549 lines
20 KiB
Matlab
549 lines
20 KiB
Matlab
function [x,fval,exitflag] = simplex_optimization_routine(objective_function,x,options,varargin)
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% Nelder-Mead like optimization routine.
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% By default, we use standard values for the reflection, the expansion, the contraction and the shrink coefficients (alpha = 1, chi = 2, psi = 1 / 2 and σ = 1 / 2).
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% See http://en.wikipedia.org/wiki/Nelder-Mead_method
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%
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% This routine uses the Nelder-Mead simplex (direct search) method.
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% As chaining could reveal interesting to reach the solution neighborhood,
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% the function automatically restarts from the current solution while
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% amelioration is possible.
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%
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% INPUTS
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% objective_function [string] Name of the objective function to be minimized.
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% x [double] n*1 vector, starting guess of the optimization routine.
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% options [structure]
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%
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% OUTPUTS
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%
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%
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% Copyright (C) 2010-2013 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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global bayestopt_
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% Set verbose mode
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verbose = 2;
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% Set number of control variables.
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number_of_variables = length(x);
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% get options.
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if isempty(simplex.maxfcall)
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max_func_calls = simplex.maxfcallfactor*number_of_variables
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end
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% Set tolerance parameter.
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if isfield(options,'tolerance') && isfield(options.tolerance,'x')
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x_tolerance = options.tolerance.x;
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else
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x_tolerance = 1e-4;
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end
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% Set tolerance parameter.
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if isfield(options,'tolerance') && isfield(options.tolerance,'f')
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f_tolerance = options.tolerance.f;
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else
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f_tolerance = 1e-4;
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end
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% Set maximum number of iterations.
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if isfield(options,'maxiter')
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max_iterations = options.maxiter;
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else
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max_iterations = 5000;
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end
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% Set reflection parameter.
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if isfield(options,'reflection_parameter')
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if isfield(options.reflection_parameter,'value')
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rho = options.reflection_parameter.value;
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else
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rho = 1.0;
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end
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if isfield(options.reflection_parameter,'random')
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randomize_rho = options.reflection_parameter.random;
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lambda_rho = 1/rho;
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else
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randomize_rho = 0;
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end
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else
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rho = 1.0;
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randomize_rho = 0;
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end
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% Set expansion parameter.
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if isfield(options,'expansion_parameter')
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if isfield(options.expansion_parameter,'value')
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chi = options.expansion_parameter.value;
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else
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chi = 2.0;
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end
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if isfield(options.expansion_parameter,'random')
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randomize_chi = options.expansion_parameter.random;
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lambda_chi = 1/chi;
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else
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randomize_chi = 0;
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end
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if isfield(options.expansion_parameter,'optim')
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optimize_expansion_parameter = options.expansion_parameter.optim;
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else
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optimize_expansion_parameter = 0;
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end
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else
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chi = 2.0;
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randomize_chi = 0;
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optimize_expansion_parameter = 1;
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end
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% Set contraction parameter.
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if isfield(options,'contraction_parameter')
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if isfield(options.contraction_parameter,'value')
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psi = options.contraction_parameter.value;
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else
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psi = 0.5;
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end
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if isfield(options.contraction_parameter,'random')
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randomize_psi = options.expansion_parameter.random;
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else
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randomize_psi = 0;
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end
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else
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psi = 0.5;
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randomize_psi = 0;
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end
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% Set shrink parameter.
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if isfield(options,'shrink_parameter')
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if isfield(options.shrink_parameter,'value')
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sigma = options.shrink_parameter.value;
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else
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sigma = 0.5;
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end
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if isfield(options.shrink_parameter,'random')
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randomize_sigma = options.shrink_parameter.random;
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else
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randomize_sigma = 0;
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end
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else
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sigma = 0.5;
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randomize_sigma = 0;
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end
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% Set delta parameter.
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if isfield(options,'delta_parameter')% Size of the simplex
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delta = options.delta_parameter;
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else
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delta = 0.05;
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end
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DELTA = delta;
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zero_delta = delta/200;% To be used instead of delta if x(i) is zero.
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% Set max_no_improvements.
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if isfield(options,'max_no_improvements')
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max_no_improvements = options.max_no_improvements;
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else
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max_no_improvements = number_of_variables*10;
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end
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% Set vector of indices.
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unit_vector = ones(1,number_of_variables);
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trend_vector_1 = 1:number_of_variables;
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trend_vector_2 = 2:(number_of_variables+1);
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% Set initial simplex around the initial guess (x).
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if verbose
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skipline(3)
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disp('+----------------------+')
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disp(' SIMPLEX INITIALIZATION ')
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disp('+----------------------+')
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skipline()
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end
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initial_point = x;
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[initial_score,junk1,junk2,nopenalty] = feval(objective_function,x,varargin{:});
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if ~nopenalty
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error('simplex_optimization_routine:: Initial condition is wrong!')
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else
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[v,fv,delta] = simplex_initialization(objective_function,initial_point,initial_score,delta,zero_delta,1,varargin{:});
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func_count = number_of_variables + 1;
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iter_count = 1;
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if verbose
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disp(['Objective function value: ' num2str(fv(1))])
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disp(['Current parameter values: '])
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fprintf(1,'%s: \t\t\t %s \t\t\t %s \t\t\t %s \t\t\t %s \t\t\t %s \n','Names','Best point', 'Worst point', 'Mean values', 'Min values', 'Max values');
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for i=1:number_of_variables
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fprintf(1,'%s: \t\t\t %+8.6f \t\t\t %+8.6f \t\t\t %+8.6f \t\t\t %+8.6f \t\t\t %+8.6f \n',bayestopt_.name{i},v(i,1), v(i,end), mean(v(i,:),2), min(v(i,:),[],2), max(v(i,:),[],2));
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end
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skipline()
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end
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end
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vold = v;
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no_improvements = 0;
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simplex_init = 1;
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simplex_iterations = 1;
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max_simplex_algo_iterations = 3;
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simplex_algo_iterations = 1;
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best_point = v(:,1);
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best_point_score = fv(1);
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convergence = 0;
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tooslow = 0;
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iter_no_improvement_break = 0;
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max_no_improvement_break = 1;
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while (func_count < max_func_calls) && (iter_count < max_iterations) && (simplex_algo_iterations<=max_simplex_algo_iterations)
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% Do we really need to continue?
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critF = max(abs(fv(1)-fv(trend_vector_2)));
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critX = max(max(abs(v(:,trend_vector_2)-v(:,unit_vector))));
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if critF <= max(f_tolerance,10*eps(fv(1))) && critX <= max(x_tolerance,10*eps(max(v(:,1))))
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convergence = 1;
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end
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if critX <= x_tolerance^2 && critF>1
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tooslow = 1;
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end
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% Set random reflection and expansion parameters if needed.
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if randomize_rho
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rho = -log(rand)/lambda_rho;
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end
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if randomize_chi
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chi = -log(rand)/lambda_chi;
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end
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% Set random contraction and shrink parameters if needed.
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if randomize_psi
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psi = rand;
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end
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if randomize_sigma
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sigma = rand;
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end
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% Compute the reflection point
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xbar = mean(v(:,trend_vector_1),2); % Average of the n best points.
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xr = xbar + rho*(xbar-v(:,end));
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x = xr;
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fxr = feval(objective_function,x,varargin{:});
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func_count = func_count+1;
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if fxr < fv(1)% xr is better than previous best point v(:,1).
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% Calculate the expansion point
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xe = xbar + rho*chi*(xbar-v(:,end));
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x = xe;
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fxe = feval(objective_function,x,varargin{:});
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func_count = func_count+1;
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if fxe < fxr% xe is even better than xr.
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if optimize_expansion_parameter
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if verbose>1
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skipline(2)
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disp('Compute optimal expansion...')
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end
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xee = xbar + rho*chi*1.01*(xbar-v(:,end));
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x = xee;
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fxee = feval(objective_function,x,varargin{:});
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func_count = func_count+1;
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if fxee<fxe
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decrease = 1;
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weight = rho*chi*1.02;
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fxeee_old = fxee;
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xeee_old = xee;
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if verbose>1
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fprintf(1,'Weight = ');
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end
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while decrease
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weight = 1.02*weight;
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if verbose>1
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fprintf(1,'\b\b\b\b\b\b\b %6.4f',weight);
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end
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xeee = xbar + weight*(xbar-v(:,end));
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x = xeee;
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fxeee = feval(objective_function,x,varargin{:});
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func_count = func_count+1;
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if (fxeee<fxeee_old) && -(fxeee-fxeee_old)>f_tolerance*10*fxeee_old
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fxeee_old = fxeee;
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xeee_old = xeee;
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else
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decrease = 0;
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end
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end
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if verbose>1
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fprintf(1,'\n');
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end
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xe = xeee_old;
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fxe = fxeee_old;
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else
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decrease = 1;
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weight = rho*chi;
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fxeee_old = fxee;
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xeee_old = xee;
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if verbose>1
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fprintf(1,'Weight = ');
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end
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while decrease
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weight = weight/1.02;
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if verbose>1
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fprintf(1,'\b\b\b\b\b\b\b %6.4f',weight);
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end
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xeee = xbar + weight*(xbar-v(:,end));
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x = xeee;
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fxeee = feval(objective_function,x,varargin{:});
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func_count = func_count+1;
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if (fxeee<fxeee_old) && -(fxeee-fxeee_old)>f_tolerance*10*fxeee_old
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fxeee_old = fxeee;
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xeee_old = xeee;
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else
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decrease = 0;
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end
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end
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if verbose>1
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fprintf(1,'\n');
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end
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xe = xeee_old;
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fxe = fxeee_old;
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end
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if verbose>1
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disp('Done!')
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skipline(2)
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end
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end
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v(:,end) = xe;
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fv(end) = fxe;
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move = 'expand';
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else% if xe is not better than xr.
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v(:,end) = xr;
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fv(end) = fxr;
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move = 'reflect-1';
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end
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else% xr is not better than previous best point v(:,1).
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if fxr < fv(number_of_variables)% xr is better than previous point v(:,n).
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v(:,end) = xr;
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fv(end) = fxr;
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move = 'reflect-0';
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else% xr is not better than previous point v(:,n).
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if fxr < fv(end)% xr is better than previous worst point [=> outside contraction].
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xc = (1 + psi*rho)*xbar - psi*rho*v(:,end);
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x = xc;
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fxc = feval(objective_function,x,varargin{:});
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func_count = func_count+1;
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if fxc <= fxr
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v(:,end) = xc;
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fv(end) = fxc;
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move = 'contract outside';
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else
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move = 'shrink';
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end
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else% xr is the worst point [=> inside contraction].
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xcc = (1-psi)*xbar + psi*v(:,end);
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x = xcc;
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fxcc = feval(objective_function,x,varargin{:});
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func_count = func_count+1;
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if fxcc < fv(end)
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v(:,end) = xcc;
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fv(end) = fxcc;
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move = 'contract inside';
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else
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% perform a shrink
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move = 'shrink';
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end
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end
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if strcmp(move,'shrink')
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for j=trend_vector_2
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v(:,j)=v(:,1)+sigma*(v(:,j) - v(:,1));
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x = v(:,j);
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fv(j) = feval(objective_function,x,varargin{:});
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end
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func_count = func_count + number_of_variables;
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end
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end
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end
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% Sort n+1 points by incresing order of the objective function values.
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[fv,sort_idx] = sort(fv);
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v = v(:,sort_idx);
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iter_count = iter_count + 1;
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simplex_iterations = simplex_iterations+1;
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if verbose>1
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disp(['Simplex iteration number: ' int2str(simplex_iterations) '-' int2str(simplex_init) '-' int2str(simplex_algo_iterations)])
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disp(['Simplex move: ' move])
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disp(['Objective function value: ' num2str(fv(1))])
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disp(['Mode improvement: ' num2str(best_point_score-fv(1))])
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disp(['Norm of dx: ' num2str(norm(best_point-v(:,1)))])
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disp(['Norm of dSimplex: ' num2str(norm(v-vold,'fro'))])
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disp(['Crit. f: ' num2str(critF)])
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disp(['Crit. x: ' num2str(critX)])
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skipline()
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end
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if verbose && max(abs(best_point-v(:,1)))>x_tolerance;
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if verbose<2
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disp(['Simplex iteration number: ' int2str(simplex_iterations) '-' int2str(simplex_init) '-' int2str(simplex_algo_iterations)])
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disp(['Objective function value: ' num2str(fv(1))])
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disp(['Mode improvement: ' num2str(best_point_score-fv(1))])
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disp(['Norm of dx: ' num2str(norm(best_point-v(:,1)))])
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disp(['Norm of dSimplex: ' num2str(norm(v-vold,'fro'))])
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disp(['Crit. f: ' num2str(critF)])
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disp(['Crit. x: ' num2str(critX)])
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skipline()
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end
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disp(['Current parameter values: '])
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fprintf(1,'%s: \t\t\t %s \t\t\t %s \t\t\t %s \t\t\t %s \t\t\t %s \n','Names','Best point', 'Worst point', 'Mean values', 'Min values', 'Max values');
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for i=1:number_of_variables
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fprintf(1,'%s: \t\t\t %+8.6f \t\t\t %+8.6f \t\t\t %+8.6f \t\t\t %+8.6f \t\t\t %+8.6f \n',bayestopt_.name{i}, v(i,1), v(i,end), mean(v(i,:),2), min(v(i,:),[],2), max(v(i,:),[],2));
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end
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skipline()
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end
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if abs(best_point_score-fv(1))<f_tolerance
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no_improvements = no_improvements+1;
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else
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no_improvements = 0;
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end
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best_point = v(:,1);
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best_point_score = fv(1);
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vold = v;
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if no_improvements>max_no_improvements
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if verbose
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disp(['NO SIGNIFICANT IMPROVEMENT AFTER ' int2str(no_improvements) ' ITERATIONS!'])
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end
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if simplex_algo_iterations<=max_simplex_algo_iterations
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% Compute the size of the simplex
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delta = delta*1.05;
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% Compute the new initial simplex.
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[v,fv,delta] = simplex_initialization(objective_function,best_point,best_point_score,delta,zero_delta,1,varargin{:});
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if verbose
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disp(['(Re)Start with a lager simplex around the based on the best current '])
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disp(['values for the control variables. '])
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disp(['New value of delta (size of the new simplex) is: '])
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for i=1:number_of_variables
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fprintf(1,'%s: \t\t\t %+8.6f \n',bayestopt_.name{i}, delta(i));
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end
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end
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% Reset counters
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no_improvements = 0;
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func_count = func_count + number_of_variables;
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iter_count = iter_count+1;
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iter_no_improvement_break = iter_no_improvement_break + 1;
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simplex_init = simplex_init+1;
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simplex_iterations = simplex_iterations+1;
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skipline(2)
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end
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end
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if ((func_count==max_func_calls) || (iter_count==max_iterations) || (iter_no_improvement_break==max_no_improvement_break) || convergence || tooslow)
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[v,fv,delta] = simplex_initialization(objective_function,best_point,best_point_score,DELTA,zero_delta,1,varargin{:});
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if func_count==max_func_calls
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if verbose
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disp(['MAXIMUM NUMBER OF OBJECTIVE FUNCTION CALLS EXCEEDED (' int2str(max_func_calls) ')!'])
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end
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elseif iter_count== max_iterations
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if verbose
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disp(['MAXIMUM NUMBER OF ITERATIONS EXCEEDED (' int2str(max_iterations) ')!'])
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end
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elseif iter_no_improvement_break==max_no_improvement_break
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if verbose
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disp(['MAXIMUM NUMBER OF SIMPLEX REINITIALIZATION EXCEEDED (' int2str(max_no_improvement_break) ')!'])
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end
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iter_no_improvement_break = 0;
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if simplex_algo_iterations==max_simplex_algo_iterations
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max_no_improvements = Inf;% Do not stop until convergence is reached!
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continue
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end
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elseif tooslow
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disp(['CONVERGENCE NOT ACHIEVED AFTER ' int2str(simplex_iterations) ' ITERATIONS! IMPROVING TOO SLOWLY!'])
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else
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disp(['CONVERGENCE ACHIEVED AFTER ' int2str(simplex_iterations) ' ITERATIONS!'])
|
||
end
|
||
if simplex_algo_iterations<max_simplex_algo_iterations
|
||
% Compute the size of the simplex
|
||
delta = delta*1.05;
|
||
% Compute the new initial simplex.
|
||
[v,fv,delta] = simplex_initialization(objective_function,best_point,best_point_score,delta,zero_delta,1,varargin{:});
|
||
if verbose
|
||
disp(['(Re)Start with a lager simplex around the based on the best current '])
|
||
disp(['values for the control variables. '])
|
||
disp(['New value of delta (size of the new simplex) is: '])
|
||
for i=1:number_of_variables
|
||
fprintf(1,'%s: \t\t\t %+8.6f \n',bayestopt_.name{i}, delta(i));
|
||
end
|
||
end
|
||
% Reset counters
|
||
func_count=0;
|
||
iter_count=0;
|
||
convergence = 0;
|
||
no_improvements = 0;
|
||
func_count = func_count + number_of_variables;
|
||
iter_count = iter_count+1;
|
||
simplex_iterations = simplex_iterations+1;
|
||
simplex_algo_iterations = simplex_algo_iterations+1;
|
||
skipline(2)
|
||
else
|
||
break
|
||
end
|
||
end
|
||
end% while loop.
|
||
|
||
x(:) = v(:,1);
|
||
fval = fv(:,1);
|
||
exitflag = 1;
|
||
|
||
if func_count>= max_func_calls
|
||
disp('Maximum number of objective function calls has been exceeded!')
|
||
exitflag = 0;
|
||
end
|
||
|
||
if iter_count>= max_iterations
|
||
disp('Maximum number of iterations has been exceeded!')
|
||
exitflag = 0;
|
||
end
|
||
|
||
|
||
|
||
|
||
function [v,fv,delta] = simplex_initialization(objective_function,point,point_score,delta,zero_delta,check_delta,varargin)
|
||
n = length(point);
|
||
v = zeros(n,n+1);
|
||
v(:,1) = point;
|
||
fv = zeros(n+1,1);
|
||
fv(1) = point_score;
|
||
if length(delta)==1
|
||
delta = repmat(delta,n,1);
|
||
end
|
||
for j = 1:n
|
||
y = point;
|
||
if y(j) ~= 0
|
||
y(j) = (1 + delta(j))*y(j);
|
||
else
|
||
y(j) = zero_delta;
|
||
end
|
||
v(:,j+1) = y;
|
||
x = y;
|
||
[fv(j+1),junk1,junk2,nopenalty_flag] = feval(objective_function,x,varargin{:});
|
||
if check_delta
|
||
while ~nopenalty_flag
|
||
if y(j)~=0
|
||
delta(j) = delta(j)/1.1;
|
||
else
|
||
zero_delta = zero_delta/1.1;
|
||
end
|
||
y = point;
|
||
if y(j) ~= 0
|
||
y(j) = (1 + delta(j))*y(j);
|
||
else
|
||
y(j) = zero_delta;
|
||
end
|
||
v(:,j+1) = y;
|
||
x = y;
|
||
[fv(j+1),junk1,junk2,nopenalty_flag] = feval(objective_function,x,varargin{:});
|
||
end
|
||
end
|
||
end
|
||
% Sort by increasing order of the objective function values.
|
||
[fv,sort_idx] = sort(fv);
|
||
v = v(:,sort_idx); |