Interactive biobjective optimization algorithms and an application to UAV routing in continuous space

We develop interactive optimization algorithms for biobjective problems with continuous nondominated frontiers to search for the most preferred solution of a decision maker who is assumed to have an underlying linear or quasiconvex preference function. We progressively acquire preference information from the decision maker through pairwise comparisons of efficient solutions. We keep reducing the search space based on the obtained preference information and the properties of the form of the preference function. Our algorithms provide a performance guarantee on the final solution's distance from the most preferred solution in the objective function space. We demonstrate the algorithms on complex Unmanned Air Vehicle routing problems in continuous space with nonconvex and continuous nondominated frontiers. We consider the objectives of minimizing the total distance traveled and minimizing the total radar detection threat. We simulate the preference function of the decision maker using several underlying preference functions. The interactive algorithms for all preference functions converge to solutions within the desired accuracies after a few pairwise comparisons.