Reference-point-based branch and bound algorithm for multiobjective optimization

In this paper, a nonconvex multiobjective optimization problem with Lipschitz objective functions is considered. A branch and bound algorithm that incorporates the decision maker's preference information is proposed for this problem. In the proposed algorithm, a new discarding test is designed to check whether a box contains preferred solutions according to the preference information expressed by means of reference points. In this way, the proposed algorithm is able to gradually guide the search towards the region of interest on the Pareto fronts during the solution process. We prove that the proposed algorithm obtains e-efficient solutions distributed among the regions of interest with respect to the given reference points. Moreover, lower bound on the total finite number of required iterations for predefined precision is also provided. Finally, the algorithm is illustrated with a number of test problems.