MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directions

Overview

Implementation code for paper MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directions published in The 39th Annual Conference on Neural Information Processing Systems (NeurIPS-2025). The manuscript can be found on arXiv.

If you find our paper or this repo to be useful for your research, please consider citing:

@article{ngo2025moboosd,
  title={MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directions},
  author={Ngo, Lam and Ha, Huong and Chan, Jeffrey and Zhang, Hongyu},
  journal={Advances in neural information processing systems},
  year={2025}
}

Requirement and dependencies

• Install Miniconda.
• Install all dependencies listed in env.yml file, or run the following to install via conda. This will create env mobo-osd in conda.

conda env create -f env.yml

Getting started

The main file is test-mobo-osd.py. To run the code for any problem, use the following syntax:

python test-mobo-osd.py -f <function_name> -d <input_dim> -m <number_of_objectives> -n <number_of_iterations>

The above command only list required arguments. Please check the following table for optional arguments, as well as possible values for each arguments.

Flag	Description
-f	A string to specify the objective function. Examples from the paper include zdt1, dtlz2, vlmop2, speed-reducer, car-impact, marine-design, and water-planning. See _test_functions/get_function.py for more options.
-d	An integer to specify the objective function input dimensionality. Only required for scalable synthetic functions, e.g., dtlz2, zdt1. See _test_functions/get_function.py for more options.
-m	An integer to specify the number of objectives. Only required for some synthetic functions, e.g., dtlz2. See _test_functions/get_function.py for more options.
-n	An integer to specify the iteration budget.
-b	(Optional) An integer to specify the batch size. Default value is 10.
--n_beta	(Optional) An integer to specify the number of discretized points on the approximated CHIM. Default value is 20.
--n_init	(Optional) An integer to specify the number of random initialization. Default value is 20.
--seed	(Optional) An integer to specify the random seed for random number generator. Default is 1.

Results from paper

To produce the main experimental results in the paper (Figures 2, 3, 8 and 9), run the bash file experiments-from-paper.sh.

Acknowledgements

This code implementation uses materials from the following public repositories to implemenent the first order approximation step [1] and the qHVI acquisition function [2]. We thank the respective repository maintainers.

[1] DGEMO: Konakovic Lukovic, M., Tian, Y., & Matusik, W. (2020). Diversity-guided multi-objective bayesian optimization with batch evaluations. Advances in Neural Information Processing Systems, 33, (NeurIPS). Code repo: https://github.com/yunshengtian/DGEMO

[2] qEHVI: Daulton, S., Balandat, M., & Bakshy, E. (2020). Differentiable expected hypervolume improvement for parallel multi-objective Bayesian optimization. Advances in Neural Information Processing Systems, 33, (NeurIPS). Code repo: https://github.com/pytorch/botorch