Improved McCormick Relaxations for the efficient Global Optimization in the Space of Degrees of Freedom

改进麦考密克松弛以实现自由度空间中的有效全局优化

• 批准号: 326011235
• 负责人: Professor Alexander Mitsos, Ph.D.
• 金额: --
• 依托单位: Lehrstuhl Systemverfahrenstechnik (SVT)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/326011235?language=en
• 关键词: Improved; McCormick; Relaxations; efficient; Global

The objective of the project is to develop an advanced procedure for deterministic global optimization problems. We aim to extend McCormicks technique for construction of convex and concave relaxations in order to directly construct valid affine relaxations of the given problem. We compare the newly developed methods to other relaxation techniques. McCormicks procedure retains the original variable space while other relaxation techniques increase the space of degrees of freedom by introducing auxiliary variables during the relaxation process. We expect that solving the affine relaxations in the original variable space will result in higher computational efficiency and thus decrease the overall computation time of algorithms based on the construction of convex and concave relaxations in the field of global optimization. Four approaches in order to obtain valid affine relaxations will be developed and compared to current state-of-the-art relaxation methods. To enable the comparison, the proposed ideas will be implemented and tested on given benchmark cases found in numerical libraries for global optimization. Furthermore, the ideas will be tested in innovative process systems engineering formulations.

该项目的目标是开发一种用于确定性全局优化问题的高级程序。我们的目的是将McCormiks技巧推广到构造凸和凹松弛，以便直接构造给定问题的有效仿射松弛。我们将新开发的方法与其他松弛技术进行了比较。McCormicks方法保留了原来的变量空间，而其他松弛技术通过在松弛过程中引入辅助变量来增加自由度空间。我们期望在原始变量空间中求解仿射松弛将导致更高的计算效率，从而减少全局优化领域中基于凸凹松弛构造的算法的整体计算时间。为了获得有效的仿射松弛，将开发四种方法，并与当前最先进的松弛方法进行比较。为了能够进行比较，建议的想法将在数字图书馆中找到的特定基准案例上进行实施和测试，以进行全局优化。此外，这些想法将在创新的过程系统工程配方中进行测试。