Discrete global descent method for discrete global optimization and nonlinear integer programming

  • Authors:

  • Chi-Kong Ng;Duan Li;Lian-Sheng Zhang

  • Affiliations:

  • Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong S.A.R., P.R.China;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong S.A.R., P.R.China;Department of Mathematics, Shanghai University, Baoshan, P.R.China 200436

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2007

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Abstract

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 脳 10104 feasible points have demonstrated the applicability and efficiency of the proposed method.