M. Okamoto, T., Nonaka, S. Ochiai and D. Tominaga, “Nonlinear Numerical Optimization with Use of a Hybrid Genetic Algorithm Incorporating the Modified Powell Method,” Applied Mathematics and Computation, Vol. 91, No. 1, 1998, pp. 63-72. doi:10.1016/S0096-3003(97)10007-8

has been cited by the following article:

• TITLE: A Genetic Algorithm with Weighted Average Normally-Distributed Arithmetic Crossover and Twinkling

  AUTHORS: George S. Ladkany, Mohamed B. Trabia

  KEYWORDS: Genetic Algorithms; Crossover Techniques; Twinkling; Engineering Design; Global Optimization

  JOURNAL NAME: Applied Mathematics, Vol.3 No.10A, November 1, 2012

  ABSTRACT: Genetic algorithms have been extensively used as a global optimization tool. These algorithms, however, suffer from their generally slow convergence rates. This paper proposes two approaches to address this limitation. First, a new crossover technique, the weighted average normally-distributed arithmetic crossover (NADX), is introduced to enhance the rate of convergence. Second, twinkling is incorporated within the crossover phase of the genetic algorithms. Twinkling is a controlled random deviation that allows only a subset of the design variables to undergo the decisions of an optimization algorithm while maintaining the remaining variable values. Two twinkling genetic algorithms are proposed. The proposed algorithmsare compared to simple genetic algorithms by using various mathematical and engineering design test problems. The results show that twinkling genetic algorithms have the ability to consistently reach known global minima, rather than nearby sub-optimal points, and are able to do this with competitive rates of convergence.