An improved chaotic optimization algorithm using a new global locally averaged strategy

Tayeb Hamaizia (1) , René Lozi (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

Recently chaotic optimization algorithms as an emergent method of global optimization have attracted much attention in engineering applications. Their good performances have been emphasized . In the frame of evolutionary algorithms, the use of chaotic sequences instead of random ones has been introduced by Caponetto and al. [4]. Since their original work, the literature on chaotic optimisation is flourishing. They are used in the scope of tuning method for determining the parameters of PID control for an automatic regulator voltage, or in order to solve economic dispatch problems, or also for engineering design optimization and in many others physical, economical and biological problems. Different chaotic mapping have been considered, combined with several working strategies. The assessments of the algorithms have been done with respect to numerous objective functions in 1, 2 or 3-dimension. In this paper we present an improvement of the COLM (Chaotic Optimization based on Lozi Map) presented in [1], which is based on a new global locally averaged strategy. The simulation results are done in 2 and 3-dimension. In 2-dimension the objective function possessing hundreds of local minima is used, in order to test this new method vs the previous one in very tough conditions. In 3-dimension both Griewank and Rosenbrock objective functions are tested. We emphasize improvement of the numerical optimization results.

Mots clés: Chaos optimization algorithms; global optimization; chaotic mapping

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]; Dynamique Chaotique [nlin.CD]

Tayeb Hamaizia, René Lozi. An improved chaotic optimization algorithm using a new global locally averaged strategy. Journal of Nonlinear Systems and Applications, 2012, 3 (3-4), pp.58-63. ⟨hal-01333653⟩