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milp_shannoncost.m
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milp_shannoncost.m
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function [x,exitflag] = milp_shannoncost(J, K, X, cond_prob, prob_act)
%MILP_GENERALCOST Summary of this function goes here
%Rational inattention test
M = 1000;
%A and b are reserved for Ax <= b
A = sparse(J*(4*K*K-J-K)+1, X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2 + 2);
rowcnt = 1;
%Aeq and beq reserved for Aeqx = beq
Aeq = sparse(2*J*(K-1)+X*J*K, X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2 + 2);
rowcnteq = 1;
%Binary indicies
intcon = [(1+2*J*(K-1)+X*J*K):(2*(J^2)*(K-1)+2*J*(K-1)+X*J*K)];
%Constraint 1
for j = 1:J
for l=1:J
for k=1:K
if(j ~= l)
s_jindx = 1+(j-1)*X+(k-1)*X*J;
e_jindx = X+(j-1)*X+(k-1)*X*J;
s_lindx = 1+(l-1)*X+(k-1)*X*J;
e_lindx = X+(l-1)*X+(k-1)*X*J;
A(rowcnt, s_jindx:e_jindx) = -cond_prob(s_jindx:e_jindx);
A(rowcnt, s_lindx:e_lindx) = cond_prob(s_jindx:e_jindx);
b(rowcnt) = -1e-3; %small negative to force strict inequality for atleast one
rowcnt = rowcnt+1;
end
end
end
end
%Constraint 2
for j=1:J
for l=1:J
for k=1:(K-1)
A(rowcnt, (j+(k-1)*J+X*J*K)) = -1;
A(rowcnt, (1+(l-1)*X+(k-1)*X*J):(X+(l-1)*X+(k-1)*X*J)) = cond_prob((1+(j-1)*X+(k-1)*X*J):(X+(j-1)*X+(k-1)*X*J));
b(rowcnt) = 0;
rowcnt = rowcnt+1;
end
end
end
%Constraint 3
for j=1:J
for l=1:J
for k=1:(K-1)
A(rowcnt, (1+(l-1)*X+(k-1)*X*J):(X+(l-1)*X+(k-1)*X*J)) = -cond_prob((1+(j-1)*X+(k-1)*X*J):(X+(j-1)*X+(k-1)*X*J));
A(rowcnt, l+(j-1)*J+(k-1)*(J^2)+2*J*(K-1)+X*J*K) = M;
A(rowcnt, j+(k-1)*J+X*J*K) = 1;
b(rowcnt) = M;
rowcnt = rowcnt+1;
end
end
end
%Constraint 4 (equality)
for j=1:J
for k=1:(K-1)
Aeq(rowcnteq, (1+(j-1)*J+(k-1)*(J^2)+2*J(K-1)+X*J*K):(J+(j-1)*J+(k-1)*(J^2)+2*J(K-1)+X*J*K)) = 1;
beq(rowcnteq) = 1;
rowcnteq = rowcnteq + 1;
end
end
%Constraint 5
for j=1:J
for l=1:J
for k=1:(K-1)
if(k <= (K-2))
A(rowcnt, (j+k*J+X*J*K+J*(K-1))) = -1;
A(rowcnt, (1+(l-1)*X+(k-1)*X*J):(X+(l-1)*X+(k-1)*X*J)) = cond_prob((1+(j-1)*X+k*X*J):(X+(j-1)*X+k*X*J));
else
A(rowcnt, (j+X*J*K+J*(K-1))) = -1;
A(rowcnt, (1+(l-1)*X+(k-1)*X*J):(X+(l-1)*X+(k-1)*X*J)) = cond_prob((1+(j-1)*X):(X+(j-1)*X));
end
b(rowcnt) = 0;
rowcnt = rowcnt+1;
end
end
end
%Constraint 6
for j=1:J
for l=1:J
for k=1:(K-1)
if(k <= (K-2))
sl_indx = 1+(l-1)*X+(k-1)*X*J;
el_indx = X+(l-1)*X+(k-1)*X*J;
sj_indx = 1+(j-1)*X+k*X*J;
ej_indx = X+(j-1)*X+k*X*J;
zeta_indx = l+(j-1)*J+k*(J^2)+(K-1)*(J^2)+2*J*(K-1)+X*J*K;
A(rowcnt, j+k*J+X*J*K+J*(K-1)) = 1;
A(rowcnt, sl_indx:el_indx) = -cond_prob(sj_indx:ej_indx);
A(rowcnt, zeta_indx) = M;
else
sl_indx = 1+(l-1)*X+(k-1)*X*J;
el_indx = X+(l-1)*X+(k-1)*X*J;
sj_indx = 1+(j-1)*X;
ej_indx = X+(j-1)*X;
zeta_indx = l+(j-1)*J+(K-1)*(J^2)+2*J*(K-1)+X*J*K;
A(rowcnt, j+X*J*K+J*(K-1)) = 1;
A(rowcnt, sl_indx:el_indx) = -cond_prob(sj_indx:ej_indx);
A(rowcnt, zeta_indx) = M;
end
b(rowcnt) = M;
rowcnt = rowcnt+1;
end
end
end
%Constraint 7 (equality)
for j=1:J
for k=1:(K-1)
if(k <= (K-2))
sl_indx = (1+(j-1)*J+k*(J^2)+(J^2)*(K-1)+2*J*(K-1)+X*J*K);
el_indx = (J+(j-1)*J+k*(J^2)+(J^2)*(K-1)+2*J*(K-1)+X*J*K);
Aeq(rowcnteq, sl_indx:el_indx) = 1;
else
sl_indx = (1+(j-1)*J+(J^2)*(K-1)+2*J*(K-1)+X*J*K);
el_indx = (J+(j-1)*J+(J^2)*(K-1)+2*J*(K-1)+X*J*K);
Aeq(rowcnteq, sl_indx:el_indx) = 1;
end
beq(rowcnteq) = 1;
rowcnteq = rowcnteq+1;
end
end
%Constraint 8
for k=1:(K-1)
if(k <= (K-2))
A(rowcnt, (1+(k-1)*J+X*J*K):(J+(k-1)*J+X*J*K)) = -prob_act((1+(k-1)*J):(J+(k-1)*J));
A(rowcnt, (1+k*J+X*J*K+J*(K-1)):(J+k*J+X*J*K+J*(K-1))) = -prob_act((1+k*J):(J+k*J));
else
A(rowcnt, (1+(k-1)*J+X*J*K):(J+(k-1)*J+X*J*K)) = -prob_act((1+(k-1)*J):(J+(k-1)*J));
A(rowcnt, (1+X*J*K+J*(K-1)):(J+X*J*K+J*(K-1))) = -prob_act(1:J);
end
b(rowcnt) = 0;
end
%Constraint 9 (equality)
for i=1:X
for j=1:J
for k=1:K
Aeq(rowcnteq, i+(j-1)*X+(k-1)*X*J) = 1;
Aeq(rowcnteq, (k-1)*2+2+2*J*(K-1)+2*(J^2)*(K-1)+X*J*K) = 1;
if cond_prob(i+(j-1)*X+(k-1)*X*J) ~= 0
Aeq(rowcnteq, (k-1)*2+1+2*J*(K-1)+2*(J^2)*(K-1)+X*J*K) = -log(cond_prob(i+(j-1)*X+(k-1)*X*J));
else
Aeq(rowcnteq, (k-1)*2+1+2*J*(K-1)+2*(J^2)*(K-1)+X*J*K) = 0;
end
beq(rowcnteq) = 0;
rowcnteq = rowcnteq+1;
end
end
end
%%
%Solve MILP to construct utility function
lb = zeros(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2 + 2,1);
lb(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2) = -Inf;
lb(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2 + 2) = -Inf;
%lb(1:(X*J*K)) = 1e-3;
ub = ones(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2+2,1);
ub(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+1:X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2 + 2) = [Inf Inf Inf Inf];
%ub(1:(X*J*K)) = 100;
f = zeros(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2+2,1); % no objective function
%options = optimoptions('intlinprog','Display','iter', 'IntegerTolerance', 1e-6);
[x,~,exitflag] = intlinprog(f,intcon,A,b,Aeq,beq,lb,ub);
end