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

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