Clustering Solutions of Multiobjective Function Inlining Problem

Authors Kateryna Muts , Heiko Falk

Thumbnail PDF


  • Filesize: 0.68 MB
  • 12 pages

Document Identifiers

Author Details

Kateryna Muts
  • Hamburg University of Technology, Germany
Heiko Falk
  • Hamburg University of Technology, Germany

Cite AsGet BibTex

Kateryna Muts and Heiko Falk. Clustering Solutions of Multiobjective Function Inlining Problem. In 21th International Workshop on Worst-Case Execution Time Analysis (WCET 2023). Open Access Series in Informatics (OASIcs), Volume 114, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Hard real time-systems are often small devices operating on batteries that must react within a given deadline, so they must satisfy their timing, code size, and energy consumption requirements. Since these three objectives contradict each other, compilers for real-time systems go towards multiobjective optimizations which result in sets of trade-off solutions. A system designer can use the solution sets to choose the most suitable system configuration. Evolutionary algorithms can find trade-off solutions but the solution set might be large which complicates the task of the system designer. We propose to divide the solution set into clusters, so the system designer chooses the most suitable cluster and examines a smaller subset in detail. In contrast to other clustering techniques, our method guarantees that the sizes of all clusters are less than a predefined limit. Our method clusters a set by using any existing clustering method, divides clusters with sizes exceeding the predefined size into smaller clusters, and reduces the number of clusters by merging small clusters. The method guarantees that the final clusters satisfy the size constraint. We demonstrate our approach by considering a well-known compiler-based optimization called function inlining. It substitutes function calls by the function bodies which decreases the execution time and energy consumption of a program but increases its code size.

Subject Classification

ACM Subject Classification
  • Information systems → Clustering
  • Software and its engineering → Compilers
  • Computer systems organization → Real-time systems
  • Mathematics of computing → Evolutionary algorithms
  • Clustering
  • multiobjective optimization
  • compiler
  • hard real-time system


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. AbsInt Angewandte Informatik, GmbH. aiT Worst-Case Execution Time Analyzers., 2022. Google Scholar
  2. Sunith Bandaru, Amos H.C. Ng, and Kalyanmoy Deb. Data mining methods for knowledge discovery in multi-objective optimization: Part B - New developments and applications. Expert Systems with Applications, 70:119-138, March 2017. URL:
  3. Lilian Astrid Bejarano, Helbert Eduardo Espitia, and Carlos Enrique Montenegro. Clustering Analysis for the Pareto Optimal Front in Multi-Objective Optimization. Computation, 10(3):37, March 2022. URL:
  4. Vincenzo Catania, Giuseppe Ascia, Maurizio Palesi, Davide Patti, and Alessandro G. Di Nuovo. Fuzzy decision making in embedded system design. In Proceedings of the 4th International Conference on Hardware/Software Codesign and System Synthesis (CODES+ISSS '06), pages 223-228, October 2006. URL:
  5. Carlos A. Coello, David A. Van Veldhuizen, and Gary B. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Springer-Verlag GmbH, October 2007. Google Scholar
  6. Kalyanmoy Deb. Multi-Objective Optimization Using Evolutionary Algorithms. Wiley-Interscience Series in Systems and Optimization. John Wiley & Sons, New York, NY, USA, 2001. Google Scholar
  7. Kalyanmoy Deb. Multi-objective Optimization. In Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pages 403-449. Springer US, Boston, MA, 2014. URL:
  8. Wilm E. Donath and Albert J. Hoffman. Algorithms for partitioning graphs and computer logic based on eigenvectors of connection matrices. IBM Technical Disclosure Bulletin, 15(3):938-944, 1972. Google Scholar
  9. Catarina Dudas, Amos H.C. Ng, and Henrik Boström. Post-analysis of multi-objective optimization solutions using decision trees. Intelligent Data Analysis, 19(2):259-278, April 2015. URL:
  10. Heiko Falk and Paul Lokuciejewski. A compiler framework for the reduction of worst-case execution times. Real-Time Systems, 46(2):251-300, July 2010. URL:
  11. Hisao Ishibuchi, Lie Meng Pang, and Ke Shang. Solution Subset Selection for Final Decision Making in Evolutionary Multi-Objective Optimization, June 2020. URL:
  12. Shashank Jadhav and Heiko Falk. Multi-Objective Optimization for the Compiler of Real-Time Systems based on Flower Pollination Algorithm. In 22nd International Workshop on Software and Compilers for Embedded Systems (SCOPES), pages 45-48. ACM, May 2019. URL:
  13. Yanjun Kong, Yadong Mei, Xianxun Wang, and Yue Ben. Solution Selection from a Pareto Optimal Set of Multi-Objective Reservoir Operation via Clustering Operation Processes and Objective Values. Water, 13(8):1046, January 2021. URL:
  14. Tobias Kuhn, Carlos M. Fonseca, Luís Paquete, Stefan Ruzika, Miguel M. Duarte, and José Rui Figueira. Hypervolume Subset Selection in Two Dimensions: Formulations and Algorithms. Evolutionary Computation, 24(3):411-425, 2016. URL:
  15. Congdong Li, Run Wu, and Weiming Yang. Optimization and selection of the multi-objective conceptual design scheme for considering product assembly, manufacturing and cost. SN Applied Sciences, 4(4):91, March 2022. URL:
  16. Paul Lokuciejewski, Sascha Plazar, Heiko Falk, Peter Marwedel, and Lothar Thiele. Approximating Pareto optimal compiler optimization sequences endash a trade-off between WCET, ACET and code size. Software: Practice and Experience, 41(12):1437-1458, May 2011. URL:
  17. James MacQueen. Some methods for classification and analysis of multivariate observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics, volume 5.1, pages 281-298. University of California Press, January 1967. Google Scholar
  18. Christopher Mattson, Anoop Mullur, and Achille Messac. Minimal Representation of Multiobjective Design Space Using a Smart Pareto Filter. In 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Multidisciplinary Analysis Optimization Conferences. American Institute of Aeronautics and Astronautics, September 2002. URL:
  19. George A. Miller. The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63:81-97, 1956. URL:
  20. Steven S. Muchnick. Advanced Compiler Design and Implementation. Morgan Kaufmann Publishers Inc., 1998. Google Scholar
  21. Kateryna Muts. Multiobjective Compiler-Based Optimizations for Hard Real-Time Systems. PhD thesis, TUHH Universitätsbibliothek, December 2022. URL:
  22. Andrew Y. Ng, Michael I. Jordan, and Yair Weiss. On spectral clustering: Analysis and an algorithm. In Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic, NIPS'01, pages 849-856, Cambridge, MA, USA, January 2001. MIT Press. Google Scholar
  23. Fabian Pedregosa, Gaël Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Andreas Müller, Joel Nothman, Gilles Louppe, Peter Prettenhofer, Ron Weiss, Vincent Dubourg, Jake Vanderplas, Alexandre Passos, David Cournapeau, Matthieu Brucher, Matthieu Perrot, and Édouard Duchesnay. Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, January 2012. URL:
  24. Jason A. Poovey, Thomas M. Conte, Markus Levy, and Shay Gal-On. A Benchmark Characterization of the EEMBC Benchmark Suite. IEEE Micro, 29(5):18-29, September 2009. URL:
  25. Mike Preuss and Simon Wessing. Measuring Multimodal Optimization Solution Sets with a View to Multiobjective Techniques. In EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV, Advances in Intelligent Systems and Computing, pages 123-137, Heidelberg, 2013. Springer International Publishing. URL:
  26. Henrik Smedberg and Sunith Bandaru. Interactive knowledge discovery and knowledge visualization for decision support in multi-objective optimization. European Journal of Operational Research, 306(3):1311-1329, May 2023. URL:
  27. Abdulhamit Subasi. Practical Machine Learning for Data Analysis Using Python. Academic Press, London [England]; San Diego, CA, 2020. Google Scholar
  28. Ling Wang, Haoqi Ni, Weifeng Zhou, Panos M. Pardalos, Jiating Fang, and Minrui Fei. MBPOA-based LQR controller and its application to the double-parallel inverted pendulum system. Engineering Applications of Artificial Intelligence, 36:262-268, November 2014. URL:
  29. Xuanli L. Xie and Gerardo Beni. A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(8):841-847, 1991. URL:
  30. Zhongliang Yue. An extended TOPSIS for determining weights of decision makers with interval numbers. Knowledge-Based Systems, 24(1):146-153, February 2011. URL: