Some Deterministic Algorithms For Global Optimization

Global optimization problems abound in economic modelling, finance, net-works and transportation, databases, chip design, image processing, chemical en-gineering design and control, molecular biology, and environmental engineering.Since there exist multiple local optima that di?er from the global solution, andthe traditional minimization techniques for nonlinear programming are devisedfor obtaining local optimal solution, how to obtain the globally optimal solutionsis very important topic.During the past four decades, many new theoretical, algorithmic and compu-tational contributions have helped to solve global optimization problems arisingfrom important practical applications. Among the contribution list, for generalglobal optimization problems, the filled function methods, the tunnelling methodsand the branch and bound methods are often talked of.In this paper, based on some new contributions, we try to improve on somealgorithms, including the filled function methods and the tunnelling methods.We also try to present some new methods and extend the filled function methodsand the tunnelling methods for the discrete global optimization and nonlinearmixed integer programming.This paper mainly consists of four chapters.In the first chapter, several basis concepts and characters on generally nonlin-ear programming are introduced. And some mainly methods for global optimiza-tion problems are brie?y presented, including the filled function methods, thetunnelling algorithms, the branch and bound methods and the integral methods.In the second chapter, for general unconstrained global optimization prob-lems, three methods are presented, including the new filled function method, themodified tunnelling method and the integral function method.In Section 2.2, a new definition of the filled function is given, it is di?erentfrom the primary definition which was given by Ge in paper [19]. Based onthe definition, a new filled function is proposed, and it has better properties.An algorithm for unconstrained global optimization is developed from the newfilled function. The implementation of the algorithms on several test problem isreported with satisfactory numerical results.In Section 2.3, we give a modified tunnelling function. Based on the function,an algorithm for global optimization is proposed, the algorithm overcomes thesedisadvantages of the tunnelling algorithm. The implementation of the algorithmon several test problem is reported with satisfactory numerical results.A new algorithm for global minimization is introduced in Section 2.4. Basedon an integral function and a vector sequence, the algorithm overcomes the short-comings of some other methods, we further prove that under some conditions the...