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%
%     This is an example call of MIDACO 6.0
%     -------------------------------------
%
%     MIDACO solves Multi-Objective Mixed-Integer Non-Linear Problems:
%
%
%      Minimize     F_1(X),... F_O(X)  where X(1,...N-NI)   is CONTINUOUS
%                                      and   X(N-NI+1,...N) is DISCRETE
%
%      subject to   G_j(X)  =  0   (j=1,...ME)      equality constraints
%                   G_j(X) >=  0   (j=ME+1,...M)  inequality constraints
%
%      and bounds   XL <= X <= XU
%
%
%     The problem statement of this example is given below. You can use 
%     this example as template to run your own problem. To do so: Replace 
%     the objective functions 'F' (and in case the constraints 'G') given 
%     here with your own problem and follow the below instruction steps.
%
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function example
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%%%%%%%%%%%%%%%%%%%%%%%%%   MAIN PROGRAM   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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 key = 'MIDACO_LIMITED_VERSION___[CREATIVE_COMMONS_BY-NC-ND_LICENSE]';   
 problem.func = @problem_function; % Call is [f,g] = problem_function(x)        
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%%% Step 1: Problem definition     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% STEP 1.A: Problem dimensions
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problem.o  = 1; % Number of objectives
problem.n  = 4; % Number of variables (in total)
problem.ni = 2; % Number of integer variables (0 <= ni <= n)
problem.m  = 3; % Number of constraints (in total)
problem.me = 1; % Number of equality constraints (0 <= me <= m)
     
% STEP 1.B: Lower and upper bounds 'xl' & 'xu'  
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problem.xl = 1 * ones(1,problem.n);
problem.xu = 4 * ones(1,problem.n); 

% STEP 1.C: Starting point 'x'  
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problem.x  = problem.xl; % Here for example: 'x' = lower bounds 'xl'
 
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%%% Step 2: Choose stopping criteria and printing options    %%%%%%%%%%%
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% STEP 2.A: Stopping criteria 
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option.maxeval  = 1000;    % Maximum number of function evaluation (e.g. 1000000)
option.maxtime  = 60*60*24; % Maximum time limit in Seconds (e.g. 1 Day = 60*60*24)

% STEP 2.B: Printing options  
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option.printeval  = 100;  % Print-Frequency for current best solution (e.g. 1000)
option.save2file  = 1;     % Save SCREEN and SOLUTION to TXT-files [ 0=NO/ 1=YES]

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%%% Step 3: Choose MIDACO parameters (FOR ADVANCED USERS)    %%%%%%%%%%%
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option.param( 1) =  0;  % ACCURACY  
option.param( 2) =  0;  % SEED      
option.param( 3) =  0;  % FSTOP
option.param( 4) =  0;  % ALGOSTOP
option.param( 5) =  0;  % EVALSTOP  
option.param( 6) =  0;  % FOCUS
option.param( 7) =  0;  % ANTS
option.param( 8) =  0;  % KERNEL
option.param( 9) =  0;  % ORACLE    
option.param(10) =  0;  % PARETOMAX   
option.param(11) =  0;  % EPSILON   
option.param(12) =  0;  % BALANCE
option.param(13) =  0;  % CHARACTER  

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%%% Step 4: Choose Parallelization Factor   %%%%%%%%%%%%%%%%%%%%%%%%%%%%
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option.parallel = 2;  % Serial: 0 or 1, Parallel: 2,3,4,5,6,7,8...  

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%%%   Call MIDACO solver   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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[ solution ] = midaco( problem, option, key);
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%%%   End of Example    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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end


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%%%%%%%%%%%%%%%%%%%%%   OPTIMIZATION PROBLEM   %%%%%%%%%%%%%%%%%%%%%%%%%
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function [ f, g ] = problem_function( x )

% Objective functions F(X)
  f(1) = (x(1)-1)^2 ...
       + (x(2)-2)^2 ...
       + (x(3)-3)^2 ...
       + (x(4)-4)^2 ...
       + 1.23456789;

% Equality constraints G(X) = 0 MUST COME FIRST in g(1:me)
  g(1) = x(1) - 1;
% Inequality constraints G(X) >= 0 MUST COME SECOND in g(me+1:m)
  g(2) = x(2) - 1.333333333;
  g(3) = x(3) - 2.666666666;
  
% Simulate CPU-Time expensive function evaluation
  pause(1.0); % A single function evaluation takes now 1 Second
  
end
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%%%%%%%%%%%%%%%%%%%%%%%%   END OF FILE   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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