Cardinality Constrained Portfolio Optimization on an Ising Machine

Matthieu Parizy, Przemyslaw Sadowski, Nozomu Togawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper, we propose an Ising-machine based method for solving the cardinality constrained mean-variance portfolio optimization problem (CCMVPOP), which is an NP-hard problem and often solved using metaheuristics. Firstly, we formulate this problem as a binary quadratic program (BQP) to be solved by an Ising machine-software system. Namely, we propose formulations for each objective and constraint using binary variables exclusively. Furthermore, we evaluate and compare well known integer to binary variable encoding as well as propose a new encoding for the CCMVPOP. The evaluation is done by studying which encoding converges the fastest to the highest return over risk collection of assets for a given data set which represent stocks involved in a capital market index. Used data range from capital market index composed of 31 assets for the smallest and up to 225 for the largest. The experimental results confirm that the proposed formulations to the CCMVPOP for an Ising machine-software system are effective.

Original languageEnglish
Title of host publicationProceedings - 2022 IEEE 35th International System-on-Chip Conference, SOCC 2022
EditorsSakir Sezer, Thomas Buchner, Jurgen Becker, Andrew Marshall, Fahad Siddiqui, Tanja Harbaum, Kieran McLaughlin
PublisherIEEE Computer Society
ISBN (Electronic)9781665459853
Publication statusPublished - 2022
Event35th IEEE International System-on-Chip Conference, SOCC 2022 - Belfast, Northern Ireland, United Kingdom
Duration: 2022 Sept 52022 Sept 8

Publication series

NameInternational System on Chip Conference
ISSN (Print)2164-1676
ISSN (Electronic)2164-1706


Conference35th IEEE International System-on-Chip Conference, SOCC 2022
Country/TerritoryUnited Kingdom
CityBelfast, Northern Ireland


  • Ising machine
  • cardinality constraint
  • integer encoding
  • optimization
  • portfolio

ASJC Scopus subject areas

  • Hardware and Architecture
  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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