This is for multivariate optimization in dispersive liquid liquid microextraction
Dear Ken,
There is no good and easy answer for your question based on this information I am afraid.
For many optimization problems the no free lunch theorem [1] is valid. The paper is maybe a bit technical but it basically states that averaged over all possible problems all optimization methods are equivalent. So the choice for an effective optimization algorithm really depends on the details of your optimization problem, there is no “magic” best algorithm for everything.
What are your design variables? How many design variables do you have?
How nonlinear do you expect the objective (and constraints if there are any) to be w.r.t. to changes in your design variables?
How big is your function evaluation budged (how many design tries can you make)?
But it also depends on what you want from you optimization, do you want a better design? or do you want the best design? or do you want the best optimization method for this type of problem? Depending on your objectives this could go very deep and take you a lot of effort and time. If on the other hand like for many/most people "any optimization" will suffice your task, you can solve it like most people and just choose something and "defend" yourself with the NFL theorem ;-)
[1] Wolpert, D. "No free lunch theorem for optimization." IEEE Transactions on Evolutionary Computation 1 (1997): 467-482. http://ti.arc.nasa.gov/m/profile/dhw/papers/78.pdf
It depends on the selection of the star points.
My new paper (it is free) can show it as a practical example (Acid Red 18 vs Acid Brown 14 and Acid Orange 7):
Article Techno-economical aspects of electrocoagulation optimization...
Techno-economical aspects of electrocoagulation optimization in three acid azo dyes’ removal comparison
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