Is there any nonlinear direct search optimization algorithm better than Nelder-Mead Simplex integrated in fminsearch of Matlab?

Helle, guys! Right now, I am using fminsearch in Matlab as the optimizer to optimize a slotted substrate integrated waveguide (SIW) antenna. There are 8 longitudinal slots in the SIW H-plane as shown in Fig.1, in order to realize a Taylor distribution with -25 dB sidelobe level. So there are 16 variables in total to be optimized, including each slot's offset length (xi) and length (li), while setting its width (w) and slot interval (l01, l02,...) to constant. As a result, the optimization process is very upset as shown in Fig. 2. It's found the capability of the fminsearch is very weak and the variables only take little change in thousands. Few good solutions can be found in the optimization process. So I'd like to ask is there any better strategy to optimize such a problem? Hopping some optimization masters can give me some hints to improve the optimization efficiency.

Figure 1 SIW Slotted Antenna with Varibles Illustration

Figure 2 Optimization Process with Fitness Function Value versus Iteration Step

Answer 1

[John D'Errico]

I would never recommend use of Nelder-Mead on problems with above about 6-8 variables. 16 is wildly too high.

Fminsearch is a basic Nelder-Mead code, nothing more.

If you need a better optimizer, then look at the optimization toolbox. I think TOMLAB is also still around. And consider YALMIP, which is on the FEX as I recall.

[JianQiang Gong]

Yes indeed, when the variable number execeeds 10, fminsearch will show its weak muscle. I have never used TOMLAB and YALMIP before. Which function in TOMLAB or YALMIP will be efficient to the structural optimization? Could you give me some hints to follow?

[John D'Errico]

That I cannot help you with, since I have never used either. The optimization toolbox has always been sufficient for my purposes. For an unconstrained problem, fminunc from the optimization toolbox would suffice. I'd not be surprised if you have constraints at some point.

YALMIP is quite cost effective though. :)

[JianQiang Gong]

Thank you John. I am now ready to try using the YALMIP by following your advise, hoping better results can be found. If so, I will let you know.

Answer 2

[sudheesh pai]

any one have code to study matlab implementation of SIW? i would like to have a basic code.