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Multi-start optimization is the simplest way to deal with the initial guess problem. Is there any heuristic you can use to generate a reasonably-sized set of gu
by blt 8y ago
Multi-start optimization is the simplest way to deal with the initial guess problem. Is there any heuristic you can use to generate a reasonably-sized set of guesses that is likely to contain at least one guess contained in the region of convergence of the global optimum?
An example of such a heuristic: when fitting a Gaussian mixture model using the E-M algorithm, you can perform K-means clustering with several sets of uniformly sampled random initial cluster centers; then use those cluster centers with the K-means hard correspondence to compute the initial fit of the Gaussians.
- sleavey 8y agoThere are some cool global minimisation algorithms which can handle certain types of problem where the initial guess is far away. Some involve switching between different algorithms until the cost function is close to its minimum. I did try the ones available in SciPy when I built a non-linear equation based constraint solver, but none really worked well enough. However, I know such algorithms exist if I put the time in to learn about them. Since I discovered cluster-rewriting based constraint solvers, I've been spending most of my time investigating those. I'm actually not against the idea of asking the user to provide a sketch, I'm just trying to solve the harder problem first and if I can't do so then I'll introduce some constraints (pun not intended).
- blt 8y agoI don't know anything about the problem domain but I'm guessing that you need to make some topological as well as geometric choices... In which case the evolutionary algorithms could be interesting