QROSS: QUBO Relaxation Parameter optimisation via Learning Solver Surrogates

Tian Huang, Siong Thye Goh, Sabrish Gopalakrishnan, Tao Luo, Qianxiao Li, Hoong Chuin Lau

Abstract: A popular method for solving a constrained combinatorial optimisation problem is to first convert it into a quadratic unconstrained binary optimisation (QUBO) problem, and solve it using a standard QUBO solver. However, this relaxation introduces hyper-parameters that balance the objective and penalty terms for the constraints, and their chosen values significantly impact performance. Hence, hyper-parameters tuning is important. Existing generic hyper-parameter tuning methods require multiple expensive calls to a QUBO solver, making them inefficient for performance critical applications when repeated solutions of similar combinatorial optimisation problems are required. In this paper, we propose the QROSS method, in which we build surrogate models of QUBO solvers via learning from solver data on a collection of instances of a problem. In this way, we are able capture the common structure of the instances and their interactions with the solver, and produce promising hyper-parameters with fewer calls to the QUBO solver. We take the Traveling Salesman Problem (TSP) as a case study, where we demonstrate QROSS finds better solutions with fewer calls to QUBO solver, compared with conventional hyper-parameter tuning techniques. Moreover, with simple adaptation methods, QROSS is shown to generalise well to out-of-distribution datasets and different types of QUBO solvers.