求解多目标多项式整数规划的Gröbner基方法
A Gröbner bases methodology for solving multiobjective polynomial integer programs
摘要：
多目标离散规划是一类著名的最优化问题，有着广泛的应用。线性的情况下，已处理了许多作者在过去几年中。然而，多项式的情况下，没有深入研究，由于其理论和计算上的困难。本文提出了一种代数方法来解决这些问题。我们提出了一种方法的基础上转换的多项式最优化问题的问题，解决一个或多个系统的多项式方程，我们使用某些Gröbner基地来解决这些系统。不同的变换给出了不同的方法，从理论的角度和一些计算实验，通过他们诱导的算法进行分析和比较。
英文摘要：
Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been deeply studied due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem in the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are analyzed and compared from a theoretical point of view and by some computational experiments via the algorithms that they induce.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
