A generator of test quadratic assignment problems with known optimal solution
USSR Computational Mathematics and Mathematical Physics
On the complexity of test case generation for NP-hard problems
Information Processing Letters
A genetic approach to the quadratic assignment problem
Computers and Operations Research - Special issue on genetic algorithms
A new exact algorithm for the solution of quadratic assignment problems
Discrete Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
Solving Large Quadratic Assignment Problems in Parallel
Computational Optimization and Applications
ACM Transactions on Mathematical Software (TOMS)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
QAPLIB – A Quadratic Assignment ProblemLibrary
Journal of Global Optimization
Hi-index | 0.00 |
In this paper we consider the rectilinear version of the quadratic assignment problem (QAP). We define a class of edge-weighted graphs with nonnegatively valued bisections. For one important type of such graphs we provide a characterization of point sets on the plane for which the optimal value of the related QAP is zero. These graphs are used in the algorithms for generating rectilinear QAP instances with known provably optimal solutions. The basic algorithm of such type uses only triangles. Making a reduction from 3-dimensional matching, it is shown that the set of instances which can be generated by this algorithm is hard. The basic algorithm is extended to process graphs larger than triangles. We give implementation details of this extension and of four other variations of the basic algorithm. We compare these five and also two existing generators experimentally employing multi-start descent heuristic for the QAP as an examiner. The graphs with nonnegatively valued bisections can also be used in the construction of lower bounds on the optimal value for the rectilinear QAP.