A Branch-and-Estimate Heuristic Procedure for Solving Nonconvex Integer Optimization Problems

Prashant Palkar, Ashutosh Mahajan
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Abstract

We present a method for solving nonconvex mixed-integer nonlinear programs using a branch-and-bound framework. At each node in the search tree, we solve the continuous nonlinear relaxation multiple times using an existing non-linear solver. Since the relaxation we create is in general not convex, this method may not find an optimal solution. In order to mitigate this difficulty, we solve the relaxation multiple times in parallel starting from different initial points. Our preliminary computational experiments show that this approach gives optimal or near-optimal solutions on benchmark problems, and that the method benefits well from parallelism.
求解非凸整数优化问题的分支估计启发式方法
给出了一种用分支定界框架求解非凸混合整数非线性规划的方法。在搜索树的每个节点上,我们使用已有的非线性求解器求解连续非线性松弛问题多次。由于我们创建的松弛通常不是凸的,所以这种方法可能找不到最优解。为了减轻这一困难,我们从不同的初始点开始并行求解多次松弛。我们的初步计算实验表明,该方法在基准问题上给出了最优或接近最优的解决方案,并且该方法从并行性中获益颇多。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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