@MrShorty: First of all, thanks for the most useful reply, and a pity you can't open the file, but seems that Alf and others can, so not sure what to do about it.
You're absolutely right regarding my use of NR and of my lacking knowledge of the two approches. I'm looking into it at this point, and I think the way to get around the problem is indeed by applying more entrypoints as you suggest. The attached file shows a simplyfied edition of my problem, which has three variables, but as they are only defined in relatively narrow ranges, a rather small number of entrypoints should be good enough to find the correct optimum. I think my biggest problem will be that of programming the thing at the end, but I'm now down to searching the forum for related threads. If you have any suggestions of where I might find the structure of a such code that I'm looking for or any other suggestions that might be useful, I would love to hear it - otherwise thanks again for the help and I'll probably be back with a new thread when I run into trouble sooner or later