Bi-objective optimisation over a set of convex sub-problems

During the last decades, research in multi-objective optimisation has seen considerable growth. However, this activity been focused on linear, non-linear, and combinatorial with multiple objectives. Multi-objective mixed integer (linear or non-linear) programming received considerably less attention. In paper we propose an algorithm to compute a finite set of non-dominated points/efficient solutions bi-objective binary problems for which sub-problems obtained when fixing variables are convex, there is feasible variable vectors. Our method uses bound sets exploits convexity property find efficient main problem. creates iteratively updates bounds each vector vectors, these guarantee that exact points generated. For instances where vectors too large generate such provably optimal within reasonable time, our approach can be used as matheuristic by heuristically selecting promising subset explore. This investigation motivated problem beam angle arising radiation therapy planning, solve provide numerical results.