Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and by the corresponding termination criteria and node selection steps. In particular, our branch-and-bound concept employs a new enclosure of the set of nondominated points by a union of boxes. On this occasion we also suggest a new discarding test based on a linearization technique. We provide a convergence proof for our general branch-and-bound framework and illustrate the results with numerical examples.

当前对单目标分支定界到多目标环境的中心思想的概括似乎并没有完全遵循其思路。本文通过从部分下限到总体下限的一般构造，以及相应的终止标准和节点选择步骤，对有关部分下限和总体上限的一般化的各种建议进行了补充。尤其是，我们的分支定界概念通过盒子的组合对一组非支配的点进行了新的封装。在这种情况下，我们还建议基于线性化技术的新的丢弃测试。我们为通用分支定界框架提供了收敛证明，并通过数值示例说明了结果。