Interactive approaches for biobjective problems with progressively changing solution sets

In this study, we develop interactive approaches to find a satisfactory alternative of a decision maker (DM) having a quasiconvex preference function where the alternative set changes progressively. In this environment, we keep searching the available set of alternatives and estimating the preference function of the DM. As new alternatives emerge, we make better use of the available preference information and eventually converge to a preferred alternative of the DM. We test our approaches on biobjective, multi-item, multi-round auction problems. The results show that our approaches work well in terms of both the preference function value of the obtained solution and the amount of preference information required.

Automated summary

The study develops interactive approaches to help decision makers find satisfactory alternatives in a quasiconvex preference function environment, continuously searching alternative sets and estimating the decision maker's preference function to converge on the preferred alternative. Testing on multi-item, multi-round auction problems shows the approaches work well in obtaining solutions with preferred preference function values and minimal preference information needed.