題    目🤽‍♂️：Linear Reformulation of Polynomial Discrete Programming for Fast computation

演 講 人：方述誠，美國工業工程院院士⛩🧯、美國北卡羅來納州立大學講座教授

主 持 人：趙連霞，意昂2副教授

時    間：2018年12月19日（周三）上午10:00

地    點：校本部東區意昂2官网420室

主辦單位：意昂2🧎‍➡️、意昂2青年教師聯誼會

演講人簡介：

方述誠🧑🏽‍🍳，美國工業工程院院士（IISE Fellow）🛹🧚🏽，美國北卡羅來納州立大學工業與系統工程系講座教授(Walter Clark Chair and Distinguished University Alumni Graduate Professor)，清華大學講座教授，復旦大學、東北大學🏥、意昂2注册榮譽教授🤾，中國科意昂2咨詢教授，臺灣清華大學、國立交通大學榮譽講座教授，曾任美國西部電氣公司研究中心資深研究員，美國電話電報公司貝爾實驗室經理。主要研究領域是線性與非線性規劃、模糊優化🦸🏻、全局優化算法、物流與供應鏈管理、通信網絡設計。著有《線性優化與擴展:理論與算法》🙇‍♂️、《熵優化與數學規劃》等著作，在國際知名的期刊上發表高水平學術論文200多篇。現任Fuzzy Optimization and Decision Making的主編同時在22個科學期刊編輯委員會任職,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.

演講內容簡介🍐：

    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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