Improving Quantum Multi-Objective Optimization with Archiving and Substitution

TL;DR

This paper enhances quantum multi-objective optimization by introducing archiving and substitution techniques, benchmarking with RMNK-landscapes, and tuning parameters to improve performance on complex problems.

Contribution

It proposes a Pareto Archive and dominated solutions substitution to improve QMOO, along with a classical-to-quantum landscape mapping for better benchmarking and tuning.

Findings

QMOO shows improved hyper-volume convergence.

Tuned QMOO performs comparably to classical solvers on small instances.

Potential advantages of QMOO on harder problems are demonstrated.

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.