Hybrid evolutionary algorithm for solving optimization problems

Abstract

A fast and efficient hybrid evolutionary algorithm (HEA) for solving constrained optimization problems is presented. The algorithm is based on the rules of the (1+μ) evolutionary algorithm, particle transportation theory, the principle of energy minimization, and the law of increasing entropy of particle systems. The rules for evolution and the fitness function for constrained optimization problems are defined using transportation theory. In the algorithm, energy minimization and increasing entropy gradually drive the particle systems in the phase space from non-equilibrium into equilibrium during the evolutionary process, so that individual particles are able to cross over and mutate during the program run and hence the process of finding the optimal solution process is accelerated. Numerical experiments demonstrate that the solutions of the constrained optimization problems found using the algorithm are very accurate and that convergence is fast. Our algorithm is able to find the global solutions of constrained optimization problems more efficiently than traditional evolutionary algorithms, and also avoids the occurrence of premature phenomena during the solution process.

Keywords:

• Hybrid
• Evolutionary algorithm
• Energy minimizing
• Entropy increasing
• Particle transportation theory

Acknowledgements

This work was supported by the National Natural Science Key Foundation of China (Grant No. 60133010), the Research Project of Science and Technology of Education Department of Jiangxi Province (Grant No. Gan-Jiao-Ji-Zi [2005] 150), and the Key Laboratory of High-Performance Computing Technology of Jiangxi Province (Grant No. JXHC-2005-003).