As you may be knowing that there are different mathematical tools and techniques which we can combine or hybridize with heuristic techniques to solve their entrapment in local minima and convergence issues. I know two techniques namely Chaos theory and Levy distribution as I have used them for increasing convergence speed of Gravitational Search Algorithm (GSA). So, my question is: can you name and briefly explain other mathematical techniques which we can combine with optimization algorithms in order to make them fit for solving complex real world problems.
Thank you.
Optimization algorithms handling a fixed number of real correlated values (non-separable) can be of 2 types: gradient-based and derivative-free.
Gradient-based procedures seem to be significantly faster than derivative-free ones.
GRADIENT-BASED METHODS (some):
Stochastic Gradient Descent (SGD)
Nonlinear Conjugate Gradient
L-BFGS
Levenberg-Marquardt Algorithm (LMA)
Regression problem solving based on Artificial Neural Network setup using Metaheurestics as the optimization algorithm for optimising the synaptic weights, bias values, no. of intermediate layers and no. of neurons perl ayer etc., instead of using the gradient based optimization method like the back propagation algorithm.
Optimization algorithms handling a fixed number of real correlated values (non-separable) can be of 2 types: gradient-based and derivative-free.
Gradient-based procedures seem to be significantly faster than derivative-free ones.
GRADIENT-BASED METHODS (some):
Stochastic Gradient Descent (SGD)
Nonlinear Conjugate Gradient
L-BFGS
Levenberg-Marquardt Algorithm (LMA)
Check out the proceedings of the "Matheuristics" conferences. The conference is devoted to the combination of heuristic methods and traditional mathematical programming methods (linear, nonlinear, integer programming, etc.)
https://mh2018.sciencesconf.org/
https://iridia.ulb.ac.be/matheuristics2016/index.php
https://link.springer.com/content/pdf/10.1007%2F978-3-319-07153-4_14-1.pdf
- Badges
- Science topic
- Similar topics
- Mathematics