Applying Ising Machines to Multi-objective QUBOs

Mayowa Ayodele, Richard Allmendinger, Manuel López-Ibáñez, Arnaud Liefooghe, Matthieu Parizy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Multi-objective optimisation problems involve finding solutions with varying trade-offs between multiple and often conflicting objectives. Ising machines are physical devices that aim to find the absolute or approximate ground states of an Ising model. To apply Ising machines to multi-objective problems, a weighted sum objective function is used to convert multi-objective into single-objective problems. However, deriving scalarisation weights that archives evenly distributed solutions across the Pareto front is not trivial. Previous work has shown that adaptive weights based on dichotomic search, and one based on averages of previously explored weights can explore the Pareto front quicker than uniformly generated weights. However, these adaptive methods have only been applied to bi-objective problems in the past. In this work, we extend the adaptive method based on averages in two ways: (i) we extend the adaptive method of deriving scalarisation weights for problems with two or more objectives, and (ii) we use an alternative measure of distance to improve performance. We compare the proposed method with existing ones and show that it leads to the best performance on multi-objective Unconstrained Binary Quadratic Programming (mUBQP) instances with 3 and 4 objectives and that it is competitive with the best one for instances with 2 objectives.

Original languageEnglish
Title of host publicationGECCO '23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation
PublisherAssociation for Computing Machinery
Pages2166-2174
Number of pages9
ISBN (Electronic)9798400701207
DOIs
Publication statusPublished - 24 Jul 2023

Keywords

  • Aggregation
  • Digital Annealer
  • Multi-objective Optimisation
  • QUBO
  • Scalarisation
  • UBQP

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