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README.md

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Genetic is a Matlab/Octave toolbox for optimisation which gathers several mono and multi-objective optimisation algorithms.

Table of Contents

Installation

Genetic should work

  • with Matlab >= R2014b,
  • with Octave >= 4.0 (some functionalities might be missing though).

To install it, download the last release and add the directory to your path in Matlab/Octave.

Getting started

Main interface for optimisation

All the optimisation methods of Genetic are called through the unified interface genetic.min as follows:

[xopt, fopt, info] = genetic.min(f, x, method)
[xopt, fopt, info] = genetic.min(f, x, method, options)
[xopt, fopt, info] = genetic.min(f, x, method, constraints, options)

where the input arguments are:

  • f: the objective function. For mono-objective optimisation, it can be only a handle function and for multi-objective optimisation, it must be a cell containing a handle function and the number of objectives, i.e. f = {f_handle, fDim}.
  • x: the dimension of the problem or an initial point/population.
  • method: the name of the method to be used.
  • options: a structure containing the parameters for the optimisation process.
  • constraints: a structure containing a description of the constraints. (not yet functional)

and the outputs are:

  • xopt: the best solution(s) found.
  • fopt: the associated objective or Parefo front.
  • info: a structure containing informations about the optimisation process.

Remark: Similarly, the main interface for maximisation is genetic.max.

Available methods

Genetic gathers both mono and multi-objective optimisation methods listed below. Note that contrary to what its name may suggest, the toolbox does not contain only evolutionary methods.

To get additional help on the methods (and references), type genetic.methods.

Mono-objective

Key Name
annealing Simulated Annealing algorithm (WIP)
pso Particle Swarm Optimisation algorithm
cmaes Covariance Matrix Adaptation Evolution Strategy
simplex Nelder-Mead Simplex algorithm
mdSearch Multi-Directional direct Search
gss Generating Set Search Method
linesearch Local descent algorithm based on line-search

Multi-objective

/!\ Multi-objective functions are being re-factored... they are not yet working

Key Name
nsga2 Non-dominated Sorting Genetic Algorithm II
nsga3 Non-dominated Sorting Genetic Algorithm III
spea2 Strength Pareto Evolutionary Algorithm II
pesa2 Pareto Envelope-based Selection Algorithm II
mopso Multi-Objective Particle Swarm Optimization algorithm
mombi2 Many-Objective Metaheuristic Based on the R2 Indicator II
moeadd Multi-Objective Evolutionary Algorithm based on Dominance and Decompositon
tdea Theta-Dominance based Evolutionary Algorithm
rveastar Reference Vector (RV) guided Evolutionary Algorithm with RV regeneration strategy

Options

The options structure contains parameters that let you tune the optimisation process. In particular, it enables to modify both general and method-specific parameters. The general parameters, i.e., those shared by all the methods, are the following:

Name Description Default
maxFunEval Maximum number of function evaluation 5000
verbosity Verbosity level of the algorithm 0
popSize Dimension of the population (for population-based methods) round(10 + 2*sqrt(n))
gradObj Availability of the gradient as second output of the objective function false

The general parameters shared by all the mono-objective methods are the following:

Name Description Default
targetY Target value of the objective function -inf
tolY Minimum decrease between two consecutive best solutions 1e-8
ntolY Number of time the minimum objective decrease must be met before stopping 1
tolX Minimum distance between two consecutive best solutions 1e-8
ntolX Number of time the minimum distance must be met before stopping 1

For method-specific parameters, refer to the corresponding help page.

Constraints

/!\ Constraints are (for the time being) only handled by static penalty

Similarly to options, constraints are added through a structure containing specific fields depending on the constraints:

  • bounds are characterized by the fields xMin and xMax such that: xminxxmax,
  • linear inequality constraints are characterized by the fields A and b such that: Axb,
  • linear equality constraints are characterized by Aeq and beq such that: Aeqx=beq,
  • non-linear inequality constraints are given as an anonymous function c such that: c(x) ≤ 0,
  • non-linear equality constraints are given as an anonymous function ceq such that: ceq(x) = 0.

Examples

Mono-objective

xDim                = 10;
f                   = @(x) norm(x)^2;
method              = 'cmaes';
options             = struct('verbosity', 3, 'maxFunEval', 3000);
[xopt, fopt, info]  = genetic.min(f, xDim, method, options);

Multi-objective

xDim                = 10;
A                   = rand(xDim,xDim);
b                   = rand(xDim,1);
fun                 = @(x) [norm(x)^2;norm(A*x - b)^2];
fDim                = 2;
f                   = {fun, fDim};
method              = 'nsga2';
options             = struct('verbosity', 3, 'maxFunEval', 10000);
[xopt, fopt, info]  = genetic.min(f, xDim, method, options);

Benchmarking tools

Benchmarks

Load and use benchmarks. Genetic is shipped with a set of mono and multi-objective academic benchmark problems gathered from the literature. These problems that can be listed with genetic.bench.list().

The data associated with a problem can then be accessed with genetic.bench.load(key, n) where key is the name of the benchmark and n is the dimension of the problem. Note that some problems have a fixed dimension that is displayed when listing the problems.

The benchmarks can also be directly called from Genetic by replacing the objective function in the call with the name of the benchmark, i.e. genetic.min(benchName, x, method).

Add your own benchmarks to genetic. You can add your own benchmark to Genetic through genetic.bench.create as follows,

% Creation of the benchmark
ben.f    = @(x) norm(x);
ben.xDim = 10;
ben.fopt = 0;
ben.xopt = zeros(10,1);
ben.name = 'norm10';
genetic.bench.create(ben);
clear ben
% Re-loading the benchmark
ben      = genetic.bench.load('norm10')

It can then be used as the other benchmarks. Note that it will fail during execution if the handle function in the benchmark requires some other function that is not in the Matlab path.

Comparing methods

Genetic contains also some elements to help you compare the performances of its methods. It is done through the creation of a genetic.bench.experiment that let you run several methods (or the same with different options) on several benchmarks (or the same at different dimensions). For instance, to compare cmaes and pso on the ackley and griewank functions,

% Creating the experiment
benchs   = {{'ackley',2}, {'griewank',2}};
methods  = {'cmaes','pso'};
xp       = genetic.bench.experiment(benchs, methods);
xp.name  = 'example';
% Run the optimisations
xp.start();

All the raw results of the optimisations are stored in xp.results. To ease the comparison, statistical elements can be displayed with xp.showTab, e.g. to show the distance with the optimal value:

>> xp.showTab('b', 'ackley', 'fopt')
+----------------------------------------------------+
|                 ackley (2 - fopt)                  |
+----------------------------------------------------+
| method |   min    |   mean   |   max    |   std    |
+--------+----------+----------+----------+----------+
| cmaes  | 9.05e-09 | 1.35e-07 | 6.46e-07 | 2.25e-07 |
|  pso   | 3.97e-09 | 8.33e-08 | 2.85e-07 | 8.55e-08 |
+----------------------------------------------------+

Other elements like nEval, elapsedTime, nImprove may also be displayed. Similarly, the statistics for one method among all the benchmarks can be displayed using xp.showTab('m', 'cmaes', 'fopt').

Contact

Feel free to contact us at: genetic [at] onera.fr

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