A Pareto communicating artificial bee colony algorithm for solving bi-objective quadratic assignment problems

Minimization of the interdepartmental flow within a given facility is often treated as a quadratic assignment problem (QAP). It is an NP-hard, combinatorial optimization problem. Multi-objective quadratic assignment problem (mQAP) is considered when there exists more than one type of flow within the same facility. Metaheuristic algorithms are commonly utilized to estimate the Pareto optimal sets of these problems. The significant challenge in developing and applying an appropriate metaheuristic algorithm for solving multi-objective optimization problems within considerably less time is the selection of an apposite neighbourhood search approach along with proper settings of the algorithm-specific parameters. This paper narrates development of a Pareto communicating multi-objective artificial bee colony (pMOABC) algorithm for efficiently solving the mQAPs. Its optimization performance is thereafter compared with that of seven other state-of-the-art multi-objective optimization algorithms to prove its efficacy in solving bi-objective quadratic assignment problems (bi-QAPs). The values of different tuning parameters of pMOABC are later estimated based on sensitivity analysis studies. The comparative results based on statistical analysis show that the performance of pMOABC is robust over various runs and it can better estimate the Pareto optimal sets for various benchmarked bi-QAPs compared to other considered state-of-the-art algorithms with at least 99.998% confidence level. The robustness of various algorithms is also accessed while contrasting average quality of the Pareto fronts developed in each run. pMOABC outperforms all other algorithms in this statistical comparison with a minimum of 98.91% confidence level.