64 Appendix Table 6.6: The mathematical <strong>for</strong>mulation <strong>for</strong> the coil spring design problem. f(x, T) = n i=1 Pi = ACi Thot Ti − 1 ⎛ Ti+1 ⎝ Ti ∆xi kdT No Constraint ∆xi ≥ 0, i = 1, ..., n + 1 g1 − T i T i−1 kdT ∆xi−1 g2 g3 Tcold ≤ T1 ≤ T2 ≤ ... ≤ Tn−1 ≤ Tn ≤ Thot n+1 i=1 ∆xi where = L C = 2.5 if T ≥ 71 K C = 4 if 71 K > T > 4.2 K C = 5 if T ≤ 4.2 K ⎞ ⎠
Bibliography [1] K. Abhishek, S. Leyffer, and J.T. Linderoth. Modeling without categorical variables: a mixed-integer nonlinear program <strong>for</strong> the <strong>optimization</strong> of thermal insulation systems. Optimization and Engineering, 11(2):185– 212, 2010. [2] M.A. Abramson. Pattern search <strong>algorithms</strong> <strong>for</strong> mixed variable general constrained <strong>optimization</strong> problems. PhD thesis, Rice University, USA, 2002. [3] M.A. Abramson. Mixed variable <strong>optimization</strong> of a load-bearing thermal insulation system using a filter pattern search algorithm. Optimization and Engineering, 5(2):157–177, 2004. [4] M.A. Abramson, C. Audet, J.W. Chrissis, and J.G. Walston. Mesh adaptive direct search <strong>algorithms</strong> <strong>for</strong> mixed variable <strong>optimization</strong>. Optimization Letters, 3(1):35–47, 2009. [5] B. Akay and D. Karaboga. Artificial bee <strong>colony</strong> algorithm <strong>for</strong> large-scale problems and engineering design <strong>optimization</strong>. Journal of Intelligent Manufacturing, pages 1–14, 2010. [6] C. Audet and J.E. Dennis Jr. Pattern search <strong>algorithms</strong> <strong>for</strong> mixed variable programming. SIAM Journal on Optimization, 11(3):573–594, 2001. [7] A. Auger and N. Hansen. A restart CMA evolution strategy with increasing population size. In Proceedings of IEEE Congress on Evolutionary Computation, CEC 2005, pages 1769–1776, Piscataway, NJ, 2005. IEEE Press. [8] A. Auger, N. Hansen, J. Perez Zerpa, R. Ros, and M. Schoenauer. Experimental comparisons of derivative free <strong>optimization</strong> <strong>algorithms</strong>. In Jan Vahrenhold, editor, Experimental Algorithms, volume 5526 of LNCS, pages 3–15, Berlin, Germany, 2009. Springer. [9] P. Balaprakash, M. Birattari, and T. Stützle. Improvement strategies <strong>for</strong> the F-Race algorithm: Sampling design and iterative refinement. In