An adaptive patch approximation algorithm for bicriteria convex mixed-integer problems

Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case mixed-integer problems, approximation frontier becomes, however, significantly harder. this paper, we propose a new algorithm for approximating programs with constraints. Such are composed patches solutions shared assignments discrete variables. By adaptively creating such patchwork, our is able to create approximations that converge quickly true frontier. As quality measure, use difference in hypervolume between At least certain number required obtain an given quality. This patch complexity gives lower bound on computations. We show performs optimization steps similar order as bound. provide efficient MIP-based implementation algorithm. The efficiency illustrated numerical results showing has strong guarantee while being competitive other state-of-the-art approaches practice.