#*-------------------------------------------------------------------
* EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC.
*
* This LIBRARY is free software; you can distribute it and/or modify
* it under the therms of the ALSOC FREE LICENSE as available at
* http://www.enq.ufrgs.br/alsoc.
*
* EMSO Copyright (C) 2004 - 2007 ALSOC, original code
* from http://www.rps.eng.br Copyright (C) 2002-2004.
* All rights reserved.
*
* EMSO is distributed under the therms of the ALSOC LICENSE as
* available at http://www.enq.ufrgs.br/alsoc.
*
*--------------------------------------------------------------------
* More test problems
*--------------------------------------------------------------------
* Author: Argimiro R Secchi		  
* $Id$
*--------------------------------------------------------------------*#
Optimization test27  # solution: x1=0.7411, x2=0.7411, obj=-17.96
	PARAMETERS
	pi as Real;

	VARIABLES
	x1 as Real(Default=0,Lower=-1,Upper=1);
	x2 as Real(Default=0,Lower=-1,Upper=1);

	SET
	pi = 4*atan(1)/'rad';

	MINIMIZE
	-(abs(20*x1)+abs(20*x2)+2*(x1+x2)) * sin(20*'rad'*x1/pi)^2 *
	sin(20*'rad'*x2/pi)^2 + 40*(x1^2+x2^2)/3;

	OPTIONS
	NLPSolver(MaxIterations=2000,
			  AbsoluteAccuracy=1e-6,
			  RelativeAccuracy=1e-4,
			  #File = "ipopt_emso", hessian_approximation = "exact"
			  #File = "complex"
	          #File = "optpp_emso"
			  #File = "arshj"
			  #File = "PSO"
			  File = "direct", MinimumRectangle=1e-4,MaxEvals=5000
			  );
	Dynamic = false;
end

# Alpina function
Optimization test28  # solution: x1=7.917, x2=7.917, obj=-7.8856
	VARIABLES
	x1 as Real(Default=3,Lower=0,Upper=10);
	x2 as Real(Default=1,Lower=0,Upper=10);

	MINIMIZE
	-sqrt(x1*x2)*sin(x1*'rad')*sin(x2*'rad');

	OPTIONS
	NLPSolver(MaxIterations=2000,
			  AbsoluteAccuracy=1e-6,
			  RelativeAccuracy=1e-4,
			  #File = "ipopt_emso", hessian_approximation = "exact"
			  #File = "complex"
	          #File = "optpp_emso"
			  #File = "arshj"
			  #File = "PSO"			  
			  File = "direct", MinimumRectangle=1e-4,MaxEvals=5000
			  );
	Dynamic = false;
end

# Griewank function
Optimization test29  # solution: x1=0, x2=0, obj=0
	VARIABLES
#	x1 as Real(Default=0,Lower=-100,Upper=100);
#	x2 as Real(Default=9,Lower=-100,Upper=100);
	x1 as Real(Default=0,Lower=-100,Upper=90);
	x2 as Real(Default=9,Lower=-100,Upper=90);

	MINIMIZE
	1+(x1^2+x2^2)/4000-cos(x1*'rad')*cos(x2*'rad'/sqrt(2));

	OPTIONS
	NLPSolver(MaxIterations=4000,
			  AbsoluteAccuracy=1e-6,
			  RelativeAccuracy=1e-4,
			  #File = "ipopt_emso", hessian_approximation = "exact"
			  #File = "complex"
	          #File = "optpp_emso"
			  #File = "arshj"
			  #File = "PSO"			  
			  #File = "direct", MinimumRectangle=1e-4,MaxEvals=5000
			  File = "direct", MinimumRectangle=1e-10,Epsilon=1e-2,MaxEvals=10000	
			  );
	Dynamic = false;
end

Optimization test31  # solution: x=8.817, obj=-8.13
	VARIABLES
	x as Real(Default=-10,Lower=-10,Upper=10);

	MINIMIZE
	(x+10)*(x+6)*(x+5)*(x+1)*(x-7)*(x-10)*1e-4;

	OPTIONS
	NLPSolver(MaxIterations=2000,
			  AbsoluteAccuracy=1e-6,
			  RelativeAccuracy=1e-4,
			  #File = "ipopt_emso", hessian_approximation = "exact"
			  #File = "complex"
	          #File = "optpp_emso"
			  #File = "arshj"
			  #File = "PSO"			  
			  File = "direct", MinimumRectangle=1e-4,MaxEvals=5000
			  );
	Dynamic = false;
end

# Levy 5 function
Optimization test32  # solution: x1=-1.3068, x2=-1.4248, obj=-176.1376
	PARAMETERS
	i(5) as Integer;

	VARIABLES
	x1 as Real(Default=0,Lower=-10,Upper=10);
	x2 as Real(Default=0,Lower=-10,Upper=10);

	SET
	i = [1:5];

	MINIMIZE
	sum(i*cos(((i-1)*x1+i)*'rad'))*sum(i*cos(((i+1)*x2+i)*'rad'))+(x1+1.42513)^2+(x2+0.80032)^2;

	OPTIONS
	NLPSolver(MaxIterations=2000,
			  AbsoluteAccuracy=1e-6,
			  RelativeAccuracy=1e-4,
			  #File = "ipopt_emso", hessian_approximation = "exact"
			  #File = "complex"
	          #File = "optpp_emso"
			  #File = "arshj"
			  #File = "PSO"			  
			  File = "direct", MinimumRectangle=1e-5,Epsilon=1e-1,MaxEvals=10000
			  );
	Dynamic = false;
end

# H1 function
Optimization test33  # solution: x1=8.6998, x2=6.7665, obj=-2
	VARIABLES
	x1 as Real(Default=0,Lower=-100,Upper=100);
	x2 as Real(Default=0,Lower=-100,Upper=100);

	MINIMIZE
	-(sin((x1-x2/8)*'rad')^2+sin((x2+x1/8)*'rad')^2)/(1+sqrt((x1-8.6998)^2+(x2-6.7665)^2));

	OPTIONS
	NLPSolver(MaxIterations=2000,
			  AbsoluteAccuracy=1e-6,
			  RelativeAccuracy=1e-4,
			  #File = "ipopt_emso", hessian_approximation = "exact"
			  #File = "complex"
	          #File = "optpp_emso"
			  #File = "arshj"
			  #File = "PSO"			  
			  File = "direct", MinimumRectangle=1e-4,Epsilon=1e-1,MaxEvals=10000
			  );
	Dynamic = false;
end

# Ackley function
Optimization test34  # solution: x=0, obj=0
	PARAMETERS
	n as Integer(Default=3);
	pi as Real;

	VARIABLES
	x(n) as Real(Default=10,Lower=-32.68,Upper=32.68/2);
#	x(n) as Real(Default=10,Lower=-32.68,Upper=32.68);

	SET
	pi = 4*atan(1)/'rad';

	MINIMIZE
	-20*exp(-0.2*sqrt(sum(x^2)/n))-exp(sum(cos(2*pi*x*'rad'))/n)+20+exp(1);

	OPTIONS
	NLPSolver(MaxIterations=2000,
			  AbsoluteAccuracy=1e-6,
			  RelativeAccuracy=1e-4,
			  #File = "ipopt_emso", hessian_approximation = "exact"
			  #File = "complex"
	          #File = "optpp_emso"
			  #File = "arshj"
			  #File = "PSO"			  
			  File = "direct", MinimumRectangle=1e-8,Epsilon=1e-1,MaxEvals=20000
			  );
	Dynamic = false;
end

# Schwefel function
Optimization test35  # solution: x=420.9687, obj=-n (approx.)
	PARAMETERS
	n as Integer(Default=4);

	VARIABLES
	x(n) as Real(Default=0,Lower=-500,Upper=500);

	MINIMIZE
	418*n-sum(x*sin(sqrt(abs(x))*'rad'));

	OPTIONS
	NLPSolver(MaxIterations=2000,
			  AbsoluteAccuracy=1e-6,
			  RelativeAccuracy=1e-4,
			  #File = "ipopt_emso", hessian_approximation = "exact"
			  #File = "complex"
	          #File = "optpp_emso"
			  #File = "arshj"
			  #File = "PSO"			  
			  File = "direct", MinimumRectangle=1e-8,Epsilon=1e-3,MaxEvals=30000
			  );
	Dynamic = false;
end