Reactive Search Optimization; Application to Multiobjective Optimization Problems

Amir Mosavi, Atieh Vaezipour

Faculty of Informatics, University of Debrecen, Debrecen, Hungary.
J?nk?ping University, J?nk?ping, Sweden.

DOI: 10.4236/am.2012.330217                

Abstract

During the last few years we have witnessed impressive developments in the area of stochastic local search techniques for intelligent optimization and Reactive Search Optimization. In order to handle the complexity, in the framework of stochastic local search optimization, learning and optimization has been deeply interconnected through interaction with the decision maker via the visualization approach of the online graphs. Consequently a number of complex optimization problems, in particular multiobjective optimization problems, arising in widely different contexts have been effectively treated within the general framework of RSO. In solving real-life multiobjective optimization problems often most emphasis are spent on finding the complete Pareto-optimal set and less on decision-making. However the com-plete task of multiobjective optimization is considered as a combined task of optimization and decision-making. In this paper, we suggest an interactive procedure which will involve the decision-maker in the optimization process helping to choose a single solution at the end. Our proposed method works on the basis of Reactive Search Optimization (RSO) algorithms and available software architecture packages. The procedure is further compared with the excising novel method of Interactive Multiobjective Optimization and Decision-Making, using Evolutionary method (I-MODE). In order to evaluate the effectiveness of both methods the well-known study case of welded beam design problem is reconsidered.

Keywords

Stochastic Local Search; Real-Life Application; Multi Criteria Decision Making; Multiobjective Optimization; Reactive Search Optimization

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Mosavi, “The Multiobjective Optimization Package of IOSO; Applications and Future Trends,” In: CSCS, Conference of PhD Students in Computer Science, University of Szeged, Szeged, 2010, p. 55
[2]	A. Mosavi, “Application of Multiobjective Optimization Packages in Design of an Evaporator Coil,” World Academy of Science, Engineering and Technology, Vol. 61, 2010, pp. 25-29.
[3]	M. Esmaeili and A. Mosavi, “Variable Reduction for Multi-Objective Optimization Using Data Mining Techniques; Application to Aerospace Structures,” Proceeding of ICCET, the 2nd IEEE International Conference on Computer Engineering and Technology, Vol. 5, Chengdu, 16-18 April 2010, pp. V5-333-V5-337.
[4]	A. Mosavi, “Computer Design and Simulation of Built Environment; Application to Forest,” Proceeding of ICECS’09, The Second IEEE International Conference on Environmental and Computer Science, Dubai, 28-30 December 2009, pp. 81-85.
[5]	A. Mosavi, “Hydrodynamic Design and Optimization: Application to Design a General Case for Extra Equipments on the Submarine’s Hull,” Proceeding on IEEE International Conference on Computer Technology and Development, ICCTD’09, Vol. 2, Kota Kinabalu, 13-15 November 2009, pp. 139-143.
[6]	A. Mosavi, “Parametric Modeling of Trees and Using Integrated CAD/CFD and Optimization Tools: Application to Creating the Optimal Planting Patterns for New Forests,” Proceedings of 2nd International Conference Wind Effects on Trees, Albert-Ludwigs-University of Freiburg, Freiburg, 2009.
[7]	H. Afaq and S. Saini, “Swarm Intelligence Based Soft Computing Techniques for the Solutions to Multiobjective Optimization Problems,” International Journal of Computer Science Issues, Vol. 8, No. 3, 2011.
[8]	R. Battiti and P. Campigotto, “Reactive Search Optimization: Learning While Optimizing. An Experiment in Interactive Multiobjective Optimization,” In: S. Voss and M. Caserta, Eds., Proceedings of MIC 2009, VIII Metaheuristic International Conference, Lecture Notes in Computer Science, Springer Verlag, Berlin, 2010.
[9]	R. Battiti, M. Brunato, “Reactive Business Intelligence. From Data to Models to Reactive Search,” Reactive Search Srl, Trento, 2011.
[10]	S. Chaudhuri and K. Deb, “An Interactive Evolutionary Multi-Objective Optimization and Decision Making Procedure,” Applied Soft Computing, Vol. 10, No. 2, 2010, pp. 496-511. doi:10.1016/j.asoc.2009.08.019
[11]	J. Branke, “Consideration of Partial User Preferences in Evolutionary Multiobjective Optimization,” Springer, Berlin, 2008, pp. 157-178.
[12]	A. Mosavi, “On Engineering Optimization the Splined Profiles,” Proceedings of International Conference on Engineering Optimization and International Mode Frontier Users’ Meeting, Trieste, 2010.
[13]	K. Miettinen and M. M. Makela, “Interactive Bundle-Based Method for Nondifferentiable Multiobjective Optimization: Nimbus,” Optimization, Vol. 34, No. 3, 1995, pp. 231-246. doi:10.1080/02331939508844109
[14]	K. Miettinen, “Nonlinear Multiobjective Optimization,” Kluwer, Boston, 1999.
[15]	A. Mosavi, “The Large Scale System of Multiple Criteria Decision Making; Pre-Processing,” Large Scale Complex Systems Theory and Applications, Vol. 9, 2010, pp. 354-359.
[16]	A. Mosavi, “Applications of Interactive Methods of MOO in Chemical Engineering Problems,” Global Journal of Researches in Engineering, Vol. 10, No. 3, 2010, p. 8.
[17]	K. Deb and H. Gupta, “Searching for Robust Pareto-Optimal Solutions in Multi-Objective Optimization,” Proceedings of the Third Evolutionary Multi-Criteria Optimization (EMO-05) Conference (Lecture Notes on Computer Science), Vol. 3410, 2005, pp. 150-164.
[18]	K. Deb and S. Chaudhuri, “I-MODE: An Interactive Multi-Objective Optimization and Decision-Making Using Evolutionary Methods,” Evolutionary Multi-Criterion Optimization, Vol. 4403, 2007, pp. 788-802.
[19]	K. C. Tan, T. H. Lee, D. Khoo and E. F. Khor, “A Multiobjective Evolutionay Algorithm Toolbox for Computer-Aided Multiobjective Optimization,” IEEE Transactions on Systems, Man and Cybernetics—Part B: Cybernetics, Vol. 31, No. 4, 2001, pp. 537-556. doi:10.1109/3477.938259
[20]	A. Mosavi, “Multiobjective Optimization of Spline Curves Using Mode Frontier,” Proceedings of International Conference on Engineering Optimization and International Mode Frontierusers’ Meeting, Trieste, 2010.
[21]	R. Battiti, M. Brunato, F. Mascia, “Reactive Search and Intelligent Optimization,” Operations research/Computer Science Interfaces, Springer Verlag, Berlin, 2008.
[22]	R. Battiti and M. Brunato, “Reactive Search Optimization: Learning While Optimizing,” In: Handbook of Metaheuristics, 2nd Edition, Springer, Berlin, 2009.
[23]	R. Battiti, M. Brunato and F. Mascia, “Reactive Search and Intelligent Optimization,” Operations Research/Computer Science Interfaces, Vol. 45, Springer Verlag, Berlin, 2008.
[24]	H. Takagi, “Interactive Evolutionary Computation: Fusion of the Capabilities of EC Optimization and Human Evaluation,” Proceedings of IEEE, Vol. 89, No. 9, 2001, pp. 1275-1296. doi:10.1109/5.949485
[25]	V. Chankong and Y. Y. Haimes, “Multiobjective Decision Making Theory and Methodology,” North-Holland, New York, 1983.
[26]	A. P. Wierzbicki, “The Use of Reference Objectives in Multiobjective Optimization,” In: G. Fandel and T. Gal, Eds., Multiple Criteria Decision Making Theory and Applications, Springer-Verlag, Berlin, 1980, pp. 468-486. doi:10.1007/978-3-642-48782-8_32
[27]	R. Kamalian, H. Takagi and A. Agogino, “Optimized Design of Mems by Evolutionary Multi-Objective Optimization with Interactive Evolutionary Computation,” Genetic and Evolutionary Computation (GECCO), Vol. 3103, 2004, pp. 1030-1041.
[28]	G. V. Rekliatis, A. Ravindrab and K. M. Ragsdell, “Engineering Optimisation Methods and Applications,” Wiley, New York, 1983.
[29]	C. V. Jones, “Feature Article—Visualization and Optimization,” INFORMS Journal on Computing, Vol. 6, No. 3, 1994, pp. 221-229. doi:10.1287/ijoc.6.3.221
[30]	P. Piero, R. Subbu and J. Lizzi, “MCDM: A Framework for Research and Applications,” IEEE Computational Intelligence Magazine, Vol. 4, No. 3, 2009, pp. 48-61.
[31]	A. Mosavi, “Multiple Criteria Decision-Making Preprocessing Using Data Mining Tools,” International Journal of Computer Science Issues, Vol. 7, No. 2, 2010, pp. 26-34.
[32]	A. Adejuwon and A. Mosavi, “Domain Driven Data Mining; Application to Business,” International Journal of Computer Science Issues, Vol. 7, No 2, 2010, pp. 41-44.
[33]	A. Mosavi, “Application of Data Mining In Multiobjective Optimization Problems,” International Journal for Simulation and Multidisciplinary Design Optimization, Vol. 4, 2010.
[34]	G. Anzellotti, R. Battiti, I. Lazzizzera, P. Lee, A. Sartori, G. Soncini, G. Tecchiolli and A. Zorat, “Totem: A Highly Parallel Chip for Triggering Applications with Inductive Learning Based on the Reactive Tabu Search,” AIHENP95, Pisa, IT, 1995.
[35]	T. Genji, T. Oomori, K. Miyazato, N. Hayashi, Y. Fukuyama and K. Co, “Service Restoration in Distribution Systems Aiming Higher Utilization Rate of Feeders,” Proceedings of the 5th Metaheuristics International Conference (MIC2003), 2003.
[36]	R. Russell, W. Chiang, D. Zepeda, “Integrating Multi-Product Production and Distribution in Newspaper Logistics,” Computers and Operations Research, Vol. 35, No. 5, 2008, pp. 1576-1588. doi:10.1016/j.cor.2006.09.002
[37]	W. Nanry and J. Wesley Barnes, “Solving the Pickup and Delivery Problem with Time Windows Using Reactive Tabu Search,” Transportation Research Part B, Vol. 34, No. 2, 2000, pp. 107-121. doi:10.1016/S0191-2615(99)00016-8
[38]	A. Login and S. Areas, “Reactive Tabu Adaptive Memory Programming Search for the Vehicle Routing Problem with Backhauls,” Journal of the Operational Research Society, Vol. 58, 2007, pp. 1630-1641. doi:10.1057/palgrave.jors.2602313
[39]	J. Chambers and J. Barnes, “New Tabu Search Results for the Job Shop Scheduling Problem,” The University of Texas, Austin, Technical Report Series ORP96-06, Graduate Program in Operations Research and Industrial Engineering, 1996.
[40]	H. Delmaire, J. Diaz, E. Fernandez and M. Ortega, “Reactive GRASP and Tabu Search Based Heuristics for the Single Source Capacitated Plant Location Problem,” INFOR 37, 1999, pp. 194-225.
[41]	A. Fink and S. Vob, “Solving the Continuous Flow-Shop Scheduling Problem by Metaheuristics,” European Journal of Operational Research, Vol. 151, No. 2, 2003, pp. 400-414. doi:10.1016/S0377-2217(02)00834-2
[42]	P. Potocnik and I. Grabec, “Adaptive Self-Tuning Neurocontrol,” Mathematics and Computers in Simulation, Vol. 51, No. 3-4, 2000, pp. 201-207. doi:10.1016/S0378-4754(99)00117-2
[43]	T. Winter and U. Zimmermann, “Real-Time Dispatch of Trams in Storage Yards,” Annals of Operations Research, Vol. 96, 2000, pp. 287-315.
[44]	M. Magdon-Ismail, M. Goldberg, W. Wallace and D. Siebecker, “Locating Hidden Groups in Communication Networks Using Hidden Markov Models,” Lecture Notes in Computer Science, Vol. 2665, 2003, pp. 126-137. doi:10.1007/3-540-44853-5_10
[45]	M. Hifi, M. Michrafy and A. Sbihi, “A Reactive Local Search-Based Algorithm for the Multiple-Choice Multi-Dimensional Knapsack Problem,” Computational Optimization and Applications, Vol. 33, No. 2, 2006, pp. 271-285. doi:10.1007/s10589-005-3057-0
[46]	B. Hu and G. R. Raidl, “Variable Neighborhood Descent with Self-Adaptive Neighborhood Ordering,” In: C. Cotta, A. J. Fernandez and J. E. Gallardo, Eds., Proceedings of the 7th EU/MEeting on Adaptive, Self-Adaptive, and Multi-Level Metaheuristics, Malaga, 2006.
[47]	J. Ryan, T. Bailey, J. Moore and W. Carlton, “Reactive tabu Search in Unmanned Aerial Reconnaissance Simulations,” Proceedings of the 30th Conference on Winter Simulation, 1998, pp. 873-880.
[48]	R. Kincaid and K. Laba, “Reactive Tabu Search and Sensor Selection inActive Structural Acoustic Control Problems,” Journal of Heuristics, Vol. 4, No. 3, 1998, pp. 199-220. doi:10.1023/A:1009681732632
[49]	P. Hansen and N. Mladenovic, “Variable Neighborhood Search,” In: E. Burke and G. Kendall, Eds., Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, Springer, Berlin, 2005, pp. 211-238.
[50]	K. Hamza, H. Mahmoud and K. Saitou, “Design Optimization of N-Shaped Roof Trusses Using Reactive Taboo Search,” Applied Soft Computing Journal, Vol. 3, No. 3, 2003, pp. 221-235. doi:10.1016/S1568-4946(03)00036-X
[51]	J. Blachut, “Tabu Search Optimization of Externally Pressurized Barrels and Domes,” Engineering Optimization, Vol. 39, No. 8, 2007, pp. 899-918. doi:10.1080/03052150701512604
[52]	A. Mosavi, A. S. Milani, M. Hoffmann and M. Komeili, “Multiple Criteria Decision Making Integrated with Mechanical Modeling of Draping for Material Selection of Textile Composites,” Paper and poster in Proceeding of 15th Eeuropean Conference on Composite Materials, Venice, 24-28 June 2012.
[53]	A. Mosavi, M. Hoffmann and A. S. Milani, “Adapting the Reactive Search Optimization and Visualization Algorithms for Multiobjective Optimization Problems; Application to Geometry,” Conference of PhD Students in Computer Science, Szeged, June 2012
[54]	A. Mosavi, M. Hoffmann and A. S. Milani, “Optimal Design of the NURBS Curves and Surfaces Utilizing Multiobjective Optimization and Decision Making Algorithms of RSO,” Conference of PhD Students in Mathematics, Szeged, Jnue 2012.
[55]	E. Foldi, A. Delavar, A. Mosavi, K. N. Hewage, A. S. Milani, A. A. Moussavi and M. Yeheyis, “Reconsidering the Multiple Criteria Decision Making Problems of Construction Projects; Using Advanced Visualization and Data Mining Tools,” Conference of PhD Students in Computer Science, Szeged, 28-30 June 2012.
[56]	A. Mosavi, M. Azodinia, Abbas S. Milani, Kasun N. Hewage and M. Yeheyis, “Reconsidering the Multiple Criteria Decision Making Problems of Construction Workers with the Aid of Grapheur,” Newsletter of Engin Soft CAE Conference 2011, No. 4, 2011.
[57]	A. Mosavi, M.Azodinia Abbas S. Milani, Kasun N. Hewage and M.Yeheyis, “Reconsidering the Multiple Criteria Decision Making Problems of Construction Workers with the Aid of Grapheur,” International ANSYS and EnginSoft Conference, 2011.
[58]	R. Lenne, C. Solnon, T. Stutzle, E. Tannier and M. Birattari, “Reactive Stochastic Local Search Algorithms for the Genomic Median Problem,” Lecture Notes in Computer Science, Vol. 4972, 2008, pp. 266-276. doi:10.1007/978-3-540-78604-7_23
[59]	http://www.lionsolver.com
[60]	R. Kunkli and M. Hoffmann, “Skinning of Circles and Spheres,” Computer Aided Geometric Design, Vol. 27, 2010, pp. 611-621.