# Using 3-Objective Evolutionary Algorithms for the Dynamic Chance Constrained Knapsack Problem

arXiv: https://arxiv.org/abs/2404.06014 · HTML: https://mlsanity.com/paper/2404.06014/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 9 Apr 2024.

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

- [Pareto Optimization for Subset Selection with Dynamic Cost Constraints](https://mlsanity.com/paper/1811.07806/) (2018)
- [Optimizing Monotone Chance-Constrained Submodular Functions Using Evolutionary Multi-Objective Algorithms](https://mlsanity.com/paper/2006.11444/) (2020)
- [Evolutionary Algorithms for Limiting the Effect of Uncertainty for the Knapsack Problem with Stochastic Profits](https://mlsanity.com/paper/2204.05597/) (2022)
- [Specific Single- and Multi-Objective Evolutionary Algorithms for the Chance-Constrained Knapsack Problem](https://mlsanity.com/paper/2004.03205/) (2020)
- [3-Objective Pareto Optimization for Problems with Chance Constraints](https://mlsanity.com/paper/2304.08774/) (2023)
- [Evolutionary Bi-objective Optimization for the Dynamic Chance-Constrained Knapsack Problem Based on Tail Bound Objectives](https://mlsanity.com/paper/2002.06766/) (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)
- [Single- and Multi-Objective Evolutionary Algorithms for the Knapsack Problem with Dynamically Changing Constraints](https://mlsanity.com/paper/2004.12574/) (2020)

## Built on by (most cited first, 4 of 4)

- [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)
- [Sampling-based Pareto Optimization for Chance-constrained Monotone Submodular Problems](https://mlsanity.com/paper/2404.11907/) (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)

Real-world optimization problems often involve stochastic and dynamic components. Evolutionary algorithms are particularly effective in these scenarios, as they can easily adapt to uncertain and changing environments but often uncertainty and dynamic changes are studied in isolation. In this paper, we explore the use of 3-objective evolutionary algorithms for the chance constrained knapsack problem with dynamic constraints. In our setting, the weights of the items are stochastic and the knapsack's capacity changes over time. We introduce a 3-objective formulation that is able to deal with the stochastic and dynamic components at the same time and is independent of the confidence level required for the constraint. This new approach is then compared to the 2-objective formulation which is limited to a single confidence level. We evaluate the approach using two different multi-objective evolutionary algorithms (MOEAs), namely the global simple evolutionary multi-objective optimizer (GSEMO) and the multi-objective evolutionary algorithm based on decomposition (MOEA/D), across various benchmark scenarios. Our analysis highlights the advantages of the 3-objective formulation over the 2-objective formulation in addressing the dynamic chance constrained knapsack problem.