Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

Abstract:

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

• Periodical: Advanced Materials Research (Volumes 984-985)
• Pages: 419-424
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.984-985.419
• Online since: July 2014
• Authors: P. Sabarinath*, M.R. Thansekhar, R. Saravanan
• Keywords: Multi-Objective, NSGA-II, TOPSIS, Two Bar Truss

References

[1] C.C.A. Coello, Handling Preferences in Evolutionary Multi-Objective Optimisation: A Survey. Congress on Evolutionary Computation, vol. 1, IEEE Service Center, Piscataway, NJ, Julio del 2000, p.30–37.

[2] Aimin Zhou, Bo-Yang Qu, Hui Li, Shi-Zheng Zhao, Ponnuthurai Nagaratnam Suganthan, Qingfu Zhang, Multiobjective evolutionary algorithms: A survey of the state of the art, Swarm and Evolutionary Computation 1 (2011) 32–490.

DOI: 10.1016/j.swevo.2011.03.001

[3] Srinivas, N. and Deb, K. Multi-Objective function optimization using non-dominated sorting genetic algorithms, Evolutionary Computation, 2(3): 221–248 (1995).

DOI: 10.1162/evco.1994.2.3.221

[4] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation 6 (2) (2002) 182–197.

DOI: 10.1109/4235.996017

[5] Hwang, C.L., Yoon, K., Multiple Attribute Decision Making – Methods and Applications. Springer-Verlag Press, Heidelberg. (1981).

[6] Ali Wagdy Mohamed & Hegazy Zaher Sabry, Constrained optimization based on modified differential evolution algorithm Information Sciences, 194, p.171–208 (2012).

DOI: 10.1016/j.ins.2012.01.008

[7] Kaveh, M. Khayatazad, A new meta-heuristic method: Ray Optimization, Computers and Structures 112-113 283–294 (2012).

DOI: 10.1016/j.compstruc.2012.09.003

[8] Deb K, Multi-objective optimization using evolutionary algorithms. Wiley, New York (2001).

[9] Li M, Azarm S, Aute V A multi-objective genetic algorithm for robust design optimization. Mech Eng 771–778 (2005a).

[10] Antonio Gaspar-Cunha, Jose Ferreira, Gustavo Recio, Evolutionary robustness analysis for multi-objective optimization: benchmark problems, Struct Multidisc Optim, (2013).

DOI: 10.1007/s00158-013-1010-x

[11] S.S. Rao, Optimization Theory and Applications, third ed., John Wiley and Sons, New York, (1996).

[12] Olcay Ersel Canyurt , Prabhat Hajela, Cellular genetic algorithm technique for the Multicriterion design optimization, Struct Multidisc Optim (2010) 40: 201–214.

DOI: 10.1007/s00158-008-0351-3