Multi-objective quadratic assignment problem instances generator with a known optimum solution

Abstract

Multi-objective quadratic assignment problems (mQAPs) are NP-hard problems that optimally allocate facilities to locations using a distance matrix and several flow matrices. mQAPs are often used to compare the performance of the multi-objective meta-heuristics. We generate large mQAP instances by combining small size mQAP with known local optimum. We call these instances composite mQAPs, and we show that the cost function of these mQAPs is additively decomposable. We give mild conditions for which a composite mQAP instance has known optimum solution.We generate composite mQAP instances using a set of uniform distributions that obey these conditions. Using numerical experiments we show that composite mQAPs are difficult for multi-objective meta-heuristics.