With non-linear optimization, when you are interested in the different possible local solutions, because it can help you towards the optimal (global) solution, and to identify the optimal solution, particularly when you have a hint or idea what it would or would not look like, what would be an effective way to surface possible local solutions?
Do you simply note and cross out the local solutions found, as they are found?
Is it simply a matter of your initial solution sample or set?
Dear Brian,
I think multi-start strategies might help you.
Multi-start strategies sample the solution space of optimisation problems in order to offer a "good" (maximal, de-correlated...) cover. This helps you finding solutions close to the global optimum.
Mutli-start strategies can be static/memoryless (points are defined and then optimisation begins) or dynamic/memory-based (points are defined according to optimisation results). You will find more on this topic in this paper: https://www.uv.es/rmarti/paper/docs/multi4.pdf
The easiest way to implement such a strategy is to couple some sampling algorithm, like Latin Hypercube Sampling and an optimisation algorithm, see e.g., Article Multi-start Space Reduction (MSSR) surrogate-based global op...
Hope it helps,
Pierre
@Pierre Mandel,
Thanks. It seems this is something one must implement yourself. Or is there a software package that can do this - locate unique/ different local solutions - for you? Or simply, conduct and output (according to) a multistart implementation.
You do not have to implement it by yourself. Many solvers have already built-in multistart routines. For example:
- Matlab uses the scatter search algorithm to sample initial points (Glover, F. “A template for scatter search and path relinking.” Artificial Evolution (J.-K. Hao, E.Lutton, E.Ronald, M.Schoenauer, D.Snyers, eds.). Lecture Notes in Computer Science, 1363, Springer, Berlin/Heidelberg, 1998, pp. 13–54.) See: https://fr.mathworks.com/help/gads/how-globalsearch-and-multistart-work.html#bsfvjv8
- Excel, Pyomo or Aimms have such routines.
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