Interactive Programming Methods for Multi-objective Optimization

Abstract

In general, there may be many Pareto solutions in multiobjective optimization problems. The final decision is made among them taking the total balance over all objectives into account. This is a problem of value judgment of decision maker (DM). The totally balancing over criteria is usually called tradeoff. Interactive multiobjective programming searches a solution in an interactive way with DM while eliciting information on his/her value judgment. Then it is important how easily DM can make tradeoff analysis to get a final solution. To this aim, several kinds of interactive techniques for multiple criteria decision making have been developed so far. For details, see the literatures [47, 86, 126, 143, 153, 156]. Above all, the aspiration level approach (reference point methods in some literatures) is now widely recognized to be effective in many practical fields, because: 1. It does not require any consistency of DM’s judgment. 2. Aspiration levels reflect the wish of DM very well. 3. Aspiration levels play the role of probe better than the weight for objective functions. In this chapter, first we will discuss the difficulty in weighting method which is commonly used in the traditional goal programming, and next explain how the aspiration level approach overcomes this difficulty.