LP_SOLVE Solves mixed integer linear programming problems.
SYNOPSIS: [obj,x,duals,stat] = lp_solve(f,a,b,e,vlb,vub,xint,scalemode,keep)
solves the MILP problem
max v = f'*x
a*x <> b
vlb <= x <= vub
x(int) are integer
ARGUMENTS: The first four arguments are required:
f: n vector of coefficients for a linear objective function.
a: m by n matrix representing linear constraints.
b: m vector of right sides for the inequality constraints.
e: m vector that determines the sense of the inequalities:
e(i) = -1 ==> Less Than
e(i) = 0 ==> Equals
e(i) = 1 ==> Greater Than
vlb: n vector of lower bounds. If empty or omitted,
then the lower bounds are set to zero.
vub: n vector of upper bounds. May be omitted or empty.
xint: vector of integer variables. May be omitted or empty.
scalemode: scale flag. Off when 0 or omitted.
keep: Flag for keeping the lp problem after it's been solved.
If omitted, the lp will be deleted when solved.
OUTPUT: A nonempty output is returned if a solution is found:
obj: Optimal value of the objective function.
x: Optimal value of the decision variables.
duals: solution of the dual problem.0001 %LP_SOLVE Solves mixed integer linear programming problems. 0002 % 0003 % SYNOPSIS: [obj,x,duals,stat] = lp_solve(f,a,b,e,vlb,vub,xint,scalemode,keep) 0004 % 0005 % solves the MILP problem 0006 % 0007 % max v = f'*x 0008 % a*x <> b 0009 % vlb <= x <= vub 0010 % x(int) are integer 0011 % 0012 % ARGUMENTS: The first four arguments are required: 0013 % 0014 % f: n vector of coefficients for a linear objective function. 0015 % a: m by n matrix representing linear constraints. 0016 % b: m vector of right sides for the inequality constraints. 0017 % e: m vector that determines the sense of the inequalities: 0018 % e(i) = -1 ==> Less Than 0019 % e(i) = 0 ==> Equals 0020 % e(i) = 1 ==> Greater Than 0021 % vlb: n vector of lower bounds. If empty or omitted, 0022 % then the lower bounds are set to zero. 0023 % vub: n vector of upper bounds. May be omitted or empty. 0024 % xint: vector of integer variables. May be omitted or empty. 0025 % scalemode: scale flag. Off when 0 or omitted. 0026 % keep: Flag for keeping the lp problem after it's been solved. 0027 % If omitted, the lp will be deleted when solved. 0028 % 0029 % OUTPUT: A nonempty output is returned if a solution is found: 0030 % 0031 % obj: Optimal value of the objective function. 0032 % x: Optimal value of the decision variables. 0033 % duals: solution of the dual problem. 0034 0035 function [obj, x, duals, stat] = lp_solve(f, a, b, e, vlb, vub, xint, scalemode, keep) 0036 0037 if nargin == 0 0038 help lp_solve; 0039 return; 0040 end 0041 0042 [m,n] = size(a); 0043 lp = mxlpsolve('make_lp', m, n); 0044 mxlpsolve('set_verbose', lp, 3); 0045 mxlpsolve('set_mat', lp, a); 0046 mxlpsolve('set_rh_vec', lp, b); 0047 mxlpsolve('set_obj_fn', lp, f); 0048 mxlpsolve('set_maxim', lp); % default is solving minimum lp. 0049 0050 for i = 1:length(e) 0051 if e(i) < 0 0052 con_type = 1; 0053 elseif e(i) == 0 0054 con_type = 3; 0055 else 0056 con_type = 2; 0057 end 0058 mxlpsolve('set_constr_type', lp, i, con_type); 0059 end 0060 0061 if nargin > 4 0062 for i = 1:length(vlb) 0063 mxlpsolve('set_lowbo', lp, i, vlb(i)); 0064 end 0065 end 0066 0067 if nargin > 5 0068 for i = 1:length(vub) 0069 mxlpsolve('set_upbo', lp, i, vub(i)); 0070 end 0071 end 0072 0073 if nargin > 6 0074 for i = 1:length(xint) 0075 mxlpsolve('set_int', lp, xint(i), 1); 0076 end 0077 end 0078 0079 if nargin > 7 0080 if scalemode ~= 0 0081 mxlpsolve('set_scaling', lp, scalemode); 0082 end 0083 end 0084 0085 result=mxlpsolve('solve', lp); 0086 if result == 0 | result == 1 | result == 11 | result == 12 0087 % [obj, x, duals, stat] = mxlpsolve('get_solution', lp), result; 0088 [obj, x, duals] = mxlpsolve('get_solution', lp); 0089 stat = result; 0090 else 0091 obj = []; 0092 x = []; 0093 duals = []; 0094 stat = result; 0095 end 0096 0097 if nargin < 9 0098 mxlpsolve('delete_lp', lp); 0099 end