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Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with BARON

机译：与男爵混合整数非线性规划问题全局优化的积分

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摘要

In this paper, we present recent developments in the global optimization software BARON to address problems with integer variables. A primary development was the addition of mixed-integer linear programming relaxations to BARON's portfolio of linear and nonlinear programming relaxations, aiming to improve dual bounds and offer good starting points for primal heuristics. Since such relaxations necessitate the solution of NP-hard problems, their introduction to a branch-and-bound algorithm raises many practical issues regarding their effective implementation. In addition to describing BARON's dynamic strategy for deciding under what conditions to activate integer programming relaxations in the course of branch-and-bound, the paper also describes cutting plane and probing techniques that originate from the literature of integer linear programming and have been adapted in BARON to solve nonlinear problems. Finally, we describe BARON's primal heuristics for finding good solutions of mixed-integer nonlinear programmes. For all these techniques, we report extensive computational results on a public data set, aiming to analyse the impact of each technique in the solution process and identify techniques that expedite solution the most.
机译：在本文中，我们在全球优化软件Baron中提出了最新的发展，以解决整数变量的问题。主要开发是将混合整数的线性编程放松添加到Baron的线性和非线性编程放松组合，旨在改善双界并为原始启发式提供良好的起点。由于这种放松需要解决NP难题的解决方案，因此它们对分支和绑定算法的引入提出了关于其有效实施的许多实际问题。除了描述Baron的动态策略，在分支和绑定过程中激活整数规划放松的条件下，本文还描述了源自整数线性编程文献的切割平面和探测技术，并进行了调整巴隆解决非线性问题。最后，我们描述了Baron的原始启发式，以寻找混合整数非线性计划的良好解决方案。对于所有这些技术，我们在公共数据集上报告了广泛的计算结果，旨在分析各种技术在解决方案过程中的影响，并确定最佳解决方案的技术。

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