The Convergence Behavior of the PBIL Algorithm: A Preliminary Approach

In this paper the simplest version of Population Based Incremental Learning (PBIL) is used to minimize the One Max function in two dimensions. After carrying out several experiments to reveal the limit behavior of the algorithm in this function we obtain that the convergence results depend on the initial vector p (0), and on the a parameter value. This experienced behavior is guaranteed for mathematical proof. The probability that the algorithm converges to any point of the search space goes to 1 when p (0) and a go to suitable values. Thus, even though the experimental results seem more stable when the α value is near to zero, we can not ensure that PBIL converges to the optimum.

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