Bézier Flow: a Surface-wise Gradient Descent Method for Multi-objective Optimization
Authors: Akiyoshi Sannai, Yasunari Hikima, Ken Kobayashi, Akinori Tanaka, Naoki Hamada
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conducted numerical experiments with synthetic and real multi-objective optimization problem instances and demonstrated that our method achieved lower generalization errors than the existing multi-objective optimization algorithms. |
| Researcher Affiliation | Collaboration | Akiyoshi Sannai EMAIL Kyoto University National Institute of Informatics Yasunari Hikima EMAIL Fujitsu Limited Kyushu University Ken Kobayashi EMAIL Institute of Science Tokyo Akinori Tanaka EMAIL RIKEN AIP RIKEN i THEMS Keio University Naoki Hamada EMAIL KLab Inc. |
| Pseudocode | Yes | Algorithm 1 Multi-objective Optimization Method M(A) from Single Optimization Method A Algorithm 2 Surface-wise Gradient Descent Method |
| Open Source Code | Yes | The source code is accessible at https://github.com/hikimay/bezier-flow. |
| Open Datasets | Yes | For real-world instances, we applied Algorithm 2 to a group LASSO problem with the Birthwt dataset from the MASS package1 in R language. In addition, to confirm the applicability of the proposed method to non-simplicial instances, we applied Algorithm 2 to DTLZ instances (Deb et al., 2002) |
| Dataset Splits | Yes | As a validation set Y , we generated approximate Pareto solutions by NSGA-III (Deb & Jain, 2013; Jain & Deb, 2013) with the population size of 1000. To construct X, we randomly sampled {ˆtn}1000 n=1 i.i.d. from the uniform distribution on M−1 and obtained sample points on the estimated Bézier simplex. |
| Hardware Specification | Yes | the experiments were performed on a Windows 10 PC with an Intel(R) Xeon(R) W-1270 CPU 3.40 GHz and 64 GB RAM. |
| Software Dependencies | Yes | We implemented these algorithms in Python 3.12.3 |
| Experiment Setup | Yes | In Algorithm 2, we set the degree of Bézier simplex as D = 3, the initial control points as P (1) = O, which is the zero matrix of appropriate size. In addition, we set the maximum number of iterations as K = 100 and the step size as α(k) = 1/k for k = 1, 2, . . . , K. The number of points to be sampled from a simplex in each iteration was tested for N {30, 50, 100}. |