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

TL;DR

This paper explores bi-objective evolutionary algorithms for solving a stochastic, dynamic multi-knapsack problem with chance constraints, comparing different MOEA paradigms under various uncertainty and change scenarios.

Contribution

It formulates a novel bi-objective model for stochastic dynamic MKP with chance constraints and empirically compares four MOEAs across multiple uncertainty and dynamic change conditions.

Findings

Decomposition-based and dominance-based MOEAs show different strengths under varying conditions.

The study provides insights into algorithm behavior for stochastic MKP with dynamic constraints.

Results highlight the importance of algorithm selection based on problem uncertainty and dynamics.

Abstract

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.