PQCLab / RandomMutations

Global optimization solver for MATLAB

Random mutations optimization

MATLAB library for global optimization of an arbitrary function by random mutations algorithm. Version 0.2.

https://arxiv.org/abs/1304.3703

Before using the library, please read the terms of use.

Getting started

To use the library download and include the files to the search path.

Initialize the optimizer by calling rm_init and use the function OptimizeRM to perform optimization.

• [global_best_f, global_best] = OptimizeRM(f, len) returns minimum value global_best_f and minimum point global_best for the function handler f with len number of point parameters
• [___] = OptimizeRM(f, len, start_point) specifies the initial point start_point of search; by default start_point is an array of zeros
• [___] = OptimizeRM(f, len, start_point, scale) specifies the mutations scale (mutations are being multiplied by scale); by default scale = 1

Optimizer parameters

Parameters of the algorithm are stored in the global variable rmparams:

• rmparams.display - display output (default: 1)
• rmparams.n_pop - size of the population (default: 50); linearly increases computation time, increases the probability of finding the global minimum
• rmparams.n_des - number of descendants (default: 10); linearly increases computation time, increases the speed of convergence nearby the obtained minimum
• rmparams.maxmut - maximum number of parameters being mutated (default: 5); should be greater than 2, depends on the function being optimized, but usually 5 works well
• rmparams.n_stall - number of iterations to stop the search when answer is less than rmparams.eps (default: 10)
• rmparams.eps - optimization function tolerance (default: 1e-6)
• rmparams.p_min - minimum scale power (default: -9); decreases convergence speed, increases accuracy of local convergence
• rmparams.p_max - maximum scale power (default: 1)
• rmparams.b - scale factor (default: 10)
• rmparams.local_search - perform local optimization at the end of iterations with fminsearch (default: 0)

Varying parameter is being changed by a factor m*rmparams.b^p, where m is uniformly distributed from -1 to 1, p is an integer uniformly distributed from rmparams.p_min to rmparams.p_max.

Calling rm_init initializes rmparams with default parameters values.

Variable rmparams also stores debug information on iterations:

• rmparams.best_f - array of minimal values on each iteration
• rmparams.funEvals - array of numbers of total evaluations of f from the start for each iteration
• rmparams.best_x - cell array of minimal points on each iteration

Example

The following MATLAB script evaluates the global maximum of the function .

rm_init; % Initialize optimizer parameters
rmparams.n_pop = 100; % Change population size
[result, result_p] = OptimizeRM(@(p)-TestFunc(p, 0.5), 100); % Evaluate minimum

function res = TestFunc(x, b) % Function to minimize
  res = sum(abs(sin(x+b)));
end

Terms of use

This library is distributed under GNU General Public License v3.0.

For using the library in research work, please cite as:

[1] Chernyavskiy A. Yu., Calculation of quantum discord and entanglement measures using the random mutations optimization algorithm, arXiv:1304.3703 [quant-ph], 2013.
[2] Chernyavskiy A. Yu., Global optimization solver for MATLAB, URL: https://github.com/PQCLab/RandomMutations