A new trisection method for solving Lipschitz bi-objective optimization problems

In this paper, we develop a branch and bounds algorithm to solve bound-construction bi-objective optimization problem. The proposed algorithm allows to determine an approximation of the Pareto optimal solutions sets in both spaces: decisions and objectives ones. By running α-dense space filling curves, we convert a multidimensional bi-objective optimization problem into a one-dimensional one. Hence it gets possible the implementation of the proposed algorithm when objectives depend on more than one decision variable. The proposed algorithm was applied on an engineering problem to find the working space of a robotic manipulator and the obtained results are promising.