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Evolutionary Monte Carlo (beta)

This program finds the global minimum in a general parameter space by combining Genetic algorithms and Monte Carlo algorithms.

References:

On learning strategies for evolutionary Monte Carlo

Evolutionary Monte Carlo for protein folding simulations

Real-parameter evolutionary Monte Carlo with applications to Bayesian mixture models

The program minimizes problems of any dimension and in general performs well despite rough energy landscapes. Problems 1-3 dimensions usually take under 1 second while 3-6 dimensions may take tens of seconds. Around 10 dimensions takes roughly a minute.

Quick Start

From command line

To build project run build.sh.

To launch program run run.sh.

From IDE

Some IDE's with CMake support can self-configure from the file CMakeLists.txt found in the project root folder. This is by far the easiest approach. Recommended: CLion or Visual Studio Code with C++ and CMake Tools extensions.

Requirements

Please install the following software before building the project.

  • C++ compiler with support for c++14 standard and OpenMP (tested with GNU GCC version >= 5.2).
  • CMake (tested with version >= 3.7).

The package manager Hunter is included to ease the building process. During the first build, the dependencies listed in CMakeLists.txt will be downloaded and installed by Hunter automatically on any platform (Linux/OSX/Win).

The following software is installed by Hunter:

  • Eigen for linear algebra calculations.

The default installation folder in Linux is ~/.hunter.

Usage

See the example_main.cpp file for syntax details. In principle it is enough to include the header source/EMC.h from your own project to gain access to the class object objective_function which has to be initialized and then passed to the function minimize(). The constructor of class object objective_function takes arguments:

    objective_function obj_fun(my_function, lower_bound, upper_bound, tolerance, aux_data1, aux_data2   ... aux_dataN);

where lower_bound and upper_bound are Eigen arrays of type Eigen::ArrayXd(n), where n is the number of parameters you wish to minimize, i.e., one lower and upper boundary per parameter. The argument tolerance has type double and tells the program when to finish: a small value (say 1e-16) takes longer than a large value (say 1e-8) but gives better accuracy. You can provide as many aux_data objects as you wish as long as they are of type Eigen::ArrayXd or Eigen::ArrayXXd. These can be used to actually compute your minimizing function and are available as members of the objective_function class, like obj_fun.aux[0], obj_fun.aux[1]... obj_fun.aux[N].

Lastly, my_function is a pointer to a function of return type long double, declared as:

    long double my_function(objective_function &obj_fun, Eigen::Array<long double, Dynamic, 1> &inputParameters);

In its definition, you will have to write a function body that maps inputParameters (and optionally obj_fun.aux[]) into a real scalar value like an "Fitness" (or "Energy") that you wish to minimize.

The Example program

If you compile and run the program as is, it will try to find the minimum of the paraboloid f(x,y) = sqrt(x^2 + y^2) with solution (0,0).

Constants

See the file constants.hpp. In particular, set the following variables to your liking:

int M sets the number of parallel subpopulations. Preferrably this number should be the same as the number cpu-threads available for OpenMP. (Usually 4 to 8, depending on your cpu).

int max_generations controls the maximum duration of the simulation (default 50000).