A Variable Neighbourhood Search Enhanced Estimation of Distribution Algorithm for Quadratic Assignment Problems

Quadratic Assignment Problem (QAP) is one of the most complex combinatorial optimization problems. Many real-world problems such as printed circuit board design, facility location problems, assigning gates to airplanes can be modelled as QAP. Problems of size greater than 35 is not able to solve optimally using conventional optimization methods. This warrants the use of evolutionary optimization methods for obtaining optimal or near optimal solutions for QAPs. This work proposes a hybridization on a univariate Estimation of Distribution Algorithm, namely the Population Based Incremental Learning Algorithm (PBILA), with Variable Neighbourhood Search (VNS) for solving QAPs. The proposed algorithm is employed to solve benchmark instances of QAP and the results are reported. The results of this work reveals that PBILA on its own is not efficient for solving the QAPs. However, when hybridised with VNS, the algorithm performs well providing best known solutions for 95 test instances out of the 101 instances considered. For most of the test instances, the percentage deviation is less than one percentage. The overall average percentage deviation of the obtained solutions from the best-known solutions is 0.037%, which is a significant improvement when compared with state-of-the-art algorithms.