DOI: 10.18738/t8/uvwxt6
title: Instances for general quadratic integer programming problem with and without linear (resource) constraints

description: There are two sets of instances: 1) general quadratic integer programming problem with linear (resource) constraints; 2) general quadratic integer programming problem without linear constraints;
&lt;BR&gt;
For general quadratic integer programming problem with linear resource constraints, 
&lt;BR&gt;
Max f(x) =dx + xqx
&lt;BR&gt;
s.t. ax &lt;= b; (resource constraints: such as people, equipment, material, and budget)
&lt;BR&gt;
 0&lt;=x &lt;=u; (lower and upper bounds of decision variables)
&lt;BR&gt;
the name of instance is nxxxmyyytt-zzz-in.txt:&lt;BR&gt;

 xxx is the size of decision variables;&lt;BR&gt;

 yyy is the number of linear resource constraints where yyy=0.2*xxx or 0.5*xxx;&lt;BR&gt;

tt='e' is the type of instance with large slack value of 'b' &lt;br&gt;
tt='d' is the type of instance with medium slack value of 'b' &lt;br&gt;
tt='h' is the type of instance with small slack value of 'b' &lt;br&gt;

zzz is the type of instances, zzz =1, 2, 3, 4, and 5&lt;BR&gt;

For zzz=1, the range of value for d and q elements is -20 to 20, the upper bound of decision variable is 10, the range of value for a is 0 to 9&lt;BR&gt;

For zzz=2, the range of value for d and q elements is -40 to 40, the upper bound of decision variable is 20, the range of value for a is 0 to 19&lt;BR&gt;

For zzz=3, the range of value for d and q elements is -80 to 80, the upper bound of decision variable is 40, the range of value for a is 0 to 39&lt;BR&gt;

For zzz=4, the range of value for d and q elements is -160 to 160, the upper bound of decision variable is 80, the range of value for a is 0 to 79&lt;BR&gt;

For zzz=5, the range of value for d and q elements is -200 to 200, the upper bound of decision variable is 100, the range of value for a is 0 to 99&lt;BR&gt;

for each instance, the input file format is:&lt;BR&gt;
name of instance&lt;BR&gt;
number of variables n, number of knapsack constraints m&lt;BR&gt;
the linear coefficients of the objective function, d&lt;BR&gt;
blank line&lt;BR&gt;
the quadratic coefficients of the objective function, q,&lt;BR&gt;
blank line&lt;BR&gt;
the right hand size of source constraints, b &lt;BR&gt;
the coefficients of source constraints, a&lt;BR&gt;
blank line&lt;BR&gt;
the upper bound of decision variable, u&lt;BR&gt;
&lt;BR&gt;
&lt;BR&gt;
For general quadratic integer programming problem without linear resource constraints:&lt;BR&gt;
Max f(x) =dx + xqx&lt;BR&gt;
s.t. 0&lt;=x &lt;=u; &lt;BR&gt;

the name of instance is nxxx-zzz-in.txt:&lt;BR&gt;
 xxx is the size of decision variables;&lt;BR&gt;
zzz is the type of instances, zzz =1, 2, 3, 4, and 5&lt;BR&gt;
For zzz=1, the range of value for d and q elements is -20 to 20, the upper bound of decision variable is 10;&lt;BR&gt;
For zzz=2, the range of value for d and q elements is -40 to 40, the upper bound of decision variable is 20;&lt;BR&gt;
For zzz=3, the range of value for d and q elements is -80 to 80, the upper bound of decision variable is 40;&lt;BR&gt;
For zzz=4, the range of value for d and q elements is -160 to 160, the upper bound of decision variable is 80;&lt;BR&gt;
For zzz=5, the range of value for d and q elements is -200 to 200, the upper bound of decision variable is 100; &lt;BR&gt;

for each instance, the input file format using is:&lt;BR&gt;
name of instance&lt;BR&gt;
number of variables n&lt;BR&gt;
the linear coefficients of the objective function, d&lt;BR&gt;
blank line&lt;BR&gt;
the quadratic coefficients of the objective function, q&lt;BR&gt;
blank line&lt;BR&gt;
the upper bound of decision variable, u&lt;BR&gt;