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Bayesian Forward-Inverse Transfer for Multiobjective Optimization

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Parallel Problem Solving from Nature – PPSN XVIII (PPSN 2024)

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Abstract

We present an evolutionary optimizer incorporating knowledge transfer through forward and inverse surrogate models for solving multiobjective problems, within a stringent computational budget. Forward knowledge transfer is employed to fully exploit solution-evaluation datasets from related tasks by building Bayesian forward multitask surrogate models that map points from decision to objective space. Inverse knowledge transfer via Bayesian inverse multitask models makes possible the creation of high-quality solution populations in decision space by mapping back from preferred points in objective space. In contrast to prior work, the proposed method can improve the overall convergence performance to multiple Pareto sets by fully exploiting information available for diverse multiobjective problems. Empirical studies conducted on benchmark and real-world multitask multiobjective optimization problems demonstrate the faster convergence rate and enhanced inverse modeling accuracy of our algorithm compared to state-of-the-art algorithms.

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Notes

  1. 1.

    The training process of the MTGP model can be found in [19].

  2. 2.

    For benchmark problems, the ground truth solutions serve as the reference solution set. For real-world problems, bi-objective and tri-objective reference solution sets are obtained using NSGA-II [13] and NSGA-III [12] with population size 500 and generation size 1000, similar to [40].

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Acknowledgement

This research is partly supported by the National Research Foundation, Singapore and DSO National Laboratories under the AI Singapore Programme (AISG Award No.: AISG2-GC-2023-010, “Design Beyond What You Know”: Material-Informed Differential Generative AI (MIDGAI) for Light-Weight High-Entropy Alloys and Multi-functional Composites (Stage 1a)”, the Distributed Smart Value Chain programme which is funded under the Singapore RIE2025 Manufacturing, Trade and Connectivity (MTC) Industry Alignment Fund-Pre-Positioning, (Award No: M23L4a0001), and the Centre for Frontier AI Research (CFAR) under Agency for Science, Technology and Research (A*STAR), and the College of Computing and Data Science, Nanyang Technological University.

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Authors and Affiliations

  1. College of Computing and Data Science, Nanyang Technological University, Singapore, Singapore

    Tingyang Wei, Jiao Liu & Yew-Soon Ong

  2. School of Mechanical Sciences, Indian Institute of Technology, Goa, India

    Abhishek Gupta

  3. Singapore Institute of Manufacturing Technology (SIMTech), Agency for Science, Technology and Research, Singapore, Singapore

    Puay Siew Tan

  4. Centre for Frontier AI Research (CFAR), Agency for Science, Technology and Research, Singapore, Singapore

    Yew-Soon Ong

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  1. Tingyang Wei
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Correspondence to Jiao Liu .

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  1. University of Applied Sciences Upper Austria, Wels, Austria

    Michael Affenzeller

  2. University of Applied Sciences Upper Austria, Hagenberg, Austria

    Stephan M. Winkler

  3. Leiden University, Leiden, The Netherlands

    Anna V. Kononova

  4. University of Paderborn, Paderborn, Germany

    Heike Trautmann

  5. Jožef Stefan Institute, Ljubljana, Slovenia

    Tea Tušar

  6. University of Coimbra, Coimbra, Portugal

    Penousal Machado

  7. Leiden University, Leiden, The Netherlands

    Thomas Bäck

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Wei, T., Liu, J., Gupta, A., Tan, P.S., Ong, YS. (2024). Bayesian Forward-Inverse Transfer for Multiobjective Optimization. In: Affenzeller, M., et al. Parallel Problem Solving from Nature – PPSN XVIII. PPSN 2024. Lecture Notes in Computer Science, vol 15151. Springer, Cham. https://doi.org/10.1007/978-3-031-70085-9_9

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