Numerical evaluation of probabilistic methods for non-continuous global optimization

Currently global optimization becomes a widely used technique for solving complex problems in physics, engineering, biology, economy and other fields of human activity. By using the developed computer program, we examine functionality and efficiency of modern global optimization methods such as Improving Hit-and-Run, Simulated Annealing, Genetic Algorithm, Modified Differential Evolution and Electromagnetism-Like-Mechanism. Furthermore, we conduct comparative statistic investigations of these methods under identical stopping conditions over a set of 50 test functions having different complexity and dimension up to 20. Crucially, we reveal that the modified method of differential evolution developed by Ali, Pant and Abraham in 2009 is the most powerful and effective technique. In general, it requires minimum computation efforts to find a global optimum and has the maximum percent of correct solutions as compared to other considered methods.

Publication year: 
2012
Issue: 
1
УДК: 
519.6
С. 81—88. Іл. 4. Табл. 3. Бібліогр.: 16 назв.
References: 

1. Haupt R., Haupt S. Practical Genetic Algorithms // Wiley-Interscience, 2004. — 254 p.
2. Weise T. Global Optimization Algorithms. Theory and Application. — Self-published, 2009. — 820 p. — http://www.it-weise.de/projects/book.pdf
3. Ali М., Zabinsky B. A numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems // J. of Global Optimization. — 2005. — 31. — Р. 635—672.
4. Storn R., Price K. Differential evolution — a simple and efficient heuristic for global optimization over continuous spaces // Ibid. — 1997. — 11. — P. 341—359.
5. Fan H., Lampinen J. A Trigonometric Mutation Operation to Differential Evolution // Ibid. — 2003. — 27. — P. 105—129.
6. Draa A., Meshoul S. A Quantum-Inspired Differential Evolution Algorithm for Solving the N-Queens Problem // The Int. Arab J. of Information Technology. — 2010. — 7. — P. 21—27.
7. Locatelli М. Simulated Annealing Algorithms for Continuous Global Optimization: Convergence Conditions // J. of Optimization Theory and Applications. — 2000. — 104. — P. 121—133.
8. Dervis K. A Simple and GO Algorithm for Engineering Problems — DE Algorithm // Turkish J. of Electrical Engineering and Computer Sciences. — 2004. — 12. — Р. 53—55.
9. Advances in Differential Evolution / Ed. Uday Ch. // Studies in Computational Intelligence. — Berlin: Springer, 2009. — P. 15—19.
10. Chunjiang Zhang. Electromagnetism-like Mechanism For Fuzzy Flow Shop Scheduling Problems Algorithm // J. of Global Optimization. — 2003. — 25. — P. 263—282.
11. Субботин С.А., Олейник А.А. Сравнительный анализ методов эволюционного поиска // Искусственный интеллект. — 2008. — № 6. — C. 125—129.
12. Aluffi-Pentini F., Parisi V., Zirilli F. Global optimization and stochastic differential equations // J. of optimization theory and applications. — 1985. — 47, Is. 1. — Р. 1—16.
13. Ali М., Storey С. Application of some stochastic global optimization algorithms to practical problems // Ibid. — 2004. — P. 545—563.
14. Тихомиров А.С. О быстрых алгоритмах метода отжига // Вестник Новгородского гос. ун-та. — 2009. — № 9. — C. 111—113.
15. Kaelo P., Ali M. Differential evolution algorithms using hybrid mutation // Computational Optimization and Applications. — 2007. — 37. — P. 231—246.
16. Huang Z., Wang Ch. A Robust Archived Differential Evolution Algorithm for Global Optimization Problems // J. of Computers. — 2009. — 4. — P. 160—167.

AttachmentSize
2012-1-11.pdf292.57 KB

Тематичні розділи журналу

,