The Generalized Rastrigin Function

Description:

      The Generalized Rastrigin Function (Equation 1) is a typical example of non-linear multimodal function. It was first proposed by Rastrigin [TZ89] as a 2-dimensional function and has been generalized by Mühlenbein et al in [MSB91]. This function is a fairly difficult problem due to its large search space and its large number of local minima.

                      (1)
        ; ;

      The Rastrigin function has a complexity of O(nln(n)), where n is the dimension of the problem. The surface of the function is determined by the external variables A and , which control the amplitude and frequency modulation respectively.

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Instances and best known solutions for those instances:

      In order to define an instance of this function we need to provide the dimension of the problem (n). The optimum solution of the problem is the vector v = (0,...,0) with F(v) = 0.

Related Papers:

[TZ89] A. Törn and A. Zilinskas. "Global Optimization". Lecture Notes in Computer Science, Nº 350, Springer-Verlag, Berlin,1989.

[MSB91] H. Mühlenbein, D. Schomisch and J. Born. "The Parallel Genetic Algorithm as Function Optimizer ". Parallel Computing, 17, pages 619-632,1991.

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