MINLP的局部分支启发式算法
A local branching heuristic for MINLPs
摘要：
局部分支是一种改进的启发式算法，在分支定界算法的背景下，MILP，这已被证明是非常有效的实践。对于二进制的情况下，它是基于定义一个邻居的当前现任解决方案，通过只允许几个二进制变量翻转其值，通过添加一个本地分支约束。然后用分支定界求解器探索该邻域。我们提出了一个局部分支计划（非凸）MINLP这是基于迭代求解MILP和NLP。初步的计算实验表明，这种方法是能够改善现任解决方案的大多数测试实例，只需要很短的CPU时间。此外，我们提供了一个原始的启发式算法的想法，其目的是找到第一个可行解，基于相同的计划。
英文摘要：
Local branching is an improvement heuristic, developed within the context of branch-and-bound algorithms for MILPs, which has proved to be very effective in practice. For the binary case, it is based on defining a neighbourhood of the current incumbent solution by allowing only a few binary variables to flip their value, through the addition of a local branching constraint. The neighbourhood is then explored with a branch-and-bound solver. We propose a local branching scheme for (nonconvex) MINLPs which is based on iteratively solving MILPs and NLPs. Preliminary computational experiments show that this approach is able to improve the incumbent solution on the majority of the test instances, requiring only a short CPU time. Moreover, we provide algorithmic ideas for a primal heuristic whose purpose is to find a first feasible solution, based on the same scheme.
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