Improving Quantum Multi-Objective Optimization with Archiving and Substitution

arXiv (Cornell University)

Abstract

Finding optimal solutions of conflicting objectives is a daily matter in many industrial applications, with multi-objective optimization trying to find the best solutions to them. The advent of quantum computing has led to researchers wondering if the promised exponential advantage can be obtained for these problems by variational quantum multi-objective optimization (QMOO) algorithm. Here, we improve it by introducing a Pareto Archive and dominated solutions substitution, clearly improving in hyper-volume convergence at additional quantum and classical cost. We propose the use of RMNK-landscapes as a unifying testbed for benchmarking QMOO, as it is common in classical multi-objective field. By devising a generic classical-to-quantum mapping of these landscapes, we perform a numerical hyperparameter tuning of QMOO, significantly enhancing its performance. Finally, we compare QMOO against well-known classical solvers for multi-objective tasks, NSGA-II/III, showing comparable results in small instances. Our results demonstrate that QMOO, when carefully tuned for the task at hand, might be advantageous on harder problems than its classical counterparts.

Authors 6

1. Linus Ekstrøm Aachen

   Leiden University

   Affiliation as printed

   Honda Research Institute Europe GmbH , Carl-Legien-Strasse 30 , 63073 Offenbach am Main , Germany

   LIACS , Universiteit Leiden , Niels Bohrweg 1 , 2333 CA Leiden , Netherlands

2. Takafumi Hosogi

   Institute of Science Tokyo

   Affiliation as printed

   Honda Research Institute Europe GmbH , Carl-Legien-Strasse 30 , 63073 Offenbach am Main , Germany

   Institute of Science Tokyo , 2-12-1 Ookayama , Meguro , Tokyo , 152-8530 , Japan

3. Xavier Bonet-Monroig
   Affiliation as printed

   Honda Research Institute Europe GmbH , Carl-Legien-Strasse 30 , 63073 Offenbach am Main , Germany

4. Hao Wang Aachen $⟨aQa^L⟩$ Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

   LIACS , Universiteit Leiden , Niels Bohrweg 1 , 2333 CA Leiden , Netherlands

   ⟨aQa L ⟩ Applied Quantum Algorithms , Universiteit Leiden

5. Thomas Bäck Aachen

   Leiden University

   Affiliation as printed

   LIACS , Universiteit Leiden , Niels Bohrweg 1 , 2333 CA Leiden , Netherlands

6. Sebastian Schmitt
   Affiliation as printed

   Honda Research Institute Europe GmbH , Carl-Legien-Strasse 30 , 63073 Offenbach am Main , Germany