DSM are designed to solve general problems with unknown derivatives, often working well in practice with noisy, nonsmooth or nonconvex functions. Also, the number of function evaluations required by a DSM is commonly considered to be higher than those required using a gradient based method, but lower than the total number of function values computed using a genetic algorithm (GA). Recent work improved the numerical performance of serial implementations of pattern search [3,4], but the structure of the algorithms belonging to the DSM class also motivates the use of parallelization techniques. Specifically, already released packages, such as NOMAD [5] or PSWARM [6], provide parallel implementations of DSM that can be used in structural optimization.

The present work accesses the numerical performance of some recent implementations of DSM and its competitiveness compared with GAs, both when considering serial and parallel codes. DSM are briefly described, focusing in their parallelization potential. Two structural examples are used to compare DSM and GAs. The first problem consists in the optimization of a press brake to produce a uniform plate bending angle. Three public domain codes, NOMAD [5], PSWARM [6] and SID-PSM [7], are used to access the capability of DSM to solve this problem. A second problem, concerning the expensive structural optimization of a semi-trailer chassis, is considered. Parallel versions of NOMAD [5] and PSWARM [6] are used to obtain the solution. In both cases comparisons are made with the GA.

1

V. Torczon, "On the convergence of pattern search algorithms", SIAM J. Optim., 7, 1-25, 1997. doi:10.1137/S1052623493250780

2

C. Audet, J.E. Dennis Jr., "Mesh adaptive direct search algorithms for constrained optimization", SIAM J. Optim., 17, 188-217, 2006. doi:10.1137/040603371

3

A.L. Custódio, L.N. Vicente, "Using sampling and simplex derivatives in pattern search methods", SIAM J. Optim., 18, 537-555, 2007. doi:10.1137/050646706

4

A.L. Custódio, H. Rocha, L.N. Vicente, "Incorporating minimum Frobenius norm models in direct search", Comput. Optim. and Appl., 46, 265-278, 2010. doi:10.1007/s10589-009-9283-0

5

http://www.gerad.ca/NOMAD/Project/Home.html

6

http://www.norg.uminho.pt/aivaz/pswarm/

7

http://www.mat.uc.pt/sid-psm/

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