Solves a mixed-integer linear optimization problem in fot_intlinprog format.
xopt = fot_intlinprog(c,intcon,A,b) xopt = fot_intlinprog(c,intcon,A,b,Aeq,beq) xopt = fot_intlinprog(c,intcon,A,b,Aeq,beq,lb,ub) xopt = fot_intlinprog(c,intcon,A,b,Aeq,beq,lb,ub,options) xopt = fot_intlinprog('path_to_mps_file') xopt = fot_intlinprog('path_to_mps_file',options) [xopt,fopt,status,output] = fot_intlinprog( ... )
a vector of double, contains coefficients of the variables in the objective
Vector of integer constraints, specified as a vector of positive integers. The values in intcon indicate the components of the decision variable x that are integer-valued. intcon has values from 1 through number of variable.
A matrix of doubles, containing the coefficients of linear inequality constraints of size (m X n) where 'm' is the number of linear inequality constraints.
A vector of doubles, related to 'A' and containing the the Right hand side equation of the linear inequality constraints of size (m X 1).
A matrix of doubles, containing the coefficients of linear equality constraints of size (m1 X n) where 'm1' is the number of linear equality constraints.
A vector of doubles, related to 'Aeq' and containing the the Right hand side equation of the linear equality constraints of size (m1 X 1).
A vector of doubles, containing the lower bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of variables.
A vector of doubles, containing the upper bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of variables.
A list, containing the option for user to specify. See below for details.
A vector of doubles, containing the computed solution of the optimization problem.
A double, containing the the function value at x.
An integer, containing the flag which denotes the reason for termination of algorithm. See below for details.
A structure, containing the information about the optimization. See below for details.
Search the minimum or maximum of a constrained mixed-integer linear programming optimization problem specified by :
CBC, an optimization library written in C++, is used for solving the linear programming problems.
options= list("IntegerTolerance", [---], "MaxNodes",[---], "MaxIter", [---], "AllowableGap",[---] "CpuTime", [---],"gradobj", "off", "hessian", "off" );
options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap')
The exitflag allows the user to know the status of the optimization which is returned by OSI-CBC. The values it can take and what they indicate is described below:
For more details on exitflag, see the Bonmin documentation which can be found on http://www.coin-or.org/Cbc
A few examples displaying the various functionalities of fot_intlinprog have been provided below. You will find a series of problems and the appropriate code snippets to solve them.
Here we build up on the previous example by adding upper and lower bounds to the variables. We add the following bounds to the problem specified above:
// Example 1: // Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. "An application of mixed-integer // programming in a Swedish steel mill." Interfaces 7, no. 2 (1977): 39-43. Modified acc. to requirements. c = [350*5,330*3,310*4,280*6,500,450,400,100]'; //Inequality constraints A = [6,4.25, 5.5, 7.75, 3, 3.25, 3.5,3.75; 1.25,1.37,1.7,1.93,2.08,2.32,2.56,2.78; 1.15,1.34,1.66,1.99,2.06,2.32,2.58,2.84 ]; b = [100 ,205, 249 ]; // Lower Bound of variable lb = repmat(0,1,8); // Upper Bound of variables ub = [repmat(1,1,4) repmat(%inf,1,4)]; //Integer Constraints intcon = [1 2 3 4]; // Calling Symphony [x,f,status,output] = fot_intlinprog(c,intcon,A,b,[],[],lb,ub) // Press ENTER to continue | ![]() | ![]() |
In this example, we proceed to add the linear equality constraints to the objective function.
// Example 2: // Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. "An application of mixed-integer // programming in a Swedish steel mill." Interfaces 7, no. 2 (1977): 39-43. Modified acc. to requirements. c = [350*5,330*3,310*4,280*6,500,450,400,100]'; //Inequality constraints A = [6,4.25, 5.5, 7.75, 3, 3.25, 3.5,3.75; 1.25,1.37,1.7,1.93,2.08,2.32,2.56,2.78; 1.15,1.34,1.66,1.99,2.06,2.32,2.58,2.84 ]; b = [100 ,205, 249 ]; // Lower Bound of variable lb = repmat(0,1,8); // Upper Bound of variables ub = [repmat(1,1,4) repmat(%inf,1,4)]; // Equality Constraints Aeq = [5,3,4,6,1,1,1,1; 5*0.05,3*0.04,4*0.05,6*0.03,0.08,0.07,0.06,0.03; 5*0.03,3*0.03,4*0.04,6*0.04,0.06,0.07,0.08,0.09;] beq = [ 25, 1.25, 1.25]; //Integer Constraints intcon = [1 2 3 4]; // Calling CBC [x,f,status,output] = fot_intlinprog(c,intcon,A,b,Aeq,beq,lb,ub) // Press ENTER to continue | ![]() | ![]() |
Unbounded Problems. Find x in R^8 such that it minimizes: