Branch and bound methods which are based on the principle "divide and conquer" are a well established solution approach in single-objective integer programming. In multi-objective optimization branch and bound algorithms are increasingly attracting interest. However, the larger number of objectives raises additional difficulties for implicit enumeration approaches like branch and bound. Since bounding and pruning is considerably weaker in multiple objectives, many branches have to be (partially) searched and may not be pruned directly. The adaptive use of objective space information can guide the search in promising directions to determine a good approximation of the Pareto front already in early stages of the algorithm. In particular we focus in this article on improving the branching and queuing of subproblems and the handling of lower bound sets. In our numerical test we evaluate the impact of the proposed methods in comparison to a standard implementation of multiobjective branch and bound on knapsack problems, generalized assignment problems and (un)capacitated facility location problems.

翻译：基于“分而治之”原则的分支定界法是单目标整数规划中成熟的求解方法。在多目标优化领域，分支定界算法正日益受到关注。然而，目标数量的增加为分支定界这类隐式枚举方法带来了额外困难。由于多目标场景下界约束与剪枝效果显著降低，大量分支仍需（部分）搜索而无法直接剪枝。通过自适应利用目标空间信息，可在算法早期阶段引导搜索向有前途的方向推进，从而获得帕累托前沿的优质近似解。本文重点改进了子问题的分支排序与队列管理以及下界集合的处理方式。在数值实验中，我们评估了所提方法相对于标准多目标分支定界实现在背包问题、广义分配问题及（有/无容量约束）设施选址问题上的性能影响。