cplex与matalb函数实例

function cplexbilpex

% Use the function cplexbilp to solve a binary integer programming problem %

% The bilp problem solved in this example is

% Maximize x1 + 2 x2 + 3 x3 + x4

% Subject to

% - x1 + x2 + x3 + 10 x4 <= 20

% x1 - 3 x2 + x3 <= 30

% x2 - 3.5x4 = 0

% Binary Integer

% x1 x2 x3 x4

%

---------------------------------------------------------------------------

% File: cplexbilpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

% Since cplexbilp solves minimization problems and the problem

% is a maximization problem, negate the objective

f = [-1 -2 -3 -1]';

Aineq = [-1 1 1 10;

1 -3 1 0];

bineq = [20 30]';

Aeq = [0 1 0 -3.5];

beq = 0;

options = cplexoptimset;

options.Diagnostics = 'on';

[x, fval, exitflag, output] = cplexbilp (f, Aineq, bineq, Aeq, beq, ... [ ], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

fprintf ('Solution value = %d\n', fval);

disp ('Values = ');

disp (x');

catch m

disp(m.message);

end

end

function cplexlpex

% Use the function cplexlp to solve a linear programming problem

%

% The LP problem solved in this example is

% Maximize x1 + 2 x2 + 3 x3

% Subject to

% - x1 + x2 + x3 <= 20

% x1 - 3 x2 + x3 <= 30

% Bounds

% 0 <= x1 <= 40

% 0 <= x2

% 0 <= x3

%

---------------------------------------------------------------------------

% File: cplexlpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

% Since cplexlp solves minimization problems and the problem

% is a maximization problem, negate the objective

f = [-1 -2 -3]';

Aineq = [-1 1 1; 1 -3 1];

bineq = [20 30]';

lb = [0 0 0]';

ub = [40 inf inf]';

options = cplexoptimset;

options.Diagnostics = 'on';

[x, fval, exitflag, output] = cplexlp ...

(f, Aineq, bineq, [], [], lb, ub, [], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

fprintf ('Solution value = %f\n', fval);

disp ('Values =');

disp (x');

catch m

disp(m.message);

end

end

function cplexlsqbilpex

% Use the function cplexlsqbilp to solve a constrained least squares

% problem Some variables are binary.

%

---------------------------------------------------------------------------

% File: cplexlsqbilpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.9501 0.7620 0.6153 0.4057

0.2311 0.4564 0.7919 0.9354

0.6068 0.0185 0.9218 0.9169

0.4859 0.8214 0.7382 0.4102

0.8912 0.4447 0.1762 0.8936];

d = [0.0578

0.3528

0.8131

0.0098

0.1388];

Aineq = [0.2027 0.2721 0.7467 0.4659

0.1987 0.1988 0.4450 0.4186

0.6037 0.0152 0.9318 0.8462];

bineq = [0.5251

0.2026

0.6721];

lb = 0.0 * ones (4, 1);

ub = 1.0 * ones (4, 1);

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqbilp (C, d, Aineq, bineq, ...

[ ], [ ], lb, ub, [ ], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp ('resnorm =');

disp (resnorm);

disp ('residual =');

catch m

throw (m);

end

end

function cplexlsqlinex

% Use the function cplexlsqlin to solve a constrained least squares problem %

---------------------------------------------------------------------------

% File: cplexlsqlinex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.9501 0.7620 0.6153 0.4057

0.2311 0.4564 0.7919 0.9354

0.6068 0.0185 0.9218 0.9169

0.4859 0.8214 0.7382 0.4102

0.8912 0.4447 0.1762 0.8936];

d = [0.0578

0.3528

0.8131

0.0098

0.1388];

Aineq = [0.2027 0.2721 0.7467 0.4659

0.1987 0.1988 0.4450 0.4186

0.6037 0.0152 0.9318 0.8462];

bineq = [0.5251

0.2026

0.6721];

lb = -0.1 * ones (4, 1);

ub = 2.0 * ones (4, 1);

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqlin (C, d, Aineq, bineq, [ ], [ ], lb, ub, [], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp (resnorm);

disp ('residual =');

disp (residual');

catch m

disp(m.message);

end

end

function cplexlsqmilpex

% Use the function cplexlsqmilp to solve a constrained least squares problem % Some variables are binary.

%

---------------------------------------------------------------------------

% File: cplexlsqmilpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.9501 0.7620 0.6153 0.4057

0.2311 0.4564 0.7919 0.9354

0.6068 0.0185 0.9218 0.9169

0.4859 0.8214 0.7382 0.4102

0.8912 0.4447 0.1762 0.8936];

d = [0.0578

0.3528

0.8131

0.0098

0.1388];

Aineq = [0.2027 0.2721 0.7467 0.4659

0.1987 0.1988 0.4450 0.4186

0.6037 0.0152 0.9318 0.8462];

bineq = [0.5251

0.2026

0.6721];

lb = [0.0 -0.1 0.0 -0.1];

ub = [1.0 2.0 1.0 2.0];

ctype = 'BCBC';

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqmilp (C, d, Aineq, bineq, ...

[ ], [ ], [ ], [ ], [ ], lb, ub, ctype, [ ], options); fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp ('resnorm =');

disp (resnorm);

disp ('residual =');

disp (residual');

catch m

throw (m);

end

end

function cplexlsqmiqcpex

% Use the function cplexlsqmiqcp to solve a constrained least squares problem % Some variables are binary and one constraint is quadratic.

%

---------------------------------------------------------------------------

% File: cplexlsqmiqcpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.9501 0.7620 0.6153 0.4057

0.2311 0.4564 0.7919 0.9354

0.6068 0.0185 0.9218 0.9169

0.4859 0.8214 0.7382 0.4102

0.8912 0.4447 0.1762 0.8936];

d = [0.0578

0.3528

0.8131

0.0098

0.1388];

Aineq = [0.2027 0.2721 0.7467 0.4659

0.1987 0.1988 0.4450 0.4186

0.6037 0.0152 0.9318 0.8462];

bineq = [0.5251

0.2026

0.6721];

lb = [0.0 -0.1 0.0 -0.1];

ub = [1.0 2.0 1.0 2.0];

l = [0 0 0 0]';

r = 1;

Q = [1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1];

ctype = 'BCBC';

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqmiqcp (C, d, Aineq, bineq,[ ], [ ], l, Q, r, [ ], [ ], [ ], ... lb, ub, ctype, [ ], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp ('resnorm =');

disp (resnorm);

disp ('residual =');

disp (residual');

catch m

throw (m);

end

end

function cplexlsqnonneglinex

% Use the function cplexlsqnonneglin to solve a nonnegative least squares % problem

%

---------------------------------------------------------------------------

% File: cplexlsqnonneglinex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.0372 0.2869

0.6861 0.7071

0.6344 0.6170];

d = [0.8587

0.1781

0.0747

0.8405];

Aineq = [0.2027 0.2721

0.1987 0.1988

0.6037 0.0152];

bineq = [0.5251

0.2026

0.6721];

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqnonneglin (C, d, Aineq, bineq, [], [], [], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp ('resnorm =');

disp (resnorm);

disp ('residual =');

disp (residual');

catch m

throw (m);

end

end

function cplexlsqnonnegmilpex

% Use the function cplexlsqnonnegmilp to solve a nonnegative least squares % problem. The variables are binary.

%

---------------------------------------------------------------------------

% File: cplexlsqnonnegmilpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.0372 0.2869

0.6861 0.7071

0.6344 0.6170];

d = [0.8587

0.1781

0.0747

0.8405];

Aineq = [0.2027 0.2721

0.1987 0.1988

0.6037 0.0152];

bineq = [0.5251

0.2026

0.6721];

ctype = 'BB';

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqnonnegmilp (C, d, Aineq, bineq, [], [], [], [], [], ctype, ... [], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp ('resnorm =');

disp (resnorm);

disp ('residual =');

disp (residual');

catch m

throw (m);

end

end

function cplexlsqnonnegmiqcpex

% Use the function cplexlsqnonnegmiqcp to solve a nonnegative least squares % problem. The variables are binary and one constraint is quadratic.

%

---------------------------------------------------------------------------

% File: cplexlsqnonnegmiqcpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.0372 0.2869

0.6861 0.7071

0.6233 0.6245

0.6344 0.6170];

d = [0.8587

0.1781

0.0747

0.8405];

Aineq = [0.2027 0.2721

0.1987 0.1988

0.6037 0.0152];

bineq = [0.5251

0.2026

0.6721];

ctype = 'BB';

l = [0 0]';

r = 1;

Q = [1 0

0 1];

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqnonnegmiqcp (C, d, Aineq, bineq, [], [], l, Q, r, ...

[], [], [], ctype, [], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp ('resnorm =');

disp (resnorm);

disp ('residual =');

disp (residual');

catch m

throw (m);

end

end

function cplexlsqnonnegqcpex

% Use the function cplexlsqnonnegqcp to solve a nonnegative least squares % problem. The variables are binary and one constraint is quadratic.

%

---------------------------------------------------------------------------

% File: cplexlsqnonnegmiqcpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.0372 0.2869

0.6861 0.7071

0.6233 0.6245

0.6344 0.6170];

d = [0.8587

0.1781

0.0747

0.8405];

Aineq = [0.2027 0.2721

0.1987 0.1988

0.6037 0.0152];

bineq = [0.5251

0.2026

0.6721];

l = [0 0]';

r = 1;

Q = [1 0

0 1];

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqnonnegqcp (C, d, Aineq, bineq, [], [], l, Q, r, [], options); fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp ('resnorm =');

disp (resnorm);

disp ('residual =');

disp (residual');

catch m

throw (m);

end

end

function cplexlsqqcpex

% Use the function cplexlsqqcp to solve a constrained least squares problem % Some variables are binary and one constraint is quadratic.

%

---------------------------------------------------------------------------

% File: cplexlsqqcpex.m

% Version 12.5

%

---------------------------------------------------------------------------

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

---------------------------------------------------------------------------

try

C = [0.9501 0.7620 0.6153 0.4057

0.2311 0.4564 0.7919 0.9354

0.6068 0.0185 0.9218 0.9169

0.4859 0.8214 0.7382 0.4102

0.8912 0.4447 0.1762 0.8936];

d = [0.0578

0.3528

0.8131

0.0098

0.1388];

Aineq = [0.2027 0.2721 0.7467 0.4659

0.1987 0.1988 0.4450 0.4186

0.6037 0.0152 0.9318 0.8462];

bineq = [0.5251

0.2026

0.6721];

lb = -0.1 * ones(4, 1);

ub = 2.0 * ones(4, 1);

l = [0 0 0 0]';

r = 1;

Q = [1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1];

options = cplexoptimset;

options.Diagnostics = 'on';

[x, resnorm, residual, exitflag, output] = ...

cplexlsqqcp (C, d, Aineq, bineq,[ ], [ ], l, Q, r, ...

lb, ub, [ ], options);

fprintf ('\nSolution status = %s\n', output.cplexstatusstring);

disp ('Values =');

disp (x');

disp ('resnorm =');

disp (resnorm);

disp ('residual =');

disp (residual');

catch m

throw (m);

end

end

function cplexmilpex

% Use the function cplexmilp to solve a mixed-integer linear programming problem

%

% The MILP problem solved in this example is

% Maximize x1 + 2 x2 + 3 x3 + x4

% Subject to

% - x1 + x2 + x3 + 10 x4 <= 20

% x1 - 3 x2 + x3 <= 30

% x2 - 3.5x4 = 0

% Bounds

% 0 <= x1 <= 40

% 0 <= x2

% 0 <= x3

% 2 <= x4 <= 3

% Integers

% x4

%

-----------------------------------------------------------------------

----

% File: cplexmilpex.m

% Version 12.5

%

-----------------------------------------------------------------------

----

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

-----------------------------------------------------------------------

----

try

% Since cplexmilp solves minimization problems and the problem

% is a maximization problem, negate the objective

f = [-1 -2 -3 -1]';

Aineq = [-1 1 1 10;

1 -3 1 0];

bineq = [20 30]';

Aeq = [0 1 0 -3.5];

beq = 0;

lb = [0; 0; 0; 2];

ub = [40; inf; inf; 3];

ctype = 'CCCI';

options = cplexoptimset;

options.Diagnostics = 'on';

[x, fval, exitflag, output] = cplexmilp (f, Aineq, bineq, Aeq, beq,... [ ], [ ], [ ], lb, ub, ctype, [ ], options);

fprintf ('\nSolution status = %s \n', output.cplexstatusstring);

fprintf ('Solution value = %f \n', fval);

disp ('Values =');

disp (x');

catch m

throw (m);

end

end

function cplexmiqpex

% Use the function cplexmiqp to solve a mixed-integer quadratic programming problem

%

% The MIQP problem solved in this example is

% Maximize x1 + 2 x2 + 3 x3 + x4

% - 0.5 ( 33x1*x1 + 22*x2*x2 + 11*x3*x3 - 12*x1*x2 - 23*x2*x3 ) % Subject to

% - x1 + x2 + x3 + 10 x4 <= 20

% x1 - 3 x2 + x3 <= 30

% x2 - 3.5x4 = 0

% Bounds

% 0 <= x1 <= 40

% 0 <= x2

% 0 <= x3

% 2 <= x4 <= 3

% Integers

% x4

%

-----------------------------------------------------------------------

----

% File: cplexmiqpex.m

% Version 12.5

%

-----------------------------------------------------------------------

----

% Licensed Materials - Property of IBM

% 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21

% Copyright IBM Corporation 2008, 2012. All Rights Reserved.

%

% US Government Users Restricted Rights - Use, duplication or

% disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

%

-----------------------------------------------------------------------

----

try

% Since cplexmiqp solves minimization problems and the problem

% is a maximization problem, negate the objective

H = [33 6 0 0;

6 22 11.5 0;

0 11.5 11 0;

0 0 0 0];

f = [-1 -2 -3 -1]';

Aineq = [-1 1 1 10;

1 -3 1 0];

bineq = [20 30]';

Aeq = [0 1 0 -3.5];

beq = 0;

lb = [ 0; 0; 0; 2];

ub = [40; inf; inf; 3];

ctype = 'CCCI';

options = cplexoptimset;

options.Diagnostics = 'on';

[x, fval, exitflag, output] = cplexmiqp (H, f, Aineq, bineq, Aeq, beq,... [], [], [], lb, ub, ctype, [], options);

fprintf ('\nSolution status = %s \n', output.cplexstatusstring);

fprintf ('Solution value = %f \n', fval);

disp ('Values =');

disp (x');

catch m

disp(m.message);

end

end