This paper describes a general method developed by 1QBit for solving continuous optimization problems inspired by diﬀerent types of simulated annealing and genetic algorithms. This method works under the assumption of the existence of a computation model with a Turing reduction of problems to either quadratic unconstrained binary optimization (QUBO) problems or to an Ising spin problem. The paper presents an application of this method to a mixed-integer optimization problem. This will demonstrate an interesting method of representing a cardinality-constrained optimization problem using analytic expressions, and the ability of the method to solve such mixed-integer optimization problems.

This research proposes a new approach for tackling cognitive radio asset allocation optimization problems. The cognitive radio optimization problem is generally an NP-hard mixed-integer programming problem due to its various constraints. In contrast to conventional methods of using meta-heuristics and evolutionary algorithms, we implement non-linear constraints as polynomial penalty functions of binary variables and build a new objective function in a quadratic unconstrained binary optimization (QUBO) format. By calling a quadratic solver only once, we can get the exact optimal asset allocation in a cognitive radio scenario, whereas conventional methods provide a sub-optimal answer.

In what follows, we explain how the Integer Optimization Toolbox approaches the problem of minimization of a (low-degree) polynomial over an integer lattice. In theory, the method illustrated here can be used for arbitrarily large polynomials with a large enough quantum annealing oracle.