intlinprog not be able to solve my problem - Mixed Integer Linear Programming Solver Problem

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Hung
Hung il 24 Apr 2025
Commentato: Walter Roberson il 24 Apr 2025
Ran in:
I need someone help with my problem.
I use 'intlinprog' to solve but it did not give me the correct (expected) result.
Does anyone know what is the issue and/or other solver can solve it?
Here is my code:
clc
clear
%
f = [2, 5, 3, 4, 5, 8, 0, 1, 3, 0, 8, 9, 4, 1, 9, 10, 2, 5,...
3, 4, 5, 8, 0, 1, 3, 0, 8, 9, 4, 1, 9, 10, 2, 5, 3, 4,...
5, 8, 0, 1, 3, 0, 8, 9, 4, 1, 9, 10, 2, 5, 3, 4, 5, 8,...
0, 1, 3, 0, 8, 9, 4, 1, 9, 10, 2, 5, 3, 4, 5, 8, 0, 1,...
3, 0, 8, 9, 4, 1, 9, 10, 2, 5, 3, 4, 5, 8, 0, 1, 3, 0,...
8, 9, 4, 1, 9, 10, 2, 5, 3, 4, 5, 8, 0, 1, 3, 0, 8, 9,...
4, 1, 9, 10];
% Matrix Aeq
Aeq = zeros(28,112);
Aeq(1,1)=1; Aeq(1,2)=1; Aeq(1,3)=1; Aeq(1,4)=1; Aeq(1,5)=1; Aeq(1,9)=1; Aeq(1,13)=1; Aeq(1,17)=1; Aeq(1,18)=1; Aeq(1,19)=1; Aeq(1,20)=1; Aeq(1,21)=1; Aeq(1,25)=1; Aeq(1,29)=1;
Aeq(2,2)=1; Aeq(2,5)=1; Aeq(2,6)=1; Aeq(2,7)=1; Aeq(2,8)=1; Aeq(2,10)=1; Aeq(2,14)=1; Aeq(2,18)=1; Aeq(2,21)=1; Aeq(2,22)=1; Aeq(2,23)=1; Aeq(2,24)=1; Aeq(2,26)=1; Aeq(2,30)=1;
Aeq(3,3)=1; Aeq(3,7)=1; Aeq(3,9)=1; Aeq(3,10)=1; Aeq(3,11)=1; Aeq(3,12)=1; Aeq(3,15)=1; Aeq(3,19)=1; Aeq(3,23)=1; Aeq(3,25)=1; Aeq(3,26)=1; Aeq(3,27)=1; Aeq(3,28)=1; Aeq(3,31)=1;
Aeq(4,4)=1; Aeq(4,8)=1; Aeq(4,12)=1; Aeq(4,13)=1; Aeq(4,14)=1; Aeq(4,15)=1; Aeq(4,16)=1; Aeq(4,20)=1; Aeq(4,24)=1; Aeq(4,28)=1; Aeq(4,29)=1; Aeq(4,30)=1; Aeq(4,31)=1; Aeq(4,32)=1;
Aeq(5,33)=1; Aeq(5,34)=1; Aeq(5,35)=1; Aeq(5,36)=1; Aeq(5,37)=1; Aeq(5,41)=1; Aeq(5,45)=1; Aeq(5,49)=1; Aeq(5,50)=1; Aeq(5,51)=1; Aeq(5,52)=1; Aeq(5,53)=1; Aeq(5,57)=1; Aeq(5,61)=1;
Aeq(6,34)=1; Aeq(6,37)=1; Aeq(6,38)=1; Aeq(6,39)=1; Aeq(6,40)=1; Aeq(6,42)=1; Aeq(6,46)=1; Aeq(6,50)=1; Aeq(6,53)=1; Aeq(6,54)=1; Aeq(6,55)=1; Aeq(6,56)=1; Aeq(6,58)=1; Aeq(6,62)=1;
Aeq(7,35)=1; Aeq(7,39)=1; Aeq(7,41)=1; Aeq(7,42)=1; Aeq(7,43)=1; Aeq(7,44)=1; Aeq(7,47)=1; Aeq(7,51)=1; Aeq(7,55)=1; Aeq(7,57)=1; Aeq(7,58)=1; Aeq(7,59)=1; Aeq(7,60)=1; Aeq(7,63)=1;
Aeq(8,36)=1; Aeq(8,40)=1; Aeq(8,44)=1; Aeq(8,45)=1; Aeq(8,46)=1; Aeq(8,47)=1; Aeq(8,48)=1; Aeq(8,52)=1; Aeq(8,56)=1; Aeq(8,60)=1; Aeq(8,61)=1; Aeq(8,62)=1; Aeq(8,63)=1; Aeq(8,64)=1;
Aeq(9,65)=1; Aeq(9,66)=1; Aeq(9,67)=1; Aeq(9,68)=1; Aeq(9,69)=1; Aeq(9,73)=1; Aeq(9,77)=1; Aeq(9,81)=1; Aeq(9,82)=1; Aeq(9,83)=1; Aeq(9,84)=1; Aeq(9,85)=1; Aeq(9,89)=1; Aeq(9,93)=1;
Aeq(10,66)=1; Aeq(10,69)=1; Aeq(10,70)=1; Aeq(10,71)=1; Aeq(10,72)=1; Aeq(10,74)=1; Aeq(10,78)=1; Aeq(10,82)=1; Aeq(10,85)=1; Aeq(10,86)=1; Aeq(10,87)=1; Aeq(10,88)=1; Aeq(10,90)=1; Aeq(10,94)=1;
Aeq(11,67)=1; Aeq(11,71)=1; Aeq(11,73)=1; Aeq(11,74)=1; Aeq(11,75)=1; Aeq(11,76)=1; Aeq(11,79)=1; Aeq(11,83)=1; Aeq(11,87)=1; Aeq(11,89)=1; Aeq(11,90)=1; Aeq(11,91)=1; Aeq(11,92)=1; Aeq(11,95)=1;
Aeq(12,68)=1; Aeq(12,72)=1; Aeq(12,76)=1; Aeq(12,77)=1; Aeq(12,78)=1; Aeq(12,79)=1; Aeq(12,80)=1; Aeq(12,84)=1; Aeq(12,88)=1; Aeq(12,92)=1; Aeq(12,93)=1; Aeq(12,94)=1; Aeq(12,95)=1; Aeq(12,96)=1;
Aeq(13,1)=1; Aeq(13,2)=1; Aeq(13,3)=1; Aeq(13,4)=1; Aeq(13,5)=1; Aeq(13,9)=1; Aeq(13,13)=1; Aeq(13,97)=1; Aeq(13,98)=1; Aeq(13,99)=1; Aeq(13,100)=1; Aeq(13,101)=1; Aeq(13,105)=1; Aeq(13,109)=1;
Aeq(14,2)=1; Aeq(14,5)=1; Aeq(14,6)=1; Aeq(14,7)=1; Aeq(14,8)=1; Aeq(14,10)=1; Aeq(14,14)=1; Aeq(14,98)=1; Aeq(14,101)=1; Aeq(14,102)=1; Aeq(14,103)=1; Aeq(14,104)=1; Aeq(14,106)=1; Aeq(14,110)=1;
Aeq(15,3)=1; Aeq(15,7)=1; Aeq(15,9)=1; Aeq(15,10)=1; Aeq(15,11)=1; Aeq(15,12)=1; Aeq(15,15)=1; Aeq(15,99)=1; Aeq(15,103)=1; Aeq(15,105)=1; Aeq(15,106)=1; Aeq(15,107)=1; Aeq(15,108)=1; Aeq(15,111)=1;
Aeq(16,4)=1; Aeq(16,8)=1; Aeq(16,12)=1; Aeq(16,13)=1; Aeq(16,14)=1; Aeq(16,15)=1; Aeq(16,16)=1; Aeq(16,100)=1; Aeq(16,104)=1; Aeq(16,108)=1; Aeq(16,109)=1; Aeq(16,110)=1; Aeq(16,111)=1; Aeq(16,112)=1;
Aeq(17,17)=1; Aeq(17,18)=1; Aeq(17,19)=1; Aeq(17,20)=1; Aeq(17,21)=1; Aeq(17,25)=1; Aeq(17,29)=1; Aeq(17,33)=1; Aeq(17,34)=1; Aeq(17,35)=1; Aeq(17,36)=1; Aeq(17,37)=1; Aeq(17,41)=1; Aeq(17,45)=1;
Aeq(18,18)=1; Aeq(18,21)=1; Aeq(18,22)=1; Aeq(18,23)=1; Aeq(18,24)=1; Aeq(18,26)=1; Aeq(18,30)=1; Aeq(18,34)=1; Aeq(18,37)=1; Aeq(18,38)=1; Aeq(18,39)=1; Aeq(18,40)=1; Aeq(18,42)=1; Aeq(18,46)=1;
Aeq(19,19)=1; Aeq(19,23)=1; Aeq(19,25)=1; Aeq(19,26)=1; Aeq(19,27)=1; Aeq(19,28)=1; Aeq(19,31)=1; Aeq(19,35)=1; Aeq(19,39)=1; Aeq(19,41)=1; Aeq(19,42)=1; Aeq(19,43)=1; Aeq(19,44)=1; Aeq(19,47)=1;
Aeq(20,20)=1; Aeq(20,24)=1; Aeq(20,28)=1; Aeq(20,29)=1; Aeq(20,30)=1; Aeq(20,31)=1; Aeq(20,32)=1; Aeq(20,36)=1; Aeq(20,40)=1; Aeq(20,44)=1; Aeq(20,45)=1; Aeq(20,46)=1; Aeq(20,47)=1; Aeq(20,48)=1;
Aeq(21,49)=1; Aeq(21,50)=1; Aeq(21,51)=1; Aeq(21,52)=1; Aeq(21,53)=1; Aeq(21,57)=1; Aeq(21,61)=1; Aeq(21,65)=1; Aeq(21,66)=1; Aeq(21,67)=1; Aeq(21,68)=1; Aeq(21,69)=1; Aeq(21,73)=1; Aeq(21,77)=1;
Aeq(22,50)=1; Aeq(22,53)=1; Aeq(22,54)=1; Aeq(22,55)=1; Aeq(22,56)=1; Aeq(22,58)=1; Aeq(22,62)=1; Aeq(22,66)=1; Aeq(22,69)=1; Aeq(22,70)=1; Aeq(22,71)=1; Aeq(22,72)=1; Aeq(22,74)=1; Aeq(22,78)=1;
Aeq(23,51)=1; Aeq(23,55)=1; Aeq(23,57)=1; Aeq(23,58)=1; Aeq(23,59)=1; Aeq(23,60)=1; Aeq(23,63)=1; Aeq(23,67)=1; Aeq(23,71)=1; Aeq(23,73)=1; Aeq(23,74)=1; Aeq(23,75)=1; Aeq(23,76)=1; Aeq(23,79)=1;
Aeq(24,52)=1; Aeq(24,56)=1; Aeq(24,60)=1; Aeq(24,61)=1; Aeq(24,62)=1; Aeq(24,63)=1; Aeq(24,64)=1; Aeq(24,68)=1; Aeq(24,72)=1; Aeq(24,76)=1; Aeq(24,77)=1; Aeq(24,78)=1; Aeq(24,79)=1; Aeq(24,80)=1;
Aeq(25,81)=1; Aeq(25,82)=1; Aeq(25,83)=1; Aeq(25,84)=1; Aeq(25,85)=1; Aeq(25,89)=1; Aeq(25,93)=1; Aeq(25,97)=1; Aeq(25,98)=1; Aeq(25,99)=1; Aeq(25,100)=1; Aeq(25,101)=1; Aeq(25,105)=1; Aeq(25,109)=1;
Aeq(26,82)=1; Aeq(26,85)=1; Aeq(26,86)=1; Aeq(26,87)=1; Aeq(26,88)=1; Aeq(26,90)=1; Aeq(26,94)=1; Aeq(26,98)=1; Aeq(26,101)=1; Aeq(26,102)=1; Aeq(26,103)=1; Aeq(26,104)=1; Aeq(26,106)=1; Aeq(26,110)=1;
Aeq(27,83)=1; Aeq(27,87)=1; Aeq(27,89)=1; Aeq(27,90)=1; Aeq(27,91)=1; Aeq(27,92)=1; Aeq(27,95)=1; Aeq(27,99)=1; Aeq(27,103)=1; Aeq(27,105)=1; Aeq(27,106)=1; Aeq(27,107)=1; Aeq(27,108)=1; Aeq(27,111)=1;
Aeq(28,84)=1; Aeq(28,88)=1; Aeq(28,92)=1; Aeq(28,93)=1; Aeq(28,94)=1; Aeq(28,95)=1; Aeq(28,96)=1; Aeq(28,100)=1; Aeq(28,104)=1; Aeq(28,108)=1; Aeq(28,109)=1; Aeq(28,110)=1; Aeq(28,111)=1; Aeq(28,112)=1;
% Matrix beq
beq = ones(28,1);
% bound
lb = zeros(112,1);
ub = ones(112,1);
% The integer variables are all.
intcon = [1:112];
% solver
[x,fval] = intlinprog(f,intcon,[],[],Aeq,beq,lb,ub)
Running HiGHS 1.7.0: Copyright (c) 2024 HiGHS under MIT licence terms Coefficient ranges: Matrix [1e+00, 1e+00] Cost [1e+00, 1e+01] Bound [1e+00, 1e+00] RHS [1e+00, 1e+00] Presolving model 28 rows, 112 cols, 392 nonzeros 0s 28 rows, 70 cols, 224 nonzeros 0s 28 rows, 70 cols, 224 nonzeros 0s Objective function is integral with scale 1 Solving MIP model with: 28 rows 70 cols (70 binary, 0 integer, 0 implied int., 0 continuous) 224 nonzeros Nodes | B&B Tree | Objective Bounds | Dynamic Constraints | Work Proc. InQueue | Leaves Expl. | BestBound BestSol Gap | Cuts InLp Confl. | LpIters Time 0 0 0 0.00% 0 inf inf 0 0 0 0 0.0s 0 0 0 0.00% 14 inf inf 0 0 5 32 0.0s Solving report Status Infeasible Primal bound inf Dual bound inf Gap inf Solution status - Timing 0.00 (total) 0.00 (presolve) 0.00 (postsolve) Nodes 1 LP iterations 32 (total) 0 (strong br.) 0 (separation) 0 (heuristics) No feasible solution found. Intlinprog stopped because no integer points satisfy the constraints. x = [] fval = []
% ---------- Correct results ------------ %
% fval = 28;
% x_opt = zeros(112,1);
% x_opt(4) = 1; x_opt(13) = 1; x_opt(24) = 1; x_opt(26) = 1; x_opt(35) = 1;
% x_opt(41) = 1; x_opt(56) = 1; x_opt(61) = 1; x_opt(64) = 1; x_opt(78) = 1;
% x_opt(88) = 1; x_opt(89) = 1; x_opt(103)= 1; x_opt(106)= 1;
  1 Commento
Walter Roberson
Walter Roberson il 24 Apr 2025
Ran in:
Your "correct" solution has the wrong fval output, and does not meet 10 of the inequality bounds
clc
clear
%
f = [2, 5, 3, 4, 5, 8, 0, 1, 3, 0, 8, 9, 4, 1, 9, 10, 2, 5,...
3, 4, 5, 8, 0, 1, 3, 0, 8, 9, 4, 1, 9, 10, 2, 5, 3, 4,...
5, 8, 0, 1, 3, 0, 8, 9, 4, 1, 9, 10, 2, 5, 3, 4, 5, 8,...
0, 1, 3, 0, 8, 9, 4, 1, 9, 10, 2, 5, 3, 4, 5, 8, 0, 1,...
3, 0, 8, 9, 4, 1, 9, 10, 2, 5, 3, 4, 5, 8, 0, 1, 3, 0,...
8, 9, 4, 1, 9, 10, 2, 5, 3, 4, 5, 8, 0, 1, 3, 0, 8, 9,...
4, 1, 9, 10];
% Matrix Aeq
Aeq = zeros(28,112);
Aeq(1,1)=1; Aeq(1,2)=1; Aeq(1,3)=1; Aeq(1,4)=1; Aeq(1,5)=1; Aeq(1,9)=1; Aeq(1,13)=1; Aeq(1,17)=1; Aeq(1,18)=1; Aeq(1,19)=1; Aeq(1,20)=1; Aeq(1,21)=1; Aeq(1,25)=1; Aeq(1,29)=1;
Aeq(2,2)=1; Aeq(2,5)=1; Aeq(2,6)=1; Aeq(2,7)=1; Aeq(2,8)=1; Aeq(2,10)=1; Aeq(2,14)=1; Aeq(2,18)=1; Aeq(2,21)=1; Aeq(2,22)=1; Aeq(2,23)=1; Aeq(2,24)=1; Aeq(2,26)=1; Aeq(2,30)=1;
Aeq(3,3)=1; Aeq(3,7)=1; Aeq(3,9)=1; Aeq(3,10)=1; Aeq(3,11)=1; Aeq(3,12)=1; Aeq(3,15)=1; Aeq(3,19)=1; Aeq(3,23)=1; Aeq(3,25)=1; Aeq(3,26)=1; Aeq(3,27)=1; Aeq(3,28)=1; Aeq(3,31)=1;
Aeq(4,4)=1; Aeq(4,8)=1; Aeq(4,12)=1; Aeq(4,13)=1; Aeq(4,14)=1; Aeq(4,15)=1; Aeq(4,16)=1; Aeq(4,20)=1; Aeq(4,24)=1; Aeq(4,28)=1; Aeq(4,29)=1; Aeq(4,30)=1; Aeq(4,31)=1; Aeq(4,32)=1;
Aeq(5,33)=1; Aeq(5,34)=1; Aeq(5,35)=1; Aeq(5,36)=1; Aeq(5,37)=1; Aeq(5,41)=1; Aeq(5,45)=1; Aeq(5,49)=1; Aeq(5,50)=1; Aeq(5,51)=1; Aeq(5,52)=1; Aeq(5,53)=1; Aeq(5,57)=1; Aeq(5,61)=1;
Aeq(6,34)=1; Aeq(6,37)=1; Aeq(6,38)=1; Aeq(6,39)=1; Aeq(6,40)=1; Aeq(6,42)=1; Aeq(6,46)=1; Aeq(6,50)=1; Aeq(6,53)=1; Aeq(6,54)=1; Aeq(6,55)=1; Aeq(6,56)=1; Aeq(6,58)=1; Aeq(6,62)=1;
Aeq(7,35)=1; Aeq(7,39)=1; Aeq(7,41)=1; Aeq(7,42)=1; Aeq(7,43)=1; Aeq(7,44)=1; Aeq(7,47)=1; Aeq(7,51)=1; Aeq(7,55)=1; Aeq(7,57)=1; Aeq(7,58)=1; Aeq(7,59)=1; Aeq(7,60)=1; Aeq(7,63)=1;
Aeq(8,36)=1; Aeq(8,40)=1; Aeq(8,44)=1; Aeq(8,45)=1; Aeq(8,46)=1; Aeq(8,47)=1; Aeq(8,48)=1; Aeq(8,52)=1; Aeq(8,56)=1; Aeq(8,60)=1; Aeq(8,61)=1; Aeq(8,62)=1; Aeq(8,63)=1; Aeq(8,64)=1;
Aeq(9,65)=1; Aeq(9,66)=1; Aeq(9,67)=1; Aeq(9,68)=1; Aeq(9,69)=1; Aeq(9,73)=1; Aeq(9,77)=1; Aeq(9,81)=1; Aeq(9,82)=1; Aeq(9,83)=1; Aeq(9,84)=1; Aeq(9,85)=1; Aeq(9,89)=1; Aeq(9,93)=1;
Aeq(10,66)=1; Aeq(10,69)=1; Aeq(10,70)=1; Aeq(10,71)=1; Aeq(10,72)=1; Aeq(10,74)=1; Aeq(10,78)=1; Aeq(10,82)=1; Aeq(10,85)=1; Aeq(10,86)=1; Aeq(10,87)=1; Aeq(10,88)=1; Aeq(10,90)=1; Aeq(10,94)=1;
Aeq(11,67)=1; Aeq(11,71)=1; Aeq(11,73)=1; Aeq(11,74)=1; Aeq(11,75)=1; Aeq(11,76)=1; Aeq(11,79)=1; Aeq(11,83)=1; Aeq(11,87)=1; Aeq(11,89)=1; Aeq(11,90)=1; Aeq(11,91)=1; Aeq(11,92)=1; Aeq(11,95)=1;
Aeq(12,68)=1; Aeq(12,72)=1; Aeq(12,76)=1; Aeq(12,77)=1; Aeq(12,78)=1; Aeq(12,79)=1; Aeq(12,80)=1; Aeq(12,84)=1; Aeq(12,88)=1; Aeq(12,92)=1; Aeq(12,93)=1; Aeq(12,94)=1; Aeq(12,95)=1; Aeq(12,96)=1;
Aeq(13,1)=1; Aeq(13,2)=1; Aeq(13,3)=1; Aeq(13,4)=1; Aeq(13,5)=1; Aeq(13,9)=1; Aeq(13,13)=1; Aeq(13,97)=1; Aeq(13,98)=1; Aeq(13,99)=1; Aeq(13,100)=1; Aeq(13,101)=1; Aeq(13,105)=1; Aeq(13,109)=1;
Aeq(14,2)=1; Aeq(14,5)=1; Aeq(14,6)=1; Aeq(14,7)=1; Aeq(14,8)=1; Aeq(14,10)=1; Aeq(14,14)=1; Aeq(14,98)=1; Aeq(14,101)=1; Aeq(14,102)=1; Aeq(14,103)=1; Aeq(14,104)=1; Aeq(14,106)=1; Aeq(14,110)=1;
Aeq(15,3)=1; Aeq(15,7)=1; Aeq(15,9)=1; Aeq(15,10)=1; Aeq(15,11)=1; Aeq(15,12)=1; Aeq(15,15)=1; Aeq(15,99)=1; Aeq(15,103)=1; Aeq(15,105)=1; Aeq(15,106)=1; Aeq(15,107)=1; Aeq(15,108)=1; Aeq(15,111)=1;
Aeq(16,4)=1; Aeq(16,8)=1; Aeq(16,12)=1; Aeq(16,13)=1; Aeq(16,14)=1; Aeq(16,15)=1; Aeq(16,16)=1; Aeq(16,100)=1; Aeq(16,104)=1; Aeq(16,108)=1; Aeq(16,109)=1; Aeq(16,110)=1; Aeq(16,111)=1; Aeq(16,112)=1;
Aeq(17,17)=1; Aeq(17,18)=1; Aeq(17,19)=1; Aeq(17,20)=1; Aeq(17,21)=1; Aeq(17,25)=1; Aeq(17,29)=1; Aeq(17,33)=1; Aeq(17,34)=1; Aeq(17,35)=1; Aeq(17,36)=1; Aeq(17,37)=1; Aeq(17,41)=1; Aeq(17,45)=1;
Aeq(18,18)=1; Aeq(18,21)=1; Aeq(18,22)=1; Aeq(18,23)=1; Aeq(18,24)=1; Aeq(18,26)=1; Aeq(18,30)=1; Aeq(18,34)=1; Aeq(18,37)=1; Aeq(18,38)=1; Aeq(18,39)=1; Aeq(18,40)=1; Aeq(18,42)=1; Aeq(18,46)=1;
Aeq(19,19)=1; Aeq(19,23)=1; Aeq(19,25)=1; Aeq(19,26)=1; Aeq(19,27)=1; Aeq(19,28)=1; Aeq(19,31)=1; Aeq(19,35)=1; Aeq(19,39)=1; Aeq(19,41)=1; Aeq(19,42)=1; Aeq(19,43)=1; Aeq(19,44)=1; Aeq(19,47)=1;
Aeq(20,20)=1; Aeq(20,24)=1; Aeq(20,28)=1; Aeq(20,29)=1; Aeq(20,30)=1; Aeq(20,31)=1; Aeq(20,32)=1; Aeq(20,36)=1; Aeq(20,40)=1; Aeq(20,44)=1; Aeq(20,45)=1; Aeq(20,46)=1; Aeq(20,47)=1; Aeq(20,48)=1;
Aeq(21,49)=1; Aeq(21,50)=1; Aeq(21,51)=1; Aeq(21,52)=1; Aeq(21,53)=1; Aeq(21,57)=1; Aeq(21,61)=1; Aeq(21,65)=1; Aeq(21,66)=1; Aeq(21,67)=1; Aeq(21,68)=1; Aeq(21,69)=1; Aeq(21,73)=1; Aeq(21,77)=1;
Aeq(22,50)=1; Aeq(22,53)=1; Aeq(22,54)=1; Aeq(22,55)=1; Aeq(22,56)=1; Aeq(22,58)=1; Aeq(22,62)=1; Aeq(22,66)=1; Aeq(22,69)=1; Aeq(22,70)=1; Aeq(22,71)=1; Aeq(22,72)=1; Aeq(22,74)=1; Aeq(22,78)=1;
Aeq(23,51)=1; Aeq(23,55)=1; Aeq(23,57)=1; Aeq(23,58)=1; Aeq(23,59)=1; Aeq(23,60)=1; Aeq(23,63)=1; Aeq(23,67)=1; Aeq(23,71)=1; Aeq(23,73)=1; Aeq(23,74)=1; Aeq(23,75)=1; Aeq(23,76)=1; Aeq(23,79)=1;
Aeq(24,52)=1; Aeq(24,56)=1; Aeq(24,60)=1; Aeq(24,61)=1; Aeq(24,62)=1; Aeq(24,63)=1; Aeq(24,64)=1; Aeq(24,68)=1; Aeq(24,72)=1; Aeq(24,76)=1; Aeq(24,77)=1; Aeq(24,78)=1; Aeq(24,79)=1; Aeq(24,80)=1;
Aeq(25,81)=1; Aeq(25,82)=1; Aeq(25,83)=1; Aeq(25,84)=1; Aeq(25,85)=1; Aeq(25,89)=1; Aeq(25,93)=1; Aeq(25,97)=1; Aeq(25,98)=1; Aeq(25,99)=1; Aeq(25,100)=1; Aeq(25,101)=1; Aeq(25,105)=1; Aeq(25,109)=1;
Aeq(26,82)=1; Aeq(26,85)=1; Aeq(26,86)=1; Aeq(26,87)=1; Aeq(26,88)=1; Aeq(26,90)=1; Aeq(26,94)=1; Aeq(26,98)=1; Aeq(26,101)=1; Aeq(26,102)=1; Aeq(26,103)=1; Aeq(26,104)=1; Aeq(26,106)=1; Aeq(26,110)=1;
Aeq(27,83)=1; Aeq(27,87)=1; Aeq(27,89)=1; Aeq(27,90)=1; Aeq(27,91)=1; Aeq(27,92)=1; Aeq(27,95)=1; Aeq(27,99)=1; Aeq(27,103)=1; Aeq(27,105)=1; Aeq(27,106)=1; Aeq(27,107)=1; Aeq(27,108)=1; Aeq(27,111)=1;
Aeq(28,84)=1; Aeq(28,88)=1; Aeq(28,92)=1; Aeq(28,93)=1; Aeq(28,94)=1; Aeq(28,95)=1; Aeq(28,96)=1; Aeq(28,100)=1; Aeq(28,104)=1; Aeq(28,108)=1; Aeq(28,109)=1; Aeq(28,110)=1; Aeq(28,111)=1; Aeq(28,112)=1;
% Matrix beq
beq = ones(28,1);
% bound
lb = zeros(112,1);
ub = ones(112,1);
% The integer variables are all.
intcon = [1:112];
% solver
[x,fval] = intlinprog(f,intcon,[],[],Aeq,beq,lb,ub)
Running HiGHS 1.7.0: Copyright (c) 2024 HiGHS under MIT licence terms Coefficient ranges: Matrix [1e+00, 1e+00] Cost [1e+00, 1e+01] Bound [1e+00, 1e+00] RHS [1e+00, 1e+00] Presolving model 28 rows, 112 cols, 392 nonzeros 0s 28 rows, 70 cols, 224 nonzeros 0s 28 rows, 70 cols, 224 nonzeros 0s Objective function is integral with scale 1 Solving MIP model with: 28 rows 70 cols (70 binary, 0 integer, 0 implied int., 0 continuous) 224 nonzeros Nodes | B&B Tree | Objective Bounds | Dynamic Constraints | Work Proc. InQueue | Leaves Expl. | BestBound BestSol Gap | Cuts InLp Confl. | LpIters Time 0 0 0 0.00% 0 inf inf 0 0 0 0 0.0s 0 0 0 0.00% 14 inf inf 0 0 5 32 0.0s Solving report Status Infeasible Primal bound inf Dual bound inf Gap inf Solution status - Timing 0.01 (total) 0.00 (presolve) 0.00 (postsolve) Nodes 1 LP iterations 32 (total) 0 (strong br.) 0 (separation) 0 (heuristics) No feasible solution found. Intlinprog stopped because no integer points satisfy the constraints. x = [] fval = []
% ---------- Correct results ------------ %
% fval = 28;
x_opt = zeros(112,1);
x_opt(4) = 1; x_opt(13) = 1; x_opt(24) = 1; x_opt(26) = 1; x_opt(35) = 1;
x_opt(41) = 1; x_opt(56) = 1; x_opt(61) = 1; x_opt(64) = 1; x_opt(78) = 1;
x_opt(88) = 1; x_opt(89) = 1; x_opt(103)= 1; x_opt(106)= 1;
f * x_opt
ans = 35
all(mod(x_opt(intcon),1)==0)
ans = logical
1
ineq = Aeq*x_opt;
bad = find(ineq ~= beq)
bad = 20×1
1 2 4 5 7 8 10 12 13 14
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<mw-icon class=""></mw-icon>
[ineq(bad), beq(bad)]
ans = 20×2
2 1 2 1 3 1 3 1 2 1 3 1 2 1 2 1 2 1 2 1
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<mw-icon class=""></mw-icon>
all(x_opt >= lb)
ans = logical
1
all(x_opt <= ub)
ans = logical
1

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