# Non-linear Multi-objective Optimization with Probabilistic Branch and Bound

arXiv: https://arxiv.org/abs/2506.04554 · HTML: https://mlsanity.com/paper/2506.04554/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 41 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 3 of 3)

- [A Bayesian approach to constrained single- and multi-objective optimization](https://mlsanity.com/paper/1510.00503/) (2015)
- [Part-X: A Family of Stochastic Algorithms for Search-Based Test Generation with Probabilistic Guarantees](https://mlsanity.com/paper/2110.10729/) (2021)
- [Revisiting Norm Optimization for Multi-Objective Black-Box Problems: A Finite-Time Analysis](https://mlsanity.com/paper/1804.11020/) (2018)

## Abstract (arXiv)

A multiple objective simulation optimization algorithm named Multiple Objective Probabilistic Branch and Bound with Single Observation (MOPBnB(so)) is presented for approximating the Pareto optimal set and the associated efficient frontier for stochastic multi-objective optimization problems. MOPBnB(so) evaluates a noisy function exactly once at any solution and uses neighboring solutions to estimate the objective functions, in contrast to a variant that uses multiple replications at a solution to estimate the objective functions. A finite-time performance analysis for deterministic multi-objective problems provides a bound on the probability that MOPBnB(so) captures the Pareto optimal set. Asymptotic convergence of MOPBnB(so) on stochastic problems is derived, in that the algorithm captures the Pareto optimal set and the estimations converge to the true objective function values. Numerical results reveal that the variant with multiple replications is extremely intensive in terms of computational resources compared to MOPBnB(so). In addition, numerical results show that MOPBnB(so) outperforms a genetic algorithm NSGA-II on test problems.