Abstract

Despite the rapid development of optimization techniques, there are still practical multiobjective optimization problems hard to solve, e.g., the large-scale portfolio selection or intensity modulated radiation therapy planning. An effective search among potential decisions to such problems can be time consuming or even beyond allotted limits. To account for this, we propose an interactive multiple criteria decision making scheme with a mix of exact and approximate optimization methods. In that concept, a relatively small set of efficient solutions, so-called shell, is derived by an exact method before the decision making process begins. A shell provides for lower and upper bounds on values of objective functions of efficient decisions and such bounds are easily calculable. During the interactive-iterative decision process such bounds are calculated for decisions corresponding to the decision maker's temporal preferences. Such bounds serve in the decision making process as replacements for the exact values of the objective functions. Bounds stemming from a shell, if not tight enough to conduct the decision process, can be strengthened by lower bounds provided by so-called lower shells, i.e., sets of feasible decisions approximating the set of efficient decisions, derivable by a population based (inexact) method. We illustrate the operations of the scheme on a selected test problem.