题 目：Linear Reformulation of Polynomial Discrete Programming for Fast computation
演 讲 人：方述诚，美国工业工程院院士、美国北卡罗来纳州立大学讲座教授
主 持 人：赵连霞，十大正规网投官网平台(中国)有限公司副教授
时 间：2018年12月19日（周三）上午10:00
地 点：校本部东区十大正规网投官网平台420室
主办单位：十大正规网投官网平台(中国)有限公司、十大正规网投官网平台(中国)有限公司青年教师联谊会
演讲人简介：
方述诚，美国工业工程院院士（IISE Fellow），美国北卡罗来纳州立大学工业与系统工程系讲座教授(Walter Clark Chair and Distinguished University Alumni Graduate Professor)，清华大学讲座教授，复旦大学、东北大学、公司荣誉教授，中国科学院咨询教授，台湾清华大学、国立交通大学荣誉讲座教授，曾任美国西部电气公司研究中心资深研究员，美国电话电报公司贝尔实验室经理。主要研究领域是线性与非线性规划、模糊优化、全局优化算法、物流与供应链管理、通信网络设计。著有《线性优化与扩展:理论与算法》、《熵优化与数学规划》等著作，在国际知名的期刊上发表高水平学术论文200多篇。现任Fuzzy Optimization and Decision Making的主编同时在22个科学期刊编辑委员会任职,其中包括Optimization, Journal of Global Optimization, Optimization Letters, Pacific Journal of Optimization, Journal of Management and Industrial Optimization, Journal of Operations and Logistics, International Journal of Operations Research, OR Transactions, Journal of Uncertainties, International Journal of Fuzzy Systems, Iranian Journal of Fuzzy Systems, Journal of Chinese Institute of Industrial Engineers and Journal of the Operations Research Society of China.
演讲内容简介：
Polynomial discrete programming problems are commonly faced but hard to solve. Treating the nonconvex cross-product terms is the key. State-of-the-art methods usually convert such a problem into a 0-1 mixedinteger linear programming problem and then adopt the branch-and-bound scheme to ?nd an optimal solution. Much effort has been spent on reducing the required numbers of variables and linear constraints as well as on avoiding unbalanced branch-and-bound trees. This study presents a set of equations that linearize the discrete cross-product terms in an extremely effective manner. It is shown that embedding the proposed "equations for linearizing discrete products" into those state-of-the-art methods in the literature not only signi?cantly reduces the required number of linear constraints from O4h3n35 to O4hn5 for a cubic polynomial discrete program with n variables in h possible values but also tighten these methods with much more balanced branch-and-bound trees. Numerical experiments con?rm a two-order (102-times) reduction in computational time for some randomly generated cubic polynomial discrete programming problems.
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