Many problems arising from diverse areas can be formulated as integer programming problems. One can argue that Combinatorial Optimization and Integer programming are synonymous terms. This is because the majority (if not all) of the combinatorial optimization problems are integer programming problems, usually involving binary variables.
During the second DIMACS Implementation Challenge a set of instances were chosen to provide the satisfiability benchmarks. These problems can be found at http://dimacs.rutgers.edu/Challenges/index.html.
A large collection of Traveling Salesman test problems is available at http://www.iwr.uniheidelberg.de/iwr/comopt/soft/TSPLIB95/TSPLIB.html.
A QAP test problem generator with a known optimal solution is available. The Fortran code of this generator can be obtained by sending an email message to coap@math.ufl.edu and in the body of the message put ``send 92006''.
There is a large collection, QAPLIB, of electronically available data instances for the Quadratic Assignment Problem. The data (and the updated best known solution) are available at http://www.diku.dk/users/karisch/qaplib/inst.html.
During the second DIMACS Implementation Challenge a set of 32 graph instances were chosen to provide benchmarks for the Graph Coloring Problem. These problems can be found at http://dimacs.rutgers.edu/Challenges/index.html.





Quadratic Integer Problem 



Quadratic Integer Problem 



Quadratic Assignment Problem 



Quadratic Assignment Problem 



Quadratic Assignment Problem 



Steiner Problems in Graphs 



Steiner Problems in Graphs 



Steiner Problems in Graphs 



Steiner Problems in Graphs 



Steiner Problems in Graphs 

