# Multi-Objective Constrained Optimization for Energy Applications via Tree Ensembles

arXiv: https://arxiv.org/abs/2111.03140 · HTML: https://mlsanity.com/paper/2111.03140/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 82 references that are in the map.
- First posted on arXiv 4 Nov 2021.

## Builds on (most cited first, 8 of 8)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife](https://mlsanity.com/paper/1311.4555/) (2013)
- [Optimization of Tree Ensembles](https://mlsanity.com/paper/1705.10883/) (2017)
- [Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded](https://mlsanity.com/paper/1803.00952/) (2018)
- [ENTMOOT: A Framework for Optimization over Ensemble Tree Models](https://mlsanity.com/paper/2003.04774/) (2020)

## Built on by (most cited first, 12 of 12)

- [OMLT: Optimization & Machine Learning Toolkit](https://mlsanity.com/paper/2202.02414/) (2022)
- [Maximizing information from chemical engineering data sets: Applications to machine learning](https://mlsanity.com/paper/2201.10035/) (2022)
- [Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian Optimization](https://mlsanity.com/paper/2211.06149/) (2022)
- [Bayesian optimization as a flexible and efficient design framework for sustainable process systems](https://mlsanity.com/paper/2401.16373/) (2024)
- [Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces](https://mlsanity.com/paper/2207.00879/) (2022)
- [Global Optimization of Gaussian Process Acquisition Functions Using a Piecewise-Linear Kernel Approximation](https://mlsanity.com/paper/2410.16893/) (2024)
- [EARL-BO: Reinforcement Learning for Multi-Step Lookahead, High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2411.00171/) (2024)
- [Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?](https://mlsanity.com/paper/2503.03625/) (2025)
- [BARK: A Fully Bayesian Tree Kernel for Black-box Optimization](https://mlsanity.com/paper/2503.05574/) (2025)
- [Practical Path-based Bayesian Optimization](https://mlsanity.com/paper/2312.00622/) (2023)
- [Deep Surrogate of Modular Multi Pump using Active Learning](https://mlsanity.com/paper/2208.02840/) (2022)
- [B3O: Scalable Boltzmann Batch Bayesian Optimization](https://mlsanity.com/paper/2606.30228/) (2026)

## Abstract (arXiv)

Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable types, e.g. continuous and categorical, are challenges commonly present in real-world applications. In some cases, proposed optimal solutions need to obey explicit input constraints related to physical properties or safety-critical operating conditions. This paper proposes a novel data-driven strategy using tree ensembles for constrained multi-objective optimization of black-box problems with heterogeneous variable spaces for which underlying system dynamics are either too complex to model or unknown. In an extensive case study comprised of synthetic benchmarks and relevant energy applications we demonstrate the competitive performance and sampling efficiency of the proposed algorithm compared to other state-of-the-art tools, making it a useful all-in-one solution for real-world applications with limited evaluation budgets.