# On the Use of Bi-Objective Evolutionary Algorithms for the Stochastic MKP under Dynamic Constraints

arXiv: https://arxiv.org/abs/2604.10930 · HTML: https://mlsanity.com/paper/2604.10930/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2026.

## Built on by (most cited first, 2 of 2)

- [On the use of evolutionary optimization for the dynamic chance constrained open-pit mine scheduling problem](https://mlsanity.com/paper/2604.13385/) (2026)
- [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)

The multiple knapsack problem (MKP) generalizes the classical knapsack problem by assigning items to multiple knapsacks subject to capacity constraints. It is used to model many real-world resource allocation and scheduling problems. In practice, these optimization problems often involve stochastic and dynamic components. Evolutionary algorithms provide a flexible framework for addressing such problems under uncertainty and dynamic changes. In this paper, we investigate a stochastic and dynamic variant of MKP with chance constraints, where the item weights are modeled as independent normally distributed random variables and knapsack capacities change during the optimization process. We formulate the problem as a bi-objective optimization formulation that balances profit maximization and probabilistic capacity satisfaction at a given confidence level. We conduct an empirical comparison of four widely used multi-objective evolutionary algorithms (MOEAs), representing both decomposition- and dominance-based search paradigms. The algorithms are evaluated under varying uncertainty levels, confidence thresholds, and dynamic change settings. The results provide comparative insights into the behavior of decomposition-based and dominance-based MOEAs for stochastic MKP under dynamic constraints.