# 3-Objective Pareto Optimization for Problems with Chance Constraints

arXiv: https://arxiv.org/abs/2304.08774 · HTML: https://mlsanity.com/paper/2304.08774/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 33 references that are in the map.
- First posted on arXiv 18 Apr 2023.

## Builds on (most cited first, 6 of 6)

- [Probabilistic Tools for the Analysis of Randomized Optimization Heuristics](https://mlsanity.com/paper/1801.06733/) (2018)
- [Optimizing Monotone Chance-Constrained Submodular Functions Using Evolutionary Multi-Objective Algorithms](https://mlsanity.com/paper/2006.11444/) (2020)
- [Runtime Analysis of Single- and Multi-Objective Evolutionary Algorithms for Chance Constrained Optimization Problems with Normally Distributed Random Variables](https://mlsanity.com/paper/2109.05799/) (2021)
- [Optimization of Chance-Constrained Submodular Functions](https://mlsanity.com/paper/1911.11451/) (2019)
- [Specific Single- and Multi-Objective Evolutionary Algorithms for the Chance-Constrained Knapsack Problem](https://mlsanity.com/paper/2004.03205/) (2020)
- [Runtime Analysis of RLS and the (1+1) EA for the Chance-constrained Knapsack Problem with Correlated Uniform Weights](https://mlsanity.com/paper/2102.05778/) (2021)

## Built on by (most cited first, 5 of 5)

- [Using 3-Objective Evolutionary Algorithms for the Dynamic Chance Constrained Knapsack Problem](https://mlsanity.com/paper/2404.06014/) (2024)
- [Bi-objective chance-constrained evolutionary optimization for large-scale open-pit mine scheduling under geological uncertainty](https://mlsanity.com/paper/2511.08275/) (2025)
- [On the use of evolutionary optimization for the dynamic chance constrained open-pit mine scheduling problem](https://mlsanity.com/paper/2604.13385/) (2026)
- [Sliding Window 3-Objective Pareto Optimization for Problems with Chance Constraints](https://mlsanity.com/paper/2406.04899/) (2024)
- [Adaptive Operator Selection in Bilevel Large Neighborhood Search for Electric Autonomous Dial-a-Ride Problem under Uncertainty](https://mlsanity.com/paper/2610.04219/) (2026)

## Abstract (arXiv)

Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for problems with chance constraints. Our formulation trades off the expected cost and variance of the stochastic component as well as the given deterministic constraint. We point out benefits that this 3-objective formulation has compared to a bi-objective one recently investigated for chance constraints with Normally distributed stochastic components. Our analysis shows that the 3-objective formulation allows to compute all required trade-offs using 1-bit flips only, when dealing with a deterministic cardinality constraint. Furthermore, we carry out experimental investigations for the chance constrained dominating set problem and show the benefit for this classical NP-hard problem.