Extension for multicriteria problems
In this chapter, our goal is to generalize the geometric branch-and-bound algorithm to multicriteria optimization problems. To this end, after a short introduction in Section 4.1 we summarize the fundamental definitions and results about multicriteria optimization in Section 4.2. We remark that most of the results in the following sections can also be found in Scholz (2010). However, we introduce the concept of multicriteria bounding operations in Section 4.3 which has not been used therein. Next, in Section 4.4 we prove the convergence of the proposed algorithm as well as properties of the output set. The method is demonstrated on bicriteria facility location problems in Section 4.5 and some numerical results are given in Section 4.6.
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