On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions

The implementation of global optimization algorithms, using the arithmetic of infinity, is considered. A relatively simple version of implementation is proposed for the algorithms that possess the introduced property of strong homogeneity. It is shown that the P-algorithm and the one-step Bayesian algorithm are strongly homogeneous.Comment: 11 pages, 1 figur

Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently

Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently

Multithreshold Segmentation by Using an Algorithm Based on the Behavior of Locust Swarms

As an alternative to classical techniques, the problem of image segmentation has also been handled through evolutionary methods. Recently, several algorithms based on evolutionary principles have been successfully applied to image segmentation with interesting performances. However, most of them maintain two important limitations: (1) they frequently obtain suboptimal results (misclassifications) as a consequence of an inappropriate balance between exploration and exploitation in their search strategies; (2) the number of classes is fixed and known in advance. This paper presents an algorithm for the automatic selection of pixel classes for image segmentation. The proposed method combines a novel evolutionary method with the definition of a new objective function that appropriately evaluates the segmentation quality with respect to the number of classes. The new evolutionary algorithm, called Locust Search (LS), is based on the behavior of swarms of locusts. Different to the most of existent evolutionary algorithms, it explicitly avoids the concentration of individuals in the best positions, avoiding critical flaws such as the premature convergence to suboptimal solutions and the limited exploration-exploitation balance. Experimental tests over several benchmark functions and images validate the efficiency of the proposed technique with regard to accuracy and robustness