EURO 2024 Copenhagen
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762. Harnessing the Power of Quantum Computing for Multiobjective Optimization Algorithms

Invited abstract in session WC-37: Theory of Multiobjective Optimization, stream Multiobjective Optimization.

Wednesday, 12:30-14:00
Room: 33 (building: 306)

Authors (first author is the speaker)

1. Pascal Halffmann
Financial Mathematics, Fraunhofer Institute for Industrial Mathematics ITWM
2. Ivica Turkalj
Fraunhofer Institute for Industrial Mathematics ITWM

Abstract

Multiobjective optimization problems (MOPs) present unique challenges, characterized by optimizing several conflicting objectives simultaneously and the, often exponential, number of Pareto-optimal solutions. Classical approaches typically involve scalarization to single objective problems obtaining at most one Pareto-optimal solution per single objective problem. The advent of quantum computing (QC), with its properties like superposition and entanglement, opens new frontiers in addressing the complexity of MOPs. So far, application-oriented problems, like MOPs, have barely been touched by quantum algorithms.
In this research, we explore the application of QC to discrete MOPs, capitalizing on its inherent capabilities to process vast and complex search spaces. We investigate how existing quantum optimization algorithms can be adapted and extended to the multiobjective domain. Based on previous work, we focus on variational algorithms and Grover Adaptive search and augment these with scalarization techniques and bound sets, among others. To demonstrate the efficacy of our approach, we apply these QC algorithms to an unconstrained multiobjective combinatorial optimization problem.
Our results showcase that, while the computational advantage over classical computing is currently tested, QC adds value when tackling conceptually hard problems. Furthermore, we are paving the way for the practical applicability of quantum computing in solving real-world optimization problems.

Keywords

Status: accepted

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