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

2026-04-12

AI Summary

This study addresses the multi-knapsack problem (MKP) under stochastic and dynamic constraints, where item weights follow normal distributions and knapsack capacities evolve over time, subject to chance constraints defined at a specified confidence level. The problem is formulated for the first time as a bi-objective optimization model that balances expected profit maximization against the probabilistic satisfaction of capacity constraints. Through a systematic comparison of decomposition-based and dominance-based multi-objective evolutionary algorithms (MOEAs), integrated with tailored mechanisms for handling chance constraints and adapting to dynamic environments, the experiments reveal distinct performance characteristics across varying levels of uncertainty, confidence thresholds, and dynamic scenarios. These findings offer practical guidance and algorithmic insights for solving stochastic dynamic resource allocation problems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• stochastic MKP
• dynamic constraints
• chance constraints
• bi-objective optimization
• evolutionary algorithms

Innovation

• bi-objective optimization
• stochastic MKP
• dynamic constraints
• chance constraints
• multi-objective evolutionary algorithms