What is the best way to choose initial solutions for a non-linear optimization problem sensitive to the initial solution?
If you have a significant number of optimization problem coefficients (50 in this case), and your optimization problem is such (non-linear with multiple possible local solutions) that it is sensitive to the initial solution, what are the best ways to choose (a set of) initial solutions?
Will the excel solver evolutionary algorithm do this?
Dear Brian
Could you clarify which is the meaning of 'sensitive solution'?
If you have an explicit representation of your problem (explicit objective function and explicit constraints), you may test one, or preferably several, globally convergent algorithms in the field of global optimization. To be very clear: I am talking about solvers that are guaranteed convergence to an optimum - in contrast to (meta-)heuristics. There are several such global solvers; start here:
https://www.mat.univie.ac.at/~neum/glopt/software_g.html
Optimization algorithms are really pretty simple. Just keep climbing up the hill until you get to the top. Take some precautions to make sure your step size isn't too big and try many different starting points far away form the optimum to make sure you have found the true optimum an not just a local optimum.
@Michael Patriksson, are these globally convergent algorithms commercially available?
Also @Michael Patriksson, how do these globally convergent algorithms manage to do just that - converge to the optimal solution?
Dear Michael
I agree with your assessment. especially in your first paragraph
Many thanks for the question and replies so far. You can try multi-start option along with GRG Nonlinear in the Solver tool in MS Excel (besides Evolutionary algorithm). Alternately, you can purchase Premium Solver and try the tools in it.
By the way, evolutionary algorithms generally do not require initial solutions (values or estimates). They and also multi-start option stated above require lower and upper bounds on decision variables.
We used Premium Solver and BARON in GAMS for optimizing water networks in petroleum refineries. Our experience is reported in the following paper: Sharma S. and Rangaiah G.P., Designing, Retrofitting and Revamping Water Networks in Petroleum Refineries using Multiobjective Optimization, Industrial & Engineering Chemistry Research, 55, 226-236 (2016). Please contact me through email ([email protected]) if you require a copy of this paper.
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