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milp_reynicost_niacs_dev_true.m
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milp_reynicost_niacs_dev_true.m
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function [x,exitflag,val_dev] = milp_reynicost_niacs_dev_true(J, K, X, cond_prob, prob_act)
%MILP_GENERALCOST Summary of this function goes here
% %Normalize the joint_prob
% for k=1:K
% joint_prob((1:X*J)+(k-1)*X*J) = joint_prob((1:X*J)+(k-1)*X*J)/sum(joint_prob((1:X*J)+(k-1)*X*J));
% end
% for i=1:X
% for k=1:K
% state_prob(i+(k-1)*K) = sum(joint_prob((i+(k-1)*X*J):(i+J+(k-1)*X*J)));
% end
% end
%Rational inattention test
M = 10000;
%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 + 1); % deviation term (+1)
rowcnt = 1;
%Aeq and beq reserved for Aeqx = beq
Aeq = sparse(J*K, X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2+2 + 1); %deviation term (+1)
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 NIAS
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);
A(rowcnt,X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2+2 + 1) = 1;
b(rowcnt) = -1e-3; %small negative to force strict inequality for atleast one
rowcnt = rowcnt+1;
end
end
end
end
%Constraint 2 m_k >=
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 M (1) (mk)
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) sum = 1
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 M (2) n_k
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) sum = 1
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 NIAC
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
A(rowcnt,X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2+2 + 1) = -1;
b(rowcnt) = 0;
end
% dumm1=0;
% dumm2=0;
% %Constraint 9 (equality) KKT
% for i=1:X
% for j=1:J
% for k=1:K
% coeff = 0;
% for si=1:X
% for sj=1:J
% %coeff = coeff+joint_prob(si+(sj-1)*X+(k-1)*X*J)*((cond_prob(si+(sj-1)*X+(k-1)*X*J)/state_prob(si+(k-1)*K))^(beta-1));
% coeff = coeff+(joint_prob(si+(sj-1)*X+(k-1)*X*J)^(beta))/[(state_prob(si+(k-1)*K)^(beta-1))*(prob_act((k-1)*J + sj)^(beta-1))];
% end
% end
% %rectify KKT for renyi case
% %coeff = coeff*((cond_prob(i+(j-1)*X+(k-1)*X*J)/state_prob(i+(k-1)*K)^(beta-1)))/(beta-1);
% %coeff=coeff*(beta-1)*(prob_act( j+(k-1)*J ))^(2*(beta-1));
% if joint_prob(1 +(j-1)*X+(k-1)*X*J) == 0
% joint_prob(1 +(j-1)*X+(k-1)*X*J) = 0.000001;
% end
% if joint_prob(2 +(j-1)*X+(k-1)*X*J) == 0
% joint_prob(2 +(j-1)*X+(k-1)*X*J) = 0.000001;
% end
% if prob_act(j+(k-1)*J) == 0
% prob_act(j+(k-1)*J) = 0.000001;
% end
% dumm1= [(beta)*(prob_act(j+(k-1)*J)^(beta-1))*(joint_prob(i+(j-1)*X+(k-1)*X*J)^(beta-1)) - (beta-1)*(prob_act(j+(k-1)*J)^(beta-2))*(joint_prob(i+(j-1)*X+(k-1)*X*J)^(beta))]/(state_prob(i+(k-1)*X)^(beta-1));
% dumm2= [(beta-1)*(prob_act(j+(k-1)*J)^(beta-2))* (joint_prob(mod(i,2)+1 +(j-1)*X+(k-1)*X*J)^(beta))]/(state_prob(mod(i,2)+1 +(k-1)*X)^(beta-1)); % can use the mod trick just because we have two states 1 and 2
%
% if ~isnan(coeff)
% coeff=(dumm1 - dumm2)/[coeff*(beta-1)*(prob_act( j+(k-1)*J ))^(2*(beta-1))];
% else
% if dumm1>=dumm2
% coeff=Inf;
% else
% coeff= -Inf;
% end
% end
% %coeff
% Aeq(rowcnteq, i+(j-1)*X+(k-1)*X*J) = 1;
% %if ~(isnan(coeff))
% Aeq(rowcnteq, (2*(k-1))+1+2*J*(K-1)+2*(J^2)*(K-1)+X*J*K) = -coeff;
% %else
% % Aeq(rowcnteq, 1+2*J*(K-1)+2*(J^2)*(K-1)+X*J*K) = (-1)*M;
% %end
% %if cond_prob(i+(j-1)*X+(k-1)*X*J) ~= 0
% % Aeq(rowcnteq, 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, 1+2*J*(K-1)+2*(J^2)*(K-1)+X*J*K) = 0;
% %end
% Aeq(rowcnteq, (2*(k-1))+2+2*J*(K-1)+2*(J^2)*(K-1)+X*J*K) = 1;
% 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+1,1);
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(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2+2 + 1) = Inf;
%ub(1:(X*J*K)) = 100;
f = zeros(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2+2+1,1); % no objective function
f(X*J*K+2*J(K-1)+2*(J^2)*(K-1)+2+2+1)=-1;
%options = optimoptions('intlinprog','Display','iter', 'IntegerTolerance', 1e-6);
[x,~,exitflag] = intlinprog(f,intcon,A,b,Aeq,beq,lb,ub);
val_dev=0;
if exitflag ~= 0
val_dev=flip(x);
val_dev=val_dev(1);
else
val_dev=Inf;
end
%Aeq
end