A comparison of multi-objective optimisation metaheuristics on the 2D airfoil design problem

Abstract

Variants of the multi-objective particle swarm optimisation (MOPSO) algorithm are investigated, mainly focusing on swarm topology, to optimise the well-known 2D airfoil design problem. The topologies used are global best, local best, wheel, and von Neumann. The results are compared to the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective tabu search (MOTS) algorithm, and it is found that the attainment surfaces achieved by some of the MOPSO variants completely dominate those of NSGA-II. In general, the MOPSO algorithms also significantly improve diversity of solutions compared to MOTS. The MOPSO algorithm proves its ability to exploit promising solutions in the presence of a large number of infeasible solutions, making it well suited to problems of this nature. References

• D. Abramson, A. Lewis, T. Peachey, and C. Fletcher. An automatic design optimization tool and its application to computational fluid dynamics. In Proceedings of the 2001 ACM/IEEE conference on Supercomputing (CDROM), pages 25--25. ACM, 2001. doi:10.1145/582034.582059.
• R. Eberhart and J. Kennedy. A new optimizer using particle swarm theory. In Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on, pages 39--43. IEEE, 1995. doi:10.1109/MHS.1995.494215.
• J. Kennedy and R. Mendes. Population structure and particle swarm performance. In Evolutionary Computation, 2002. CEC'02. Proceedings of the 2002 Congress on, volume 2, pages 1671--1676. IEEE, 2002. doi:10.1109/CEC.2002.1004493.
• J. Kennedy. Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In Evolutionary Computation, 1999. CEC'99. Proceedings of the 1999 Congress on, volume 3. IEEE, 1999. doi:10.1109/CEC.1999.785509.
• K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. A fast and elitist multiobjective genetic algorithm: NSGA-II. Evolutionary Computation, IEEE Transactions on, 6(2):182--197, 2002. doi:10.1109/4235.996017.
• D. M. Jaeggi, G. T. Parks, T. Kipouros, and P. J. Clarkson. The development of a multi-objective tabu search algorithm for continuous optimisation problems. European Journal of Operational Research, 185(3):1192--1212, 2008. doi:10.1016/j.ejor.2006.06.048.
• C. A. Coello Coello and M. S. Lechuga. MOPSO: A proposal for multiple objective particle swarm optimization. In Evolutionary Computation, 2002. CEC'02. Proceedings of the 2002 Congress on, volume 2, pages 1051--1056. IEEE, 2002. doi:10.1109/CEC.2002.1004388.
• J. Kennedy and R. Eberhart. Particle swarm optimization. In Neural Networks, 1995. Proceedings., IEEE International Conference on, volume 4, pages 1942--1948. IEEE, 1995. doi:10.1109/ICNN.1995.488968.
• E. N. Jacobs, K. E. Ward, and R. M. Pinkerton. NACA report no. 460: The characteristics of 78 related airfoil sections from test in the variable-density wind tunnel, 1933. http://www.esdu.com/cgi-bin/ps.pl?sess=unlicensed_1130622070421svf&t=doc&p=naca_tr460.
• M. Drela. XFOIL: An analysis and design system for low Reynolds number airfoils. In T. J. Mueller, editor, Low Reynolds Number Aerodynamics, volume 54 of Lecture Notes in Engineering, pages 1--12. Springer Berlin Heidelberg, 1989. doi:10.1007/978-3-642-84010-4_1.
• T. W. Sederberg and S. R. Parry. Free-form deformation of solid geometric models. ACM Siggraph Computer Graphics, 20(4):151--160, 1986. doi:10.1145/15886.15903.
• R. C. Eberhart and Y. Shi. Particle swarm optimization: developments, applications and resources. In Evolutionary Computation, 2001. Proceedings of the 2001 Congress on, volume 1, pages 81--86. IEEE, 2001. doi:10.1109/CEC.2001.934374.
• T. Kipouros, M. Mleczko, and A. M Savill. Use of parallel coordinates for post-analyses of multi-objective aerodynamic design optimisation in turbomachinery. In 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, page 2138. AIAA, 2008. doi:10.2514/6.2008-2138.
• A. Inselberg. The plane with parallel coordinates. The Visual Computer, 1(2):69--91, 1985. doi:10.1007/BF01898350.