# fixanddive.m

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### fixanddive.m

function fixanddive(filename)
%
% Copyright 2020, Gurobi Optimization, LLC
%
% Implement a simple MIP heuristic.  Relax the model,
% sort variables based on fractionality, and fix the 25% of
% the fractional variables that are closest to integer variables.
% Repeat until either the relaxation is integer feasible or
% linearly infeasible.

cols = size(model.A, 2);
ivars = find(model.vtype ~= 'C');

if length(ivars) <= 0
fprintf('All variables of the model are continuous, nothing to do\n');
return;
end

% save vtype and set all variables to continuous
vtype = model.vtype;
model.vtype = repmat('C', cols, 1);

params.OutputFlag = 0;

result = gurobi(model, params);

% Perform multiple iterations. In each iteration, identify the first
% quartile of integer variables that are closest to an integer value
% in the relaxation, fix them to the nearest integer, and repeat.

frac = zeros(cols, 1);
for iter = 1:1000
% See if status is optimal
if ~strcmp(result.status, 'OPTIMAL')
fprintf('Model status is %s\n', result.status);
fprintf('Can not keep fixing variables\n');
break;
end
% collect fractionality of integer variables
fracs = 0;
for j = 1:cols
if vtype(j) == 'C'
frac(j) = 1; % indicating not integer variable
else
t = result.x(j);
t = t - floor(t);
if t > 0.5
t = t - 0.5;
end
if t > 1e-5
frac(j) = t;
fracs = fracs + 1;
else
frac(j) = 1; % indicating not fractional
end
end
end

fprintf('Iteration %d, obj %g, fractional %d\n', iter, result.objval, fracs);

if fracs == 0
fprintf('Found feasible solution - objective %g\n', result.objval);
break;
end

% sort variables based on fractionality
[~, I] = sort(frac);

% fix the first quartile to the nearest integer value
nfix = max(fracs/4, 1);
for i = 1:nfix
j = I(i);
t = floor(result.x(j) + 0.5);
model.lb(j) = t;
model.ub(j) = t;
end

% use warm start basis and reoptimize
model.vbasis = result.vbasis;
model.cbasis = result.cbasis;
result = gurobi(model, params);
end