Multi-objective Optimization - Interactive Methods

Interactive Methods

In interactive methods, the solution process is iterative and the decision maker continuously interacts with the method when searching for the most preferred solution (see e.g.,,). In other words, the decision maker is expected to express preferences at each iteration in order to get Pareto optimal solutions that are of interest to him/her and learn what kind of solutions are attainable. The following steps are commonly present in interactive methods :

1. initialize (e.g., calculate ideal and approximated nadir objective vectors and show them to the decision maker)
2. generate a Pareto optimal starting point (by using e.g. some no-preference method or solution given by the decision maker)
3. ask for preference information from the decision maker (e.g., aspiration levels or number of new solutions to be generated)
4. generate new Pareto optimal solution(s) according to the preferences and show it/them and possibly some other information about the problem to the decision maker
5. if several solutions were generated, ask the decision maker to select the best solution so far
6. stop, if the decision maker wants to; otherwise, go to step 3).

Above, aspiration levels refer to desirable objective function values forming a reference point. Instead of mathematical convergence that is often used as a stopping criterion in mathematical optimization methods, a psychological convergence is emphasized in interactive methods. Generally speaking, a method is terminated when the decision maker is confident that (s)he has found the most preferred solution available.

Different interactive methods involve different types of preference information. For example, three types can be identified: methods based on 1) trade-off information, 2) reference points and 3) classification of objective functions. On the other hand, a fourth type of generating a small sample of solutions is included in and. An example of interactive method utilizing trade-off information is the Zionts-Wallenius method, where the decision maker is shown several objective trade-offs at each iteration, and (s)he is expected to say whether (s)he likes, dislikes or is indifferent with respect to each trade-off. In reference point based methods (see e.g.,,), the decision maker is expected at each iteration to specify a reference point consisting of desired values for each objective and a corresponding Pareto optimal solution(s) is then computed and shown to him/her for analysis. In classification based interactive methods, the decision maker is assumed to give preferences in the form of classifying objectives at the current Pareto optimal solution into different classes indicating how the values of the objectives should be changed to get a more preferred solution. Then, the classification information given is taken into account when new (more preferred) Pareto optimal solution(s) are computed. In the satisficing trade-off method (STOM) three classes are used: objectives whose values 1) should be improved, 2) can be relaxed, and 3) are acceptable as such. In the NIMBUS method, two additional classes are also used: objectives whose values 4) should be improved until a given bound and 5) can be relaxed until a given bound.