Semidefinite programming-based approaches for hard combinatorial optimization problems in engineering: modelling, algorithms and applications

组合优化问题在现实生活中的应用非常广泛。例如，设计工厂的人必须决定如何放置不同大小的机器，以便工厂尽可能平稳地运行。这个问题被称为设施布局问题，因为机器的可能布置数量非常多，所以出了名的难。更广泛地说，布局问题出现在工程中的各种应用中。例如，使用宏单元设计技术来设计复杂的电子电路，例如移动电话中使用的那些电路，并且宏单元设计的一些芯片设计问题可以建模为设施布局问题。由于这些电路的内在复杂性，设计过程非常耗时，因此开发新的算法来提高计算机自动化设计过程的效率至关重要。此外，针对这些问题的更好的算法可能会改进电路元件的布局。

Combinatorial optimization problems occur in a wide variety of real-life applications. For example, the person designing a factory must decide how to place the various machines of different sizes so that the factory will operate as smoothly as possible. This problem is known as the facility layout problem and is notoriously difficult because of the very large number of possible arrangements for the machines. More generally, layout problems arise from a variety of applications in engineering. For instance, complex electronic circuits, such as those used in mobile telephones, are designed using macro-cell design techniques, and some chip design problems of macro-cell design can be modelled as facility layout problems. Because of the inherent complexity of these circuits, the design process is extremely time-consuming, hence the development of new algorithms to improve the efficiency of computer-automated design processes is of paramount importance. Furthermore, better algorithms for these problems are likely to lead to improved placements for the circuit components.