In this article, a new algorithm for solving multi-objective optimization problems is proposed by extending the single objective scatter search template to deal with multiple objectives. The features like Pareto dominance, density estimation, and an external archive to store the nondominated solutions are added. The traditional solution combination of scatter search template is however replaced with two-point crossover operator being used in evolutionary algorithms in order to improve the convergence characteristics of the proposed scatter search algorithm. The resulting hybrid scatter search algorithm is employed to solve stacking sequence optimization of hybrid fiber-reinforced composite plate, cylindrical shell, and pressure vessel. Performance metrics are used to demonstrate the effectiveness of the proposed algorithm over other popular evolutionary algorithms like NSAGA-II, PAES, Micro-GA, and MOPSO.
Callahan, K.J. and Weeks, G.E. (1992). Optimum Design of Composite Laminates Using Genetic Algorithms, International Journal of Composites Engineering, 2: 149-160.
2.
Le Riche, R. and Haftka, R.T. (1993). Optimisation of Laminate Stacking Sequence for Buckling Load Maximisation by Genetic Algorithm , AIAA Journal, 31(5): 951-956.
3.
Bert, C.W. ( 1977). Optimal Design of Composite Material Plates to Maximise its Fundamental Frequency, Journal of Sound and Vibration , 50: 229-237.
4.
Reiss, R. and Ramachandran, S. ( 1987). Maximum Frequency Design of Symmetric Angle Ply-laminates , Composite Structures, 100: 476-487.
5.
Adali, S. ( 1995). Lay-up Optimization of Laminated Plates under Buckling loads, In: Turvey, G.J. and Marshall, I.H. (eds), Buckling and Post Buckling of Composite Plates, Chapman & Hall, London.
6.
Venkataraman, S. and Haftka, R. ( 1999). Optimization of Composite Panels-A Review, In: Proceedings of the American Society of Composites - 14th Annual Technical Conference, Fairborn, OH, pp. 479-488.
7.
Kumar, N. and Tauchert, T.R. ( 1992). Multiobjective Desing of Symmetrically Laminated Plates , Journal of Mechanical Design, 114(4): 620-625.
8.
Adali, S., Walker, M. and Verijenko, V.E. ( 1996). Multi-objective Optimization of Laminated Plates for Maximum Pre Buckling, Buckling and Post buckling Strengths Using Continuous and Discrete Ply Angles, Composite Structures, 35(1): 117-130.
9.
Walker, M., Reiss, T. and Adali, S. ( 1997). Multi-objective Design of Laminated Cylindrical Shells for Maximum Torsional and Axial Buckling Loads, Computers and Structures, 62: 237-242.
10.
Walker, M. and Smith, R. ( 2003). A Technique for the Multi-objective Optimization of Laminated Composite Structures Using Genetic Algorithms and Finite Element Analysis , Composite Structures, 62: 123-128.
11.
Deb, K. , Pratap, A., Agarwal, S. and Meyarivan, T. ( 2002). A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6(2): 182-197.
12.
Zitzler, E., Laumanns, M. and Thiele, L. ( 2001). SPEA2: Improving the Strength Pareto Evolutionary Algorithm, Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) , Zurich, Switzerland.
13.
Knowles, J. and Corne, D. ( 1999). The Pareto Archived Evolution Strategy: A New Baseline Algorithm for Multiobjective Optimization, In: Proceedings of the 1999 Congress on Evolutionary Computation, IEEE Press, Piscataway, NJ, pp. 99-105.
14.
Coello, C. and Pulido, T. ( 2001). A Micro-Genetic Algorithm for Multiobjective Optimization, Evolutionary Multi-Criterion Optimization, pp. 126-140, Springer-Verlag , Berlin/Heidelberg.
15.
Coello, C.A.C. , Pulido, G.T. and Lechuga, M.S. (2004). Handling Multiple Objectives with Particle Swarm Optimization, IEEE Transactions on Evolutionary Computing, 8: 256-279.
16.
Coello, C., Van Veldhuizen, D. and Lamont, G. ( 2002). Evolutionary Algorithms for Solving Multi-Objective Problems, Genetic Algorithms and Evolutionary Computation, Kluwer Academic Publishers, New York.
17.
Deb, K. ( 2001). Multi-objective Optimization Using Evolutionary Algorithms , John Wiley & Sons , Chichester .
Spallino, R. and Rizzo, S. (2002). Multi-objective Optimisation of Laminated Structures, Mechanics of Research Communications , 29: 17-25.
20.
Costa, L., Fernandes, L., Figueiredo, I., Jú dice, J., Leal, R. and Oliveira, P. ( 2004). Multiple and Single-objective Approaches to Laminate Optimization with Genetic Algorithms, Structural Multidisciplinary Optimisation, 27: 55-65.
21.
Pelletier, J.L. and Senthil, S.V. (2006). Multi-objective Optimization of Fibre Reinforced Composite Laminates for Strength, Stiffness and Minimal Mass, Computers & Structures, 84: 2065-2080.
22.
Omkar, S.N. , Mudigere, D., Narayana Naik, G. and Gopalakrishnan , S. (2008 ). Vector Evaluated Particle Swarm Optimization (VEPSO) for Multi-objective Design Optimization of Composite Structures, Computers and Structures , 86(1-2): 1-14.
23.
Rama MohanRao, A. and Arvind, N. (2005). A Scatter Search Algorithm for Stacking Sequence Optimisation of Laminate Composites, Composite Structures, 70(4): 383-402.
24.
Glover, F., Laguna, M. and MartjI, R. ( 2000). Fundamentals of Scatter Search and Path Relinking , Control and Cybernetics, 29(3): 653-684.
25.
López, F.G., Melián , B., Moreno, J.A. and Moreno-Vega, J.M. (2003). Parallelization of the Scatter Search for the p-Median Problem, Parallel Computing, 29(5): 575-589.
26.
Glover, F., Laguna, M. and MartI, R. ( 2003). Scatter search, In: Ghosh, A. and Tsutsui, S. (eds), Advances in Evolutionary Computing: Theory and Applications, Springer-Verlag, New York, Inc., New York, NY, USA.
27.
Beausoleil, R.P. (2006). MOSS: Multiobjective Scatter Search Applied to Nonlinear Multiple Criteria Optimization, European Journal of Operational Research, 169: 426-449.
28.
Vasconcelos, J.A., Maciel, J.H.R.D. and Parreiras , R.O. (2005). Scatter Search Techniques Applied to Electromagnetic Problems, IEEE Transactions on Magnetics, 4(5): 1804-1807.
29.
Vinson, J.R. and Sierakowski, R.L. ( 1987). The Behaviour of Structures Composed of Composite Materials , Kluwer Academic Publishers, Dordrecht , Netherlands.
30.
Todoroki, A. and Sasai, M. (1999). Improvement of Design Reliability for Buckling Load Maximization of Composite Cylinder Using Genetic Algorithm with Recessive-Gene-Like Repair, JSME International Journal, Series A, 42-4: 530-536.
31.
Tasi, J. ( 1966). Effect of Heterogeneity on the Stability of Composite Cylindrical Shells under Axial Compression, AIAA Journal, 4: 1058-1062.
32.
Nemeth, M.P. ( 1995). Importance of Anisotropy on Buckling of Compression-Loaded Symmetric Composite Plates, AIAA Journal, 24: 1831.
33.
Grosset, L., Venkataraman, S. and Haftka, R.T. ( 2001). Genetic Optimization of Two-material Composite Laminates , In: Proceedings, 16th ASC Technical Meeting, Blacksburg, VA.
