Constrained Multi-Objective Optimization Problems in Mechanical Engineering Design Using Bees Algorithm

Journal of Solid Mechanics

مقاله 5، دوره 3، شماره 4، اسفند 2011، صفحه 353-364   

نوع مقاله: Research Paper

نویسندگان

A Mirzakhani Nafchi^{* 1}؛ A Moradi²

¹Department of Mechanical Engineering, Payame Noor University

²Department of Mechanical Engineering, Chamran University

چکیده

Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using classical optimization methods, this paper presents a Multi-Objective Bees Algorithm (MOBA) for solving the multi-objective optimal of mechanical engineering problems design. In the present study, a satellite heat pipe design, a space truss design and pressure vessel problems are considered. Multi-objective optimization using the bees algorithm which is a new multi-object obtain a set of geometric design parameters, leads to optimum solve. This method is developed in order to obtain a set of geometric design parameters leading to minimum heat pipe mass and the maximum thermal conductance. Hence, a set of geometric design parameters, lead to minimum pressure total cost and maximum pressure vessel volume. Numerical results reveal that the proposed algorithm can find better solutions when compared to other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems.

کلیدواژه‌ها

Bees Algorithm؛ Multi-objective optimization؛ Satellite heat pipe design؛ Pressure vessel design؛ Truss design

مراجع

[1] Deb K., 2001, Multi-Objective Optimization using Evolutionary Algorithms, First edition, Wiley, Chichester, UK.

[2] Schaffer J.D., 1985, Multiple objective optimization with vector evaluated genetic algorithms and their applications, in: Proceedings of the first international conference on Genetic Algorithms, Pittsburgh, PA, USA, 93-100.

[3] Fonseca C.M., Fleming P.J., 1993, Genetic algorithms for multi-objective optimization: Formulation, discussion, and generalization, in: Proceedings of the 5th international conference on Genetic Algorithms, University of Illinois at Urbana-Champaign, July 17-21, 416-423.

[4] Horn J., Nafploitis N., Goldberg D.E., 1994, A niched Pareto genetic algorithm for multi-objective optimization, in:

Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, June 27-29, Orlando, Florida, USA, 82-87.

[5] Srinivas N., Deb K., 1995, Multi-objective function optimization using non-dominated sorting genetic algorithms, Evolutionary Computation Journal 2: 221-248.

[6] Knowles J., Corne D., 1999, The Pareto archived evolution strategy: A new baseline algorithm for multi-objective optimization, in: Proceedings of the Congress on Evolutionary Computation, New Jasery, IEEE Service Center, 98-105.

[7] Deb K., Pratap A., Agrawal S., Meyarivan T., 2000, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, in: Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, Paris, France, 846-858.

[8] Zitzler E., Theiele L., 1999, Multi-objective evolutionary algorithm: a comparartive case study and the strength Pareto approach, Evolutionary Computation Journal 3(4): 257-271.

[9] Zitzler E., Deb K., Thiele L., 2000, Comparison of multi-objective evolutionary algorithms: Empirical results, Evolutionary ComputationJournal 8( 2): 173-195.

[10] Farina M., Deb K., Amato P., 2004, Dynamic multi-objective optimization problems: test cases, approximations, and applications, IEEE Transactions On Evolutionary Computation 8(5): 425-442.

[11] Nebro A.J., Durillo J.J., Luna F., Dorronsoro B., Alba E., 2009, A cellular genetic algorithm for multiojective optimization, International Journal of Intelligent Systems 14(7):726-746

[12] Mainenti I., DeSouza L., Sousa F., Kuga H., Galski R., 2007, Satellite attitude control using the generalized extremal optimization with a multi-objective approach, in: Proceedings of the 19th International Congress of Mechanical Engineering, DF, Brazil.

[13] Copiello D., Fabbri G., 2008, Multi-objective heat transfer optimization in corrugated wall channels by hybrid genetic algorithms, in: Proceedings of the 5th European Congress on Computational Methods in Applied Sciences and Engineeering (ECCOMAS), Venice, Italy, 81-88..

[14] Cuco A., Sousa F., Vlassov V., Neto v., 2008, Multi-Objetive Design Optimization of a New Space Radiator, in: Proceedings of the International Conference on Engineering Optimization, Rio de Janeiro, Brazil, 201-209.

[15] Oliveira L., Saramago S., 2010, Multi-objective optimization techniques applied to engineering problems, Journal of the Brazilian Society of Mechanical Sciences and Engineering 32(1): 94-105.

[16] Khalkhali A., Sadafi M., Rezapour J., Safikhani H., 2010, Pareto based multi-objective optimization of solar thermal energy storage using genetic algorithms, Transactions of the Canadian Society for Mechanical Engineering 34(4): 463-474.

[17] Szparaga L., Ratajski J., Zarychta A., 2011, Multi objective optimization of wear resistant TiAlN and TiN coatings deposite by PVD techniques, Achievements in Materials and Manufacturing Engineering Journal 48(1): 33-39.

[18] Shrivastava R., Singh S., Dubey G.C., 2012, Multi-objective optimization of time cost quality quantity using multi colony ant algorithm, International Journal of Contemporary Mathematical Sciences 7(16): 773-784.

[19] Pham D.T., Ghanbarzadeh A., Koc E., Otri S., Rahim S., Zaidi M., 2005, Technical Note: Bees Algorithm, Technical Report No MEC 0501, Manufacturing Engineering Centre, Cardiff University, Cardiff.

[20] Pham D. T., Ghanbarzadeh A., Koc E., Otri S., Rahim S., Zaidi M., 2006, The Bees Algorithm. A novel tool for complex optimization problems, in: Proceedings of the Second International Conference on Intelligent Production Machines and Systems, 454–459.

[21] Pham D.T., Ghanbarzadeh A., Koc E., Otri S., 2006, Application of the bees algorithm to the training of radial basis function networks for control chart pattern recognition, in: Proceedings of 5th CIRP International Seminar on Intelligent Computation in Manufacturing Engineering, Ischia, Italy, 711-716.

[22] Frisch K., 1967, The Dance Language and Orientation Of Bees, First edition, Harvard University Press, Massachusetts, USA.

[23] Michelsen A., Andersen B., Storm J., Kirchner W., Lindauer M., 1992, How honeybees perceive communication dances, studied by means of a mechanical model, Behavioral Ecology and Sociobiology Journal 30(3-4): 143-150.

[24] Dyer F., 2002, When it pays to waggle, Nature Journal 419(6910): 885-886.

[25] Camazine S., Sneyd J., 1990, A model of collective nectar source by honey bees: self-organization through simple rules, Journal Theoretical Biology Journal 149: 547-571.

[26] Lambrinos D., M¨oller R., Labhart T., Pfeifer R., Wehner R., 2000, A mobile robot employing insect strategies for navigation, Robotics and Autonomous Systems Journal 30(1-2): 39-64.

[27] Müller M., Wehner R., 1988, Path integration in desert ants, Cataglyphis Fortis, Experimental Biology Journal 85(14): 5287-5290.

[28] Collett P., Graham T.S., Durier V., 2003, Route learning by insects, Current Opinion in Neurobiology Journal 13(6): 718-725.

[29] Collett T., Collett M., 2004, How do insects represent familiar terrain, Journal of Physiology 98:259-264.

[30] Barth F. G., 1982, Insects and Flowers: The Biology of a Partnership, First edition, Princeton University Press, Princeton, NJ, USA.

[31] Pham D.T., Otri S., Ghanbarzadeh A., Koc E., 2006, Application of the bees algorithm to the training of learning vector quantization networks for control chart pattern recognition, in: Proceedings of Information and Communication Technologies Conference, Syria, 1624-1629.

[32] Pham D.T., Koç E., Ghanbarzadeh A. Otri S., 2006, Optimization of the weights of multi-layered perceptions using the Bees Algorithm, in: Proceedings of the 5th International Symposium on Intelligent Manufacturing Systems, Turkey, 38-46.

[33] Pham D.T., Castellani M., Ghanbarzadeh A., 2007, Preliminary design using the bees algorithm, in: Proceedings of the International Conference on Laser Metrology, CMM and Machine Tool Performance, LAMDAMAP, Cardiff: euspan Ltd, UK, 420-429.

[34] Jeong M.J., Kobayashi T., Yoshimura Sh., 2005, extraction of design characteristics of multi-objective optimization- Its application to design of artificial satellite heat pipe, Lecture Notes in Computer Science Journal 3410: 561-575.

[35] Geem Z.W., Hwangbo H., 2006, Application of harmony search to multi-objective optimization for satellite heat pipe design, US-Korea Conference on Science, Technology, and Entrepreneurship, Teaneck, NJ, 157-165.

[36] Deb K., Srinivasan A., 2006, Monotonicity analysis, evolutionary multi-objective optimization, and discovery of design principles, in: Proceedings of the Bio-Inspired Computing: Theory and Applications, Wuhan, China, 89-96.

[37] Kelesoglu O., Ulker M., 2005, Fuzzy optimization of geometrical nonlinear space truss design, Engineering Turkish Journal 29: 321- 329.