Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems.

Area of Science:

• Computational intelligence
• Optimization algorithms
• Machine learning

Background:

• Offline data-driven multiobjective optimization problems (MOPs) rely on pre-existing data for surrogate model building.
• Gaussian Process Regression (GPR) is common for surrogates due to uncertainty quantification but becomes computationally expensive with large datasets.
• Existing sparse GPR methods are not optimized for the high-accuracy requirements near Pareto optimal fronts in offline MOPs.

Purpose of the Study:

• To propose Treed GPR with Multiobjective Optimization (TGPR-MO) surrogates tailored for offline data-driven MOPs.
• To enhance approximation accuracy specifically in regions relevant to Pareto optimal solutions.
• To reduce the computational burden associated with large datasets in MOPs.

Main Methods:

• TGPR-MO utilizes regression trees to partition the decision space into subregions.
• Gaussian Process Regressions (GPRs) are built sequentially within relevant subregions near potential Pareto optimal solutions.
• This approach leverages a subset of data for GPR construction, reducing computational complexity.

Main Results:

• TGPR-MO surrogates demonstrate significant computational cost reduction compared to full GPRs and sparse GPRs.
• The proposed method effectively handles large datasets and various problem configurations (data size, objectives, variables).
• TGPR-MO achieved solutions closer to the true Pareto optimal front than traditional full GPR and sparse GPR methods.

Conclusions:

• TGPR-MO offers a computationally efficient and accurate surrogate modeling approach for offline data-driven MOPs.
• The method's ability to focus on relevant decision space regions improves performance for finding Pareto optimal solutions.
• TGPR-MO presents a viable alternative for tackling complex MOPs with large, static datasets.