Journal of Global Optimization

, Volume 31, Issue 4, pp 635–672 | Cite as

A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems

  • M. Montaz AliEmail author
  • Charoenchai Khompatraporn
  • Zelda B. Zabinsky


There is a need for a methodology to fairly compare and present evaluation study results of stochastic global optimization algorithms. This need raises two important questions of (i) an appropriate set of benchmark test problems that the algorithms may be tested upon and (ii) a methodology to compactly and completely present the results. To address the first question, we compiled a collection of test problems, some are better known than others. Although the compilation is not exhaustive, it provides an easily accessible collection of standard test problems for continuous global optimization. Five different stochastic global optimization algorithms have been tested on these problems and a performance profile plot based on the improvement of objective function values is constructed to investigate the macroscopic behavior of the algorithms. The paper also investigates the microscopic behavior of the algorithms through quartile sequential plots, and contrasts the information gained from these two kinds of plots. The effect of the length of run is explored by using three maximum numbers of function evaluations and it is shown to significantly impact the behavior of the algorithms.


Controlled random search Differential evolution Empirical comparison of algorithms Genetic algorithm Global optimization Hide-and-Seek Improving Hit-and-Run Performance profile and Test problems Population set based global optimization Simulated annealing 


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Copyright information

© Springer 2005

Authors and Affiliations

  • M. Montaz Ali
    • 1
    Email author
  • Charoenchai Khompatraporn
    • 2
  • Zelda B. Zabinsky
    • 2
  1. 1.School of Computational and Applied MathematicsWitwatersrand UniversityJohannesburgSouth Africa
  2. 2.Industrial EngineeringUniversity of WashingtonSeattleUSA

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