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 $\alpha$-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.

在本文中，我们开发了一种分支定界算法来解决边界构造双目标优化问题。所提出的算法允许确定两个空间中帕累托最优解集的近似值：决策空间和目标空间。通过跑步$\alpha$-密集空间填充曲线，我们将多维双目标优化问题转化为一维优化问题。因此，当目标依赖于多个决策变量时，所提出的算法的实现成为可能。将所提出的算法应用于寻找机器人机械手工作空间的工程问题，获得的结果很有希望。