A new tool for automated transformation of Quadratic Assignment Problem instances to Quadratic Unconstrained Binary Optimisation models

Abstract

Growing class of optimisation problems are reported to attract increasing interest even though they are very challenging and difficult to solve exactly. Quadratic Assignment Problem (QAP), Travelling salesman, weapon target assignment, and query optimisation in distributed databases are some of these well known problems. QAP is considered to be one of the most prominent combinatorial optimisation problems with various application areas. Economic aspects of design and location of factories, hospitals, industrial plants, network models, transportation infrastructures, and military bases can all be addressed by QAP. There is no known polynomial time algorithm reported for the solution of the problem since it is NP-hard. Even small problem instances take long times to be solved exhaustively. Exact solution techniques and parallelisation of these algorithms end up with only little or negligible increase in performance. Recent meta-heuristics based on genetic algorithms, simulated annealing, and tabu search provide promising results even for problem instances up to instance sizes of 256 which is currently the largest instance in the QAPLIB. The Quadratic Unconstrained Binary Optimisation (QUBO) model has a critical role for experiments conducted with quantum computers of D-Wave Systems and IBM. Quantum Annealing is a technique which exploits quantum fluctuations to reach the global minimum of a given cost function. The QUBO model and its connection with Ising problem constitute the foundations for quantum annealing. Advances in quantum computing highlight the fact that QUBO models can be an efficient alternative to traditional models. Even though QAP can be formulated by QUBO using penalty functions, there is no known automated transformation method to map a QAP instance to a QUBO model. In this paper, we propose an automated model for QAP to QUBO mappings which can generate these formulations using the pre-defined penalty functions. We also present the benchmark results for a group of QAPLIB instances using exact solver for our QUBO models.