Multi-Objective Evolutionary Optimization of Chance-Constrained Multiple-Choice Knapsack Problems with Implicit Probability Distributions

2026-03-09

AI Summary

This work addresses the multi-objective chance-constrained multiple-choice knapsack problem under implicit probability distributions by proposing a hybrid evolutionary algorithm, NHILS, which jointly optimizes cost minimization and the confidence level of satisfying capacity constraints. Built upon the NSGA-II framework, NHILS integrates an adaptive Monte Carlo sampling strategy—OPERA-MC—for efficiently evaluating chance constraints while preserving solution dominance relationships, along with a tailored initialization scheme and a local search mechanism. These components collectively mitigate the challenges posed by sparse feasible regions and high computational costs. Experimental results on both synthetic and real-world 5G network configuration benchmarks demonstrate that NHILS significantly outperforms state-of-the-art multi-objective optimizers in terms of convergence, solution diversity, and feasibility.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

The multiple-choice knapsack problem (MCKP) is a classic combinatorial optimization with wide practical applications. This paper investigates a significant yet underexplored extension of MCKP: the multi-objective chance-constrained MCKP (MO-CCMCKP) under implicit probability distributions. The goal of the problem is to simultaneously minimize the total cost and maximize the confidence level of satisfying the capacity constraint, capturing essential trade-offs in domains like 5G network configuration. To address the computational challenge of evaluating chance constraints under implicit distributions, we first propose an order-preserving efficient resource allocation Monte Carlo (OPERA-MC) method. This approach adaptively allocates sampling resources to preserve dominance relationships while reducing evaluation time significantly. Further, we develop NHILS, a hybrid evolutionary algorithm that integrates specialized initialization and local search into NSGA-II to navigate sparse feasible regions. Experiments on synthetic benchmarks and real-world 5G network configuration benchmarks demonstrate that NHILS consistently outperforms several state-of-the-art multi-objective optimizers in convergence, diversity, and feasibility. The benchmark instances and source code will be made publicly available to facilitate research in this area.

Problem

• multi-objective optimization
• chance-constrained
• multiple-choice knapsack problem
• implicit probability distributions
• combinatorial optimization

Innovation

• chance-constrained optimization
• implicit probability distributions
• multi-objective evolutionary algorithm
• Monte Carlo sampling
• multiple-choice knapsack problem