An Evolutionary Algorithm for Global Optimization Based on Level-Set Evolution and Latin Squares

• Published in: IEEE transactions on evolutionary computation Vol. 11; no. 5; pp. 579 - 595
• Main Authors: Wang, Yuping, Dang, Chuangyin
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Artificial intelligence; Computer science; control theory; systems; Computer simulation; Crossovers; Design optimization; Evolutionary algorithm (EA); Evolutionary algorithms; Evolutionary computation; Exact sciences and technology; Genetic mutations; global optimization; Latin squares; Learning and adaptive systems; Level set; level-set evolution; Mathematical analysis; Mathematical models; Monte Carlo methods; Numerical simulation; Operators; Optimization; Scattering; Space exploration; Studies; Testing; Monte Carlo method; Probabilistic approach; Information system; Evolutionary algorithm (EA); Evolutionary algorithm; Contour line; Global optimum; Mean value; Modeling; global optimization; Image segmentation; level-set evolution; Genetic algorithm; Optimal solution; Latin squares; Objective function; Mathematical programming
• ISSN: 1089-778X; 1941-0026
• DOI: 10.1109/TEVC.2006.886802

In this paper, the level-set evolution is exploited in the design of a novel evolutionary algorithm (EA) for global optimization. An application of Latin squares leads to a new and effective crossover operator. This crossover operator can generate a set of uniformly scattered offspring around their parents, has the ability to search locally, and can explore the search space efficiently. To compute a globally optimal solution, the level set of the objective function is successively evolved by crossover and mutation operators so that it gradually approaches the globally optimal solution set. As a result, the level set can be efficiently improved. Based on these skills, a new EA is developed to solve a global optimization problem by successively evolving the level set of the objective function such that it becomes smaller and smaller until all of its points are optimal solutions. Furthermore, we can prove that the proposed algorithm converges to a global optimizer with probability one. Numerical simulations are conducted for 20 standard test functions. The performance of the proposed algorithm is compared with that of eight EAs that have been published recently and the Monte Carlo implementation of the mean-value-level-set method. The results indicate that the proposed algorithm is effective and efficient.