確定性演算法應用於工程最佳化問題

A Deterministic Approach for Solving Engineering Optimization Problems

徐雯雯(Cholada Kittipittayakorn)

指導教授 ： 蔡榮發

國立臺北科技大學/管理學院/管理國際學生碩士專班 (IMBA)/碩士(2011年)

摘要

Mixed-integer nonlinear programming (MINLP) problems have been intensively studied in the last decades due to its theoretical interest and its wide applicability. Several strategies and software for solving nonconvex MINLP problems have been proposed. Although many optimization approaches have been developed for MINLP problems, these methods can only find a local or approximate solution or use too many extra binary variables and constraints to reformulate the problem. Therefore, this study proposes a method for solving an MINLP problem in engineering optimization to obtain a global solution. The MINLP problem is transformed into a convex mixed-integer program by the convexification strategies and piecewise linearization techniques. A global optimum of the MINLP problem can then be found within the tolerable error. Numerical examples are also presented to demonstrate the effectiveness of the proposed method.

關鍵字

工程問題 ； 線性化

並列摘要

Mixed-integer nonlinear programming (MINLP) problems have been intensively studied in the last decades due to its theoretical interest and its wide applicability. Several strategies and software for solving nonconvex MINLP problems have been proposed. Although many optimization approaches have been developed for MINLP problems, these methods can only find a local or approximate solution or use too many extra binary variables and constraints to reformulate the problem. Therefore, this study proposes a method for solving an MINLP problem in engineering optimization to obtain a global solution. The MINLP problem is transformed into a convex mixed-integer program by the convexification strategies and piecewise linearization techniques. A global optimum of the MINLP problem can then be found within the tolerable error. Numerical examples are also presented to demonstrate the effectiveness of the proposed method.

並列關鍵字

Engineering optimization ； mixed-integer nonlinear programming ； convexification ； piecewise linearization

參考文獻

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