CMA_ES_Optimization¶

Purpose¶

The purpose of the driver is to identify a parameter vector $\mathbf{p}\in\mathcal{X}\subset\mathbb{R}^d$ that minimizes the value of an objective function $f_\text{objective}: \mathcal{X} \rightarrow \mathbb{R}$ . The search domain $\mathcal{X}$ is bounded by box constraints $l_i\leq p_i \leq u_i$ for $1\leq i\leq d$ and may be subject to several constraints $c_j: \mathbb{R}^d \rightarrow \mathbb{R}$ such that $\mathbf{p} \in \mathcal{X}$ only if $c_j(\mathbf{p}) \leq 0$ (see jcmwave_optimizer_create_study()).

The driver uses the heuristic CMA-ES method to search globally for a minimum of the objective function. We recommend to use Bayesian optimization to search globally for a minimum. Only if the evaluation times of the objective function are very short (smaller than 1-3 seconds) it can be beneficial to use CMA-ES.

The implementation of the driver is based on the open source implementation if CyberAgent, Inc. (see https://github.com/CyberAgentAILab/cmaes).

Usage Example¶

addpath(fullfile(getenv('JCMROOT'), 'ThirdPartySupport', 'Matlab'));
client = jcmwave_optimizer_client();

% Definition of the search domain
domain = {...
    struct('name','x1', 'type','continuous', 'domain', [-1.5,1.5]),...
    struct('name','x2', 'type','continuous', 'domain', [-1.5,1.5]),...
    struct('name','radius', 'type','fixed', 'domain', 2)...
};

% Definition of a constraint on the search domain
constraints = [...
    struct('name', 'circle', 'constraint','sqrt(x1^2 + x2^2) - radius')...
];

% Creation of the study object with study_id 'example'
study = client.create_study('domain',domain, 'constraints',constraints, ...
                'driver','CMA_ES_Optimization',...
                'name','CMA_ES_Optimization example', ...
                'study_id','CMA_ES_Optimization_example');

% Definition of a simple analytic objective function.
% Typically, the objective value is derived from a FEM simulation
% using jcmwave.solve(...)
function observation = objective(sample)
  pause(2.0); % makes objective expensive
  observation = study.new_observation();
  x1 = sample.x1;
  x2 = sample.x2;
  observation.add(10*2 + (x1.^2-10*cos(2*pi*x1)) + (x2.^2-10*cos(2*pi*x2)));
  end

study.set_parameters('max_iter', 50);

% Run the minimization
while(not(study.is_done))
    sug = study.get_suggestion();
    obs = objective(sug.sample);
    study.add_observation(obs, sug.id);
end

info = study.info();
fprintf('\nMinimum %0.3e found at (x1=%0.3e, x2=%0.3e)',...
        info.min_objective, info.min_params.x1, info.min_params.x2)

Parameters¶

The following parameters can be set by calling, e.g.

study.set_parameters('example_parameter1',[1,2,3], 'example_parameter2',true);

mean0 (list):	Initial mean vector of multi-variate gaussian distributions. If not set, a random initial vector is chosen. (default: None)

sigma0 (float):	Initial standard deviation. The problem is internally rescaled such that all variables lie in the interval [0,1]. The standard deviation is defined on these rescaled variables. (default: 0.4)

population_size (int):
	The population size. (default: None)

max_iter (int):	Maximum number of evaluations of the objective function (default: inf)

max_time (int):	Maximum run time in seconds (default: inf)

num_parallel (int):
	Number of parallel observations of the objective function (default: 1)

eps (float):	Stopping criterium. Minimum distance in the parameter space to the currently known minimum (default: 0.0)

min_val (float):
	Stopping criterium. Minimum value of the objective function (default: -inf)