Abstract
In this work we show how to use a quantum adiabatic algorithm to solve multiobjective optimization problems. For the first time, we demonstrate a theorem proving that the quantum adiabatic algorithm can find Pareto-optimal solutions in finite-time, provided some restrictions to the problem are met. A numerical example illustrates an application of the theorem to a well-known problem in multiobjective optimization. This result opens the door to solve multiobjective optimization problems using current technology based on quantum annealing.
Highlights
Quantum computation has many practical applications in engineering and computer science like machine learning, bioinformatics and artificial intelligence [1]
We show how to use a quantum adiabatic algorithm in multiobjective combinatorial optimization problems or MCO
In Theorem 2 we identify two structural features that a given MCO must satisfy in order to make an effective use of the quantum adiabatic algorithm presented in this work
Summary
Quantum computation has many practical applications in engineering and computer science like machine learning, bioinformatics and artificial intelligence [1]. In [8], a general algorithm for MCO was presented and experimentally compared against a state-of-the-art metaheuristic Both papers [7,8] use Grover’s search algorithm to solve an MCO; Grover’s algorithm is not naturally constructed for optimization problems. Having Grover’s algorithm as the main subrutine for optimization gives place to an “ad hoc” heuristic method whose finite time convergence has not yet been proved. These previous works [7,8] relied on numerical experiments instead of rigorous proofs.
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