Enhancing Variational Quantum Algorithms for Multicriteria Optimization

TL;DR

This paper enhances variational quantum algorithms for multicriteria optimization by reformulating the problem for classical hybrid methods and improving Pareto front diversity, leading to better coverage and performance.

Contribution

It introduces a hybrid framework reformulating VQAs as multicriteria problems and a new method to improve Pareto front diversity using hypervolume-based cost functions.

Findings

Hybrid framework outperforms single-criteria VQAs in diverse benchmarks.

Coverage of Pareto front improves by up to 40%.

Minimal loss in hypervolume with diversity enhancement.

Abstract

This paper presents methodological improvements to variational quantum algorithms (VQAs) for solving multicriteria optimization problems. We introduce two key contributions. First, we reformulate the parameter optimization task of VQAs as a multicriteria problem, enabling the direct use of classical algorithms from various multicriteria metaheuristics. This hybrid framework outperforms the corresponding single-criteria VQAs in both average and worst-case performance across diverse benchmark problems. Second, we propose a method that augments the hypervolume-based cost function with coverage-oriented indicators, allowing explicit control over the diversity of the resulting Pareto front approximations. Experimental results show that our method can improve coverage by up to 40\% with minimal loss in hypervolume. Our findings highlight the potential of combining quantum variational methods with classical population-based search to advance practical quantum optimization.