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

TL;DR

This paper introduces a novel multi-objective chance-constrained knapsack problem framework with implicit probability distributions, proposing efficient algorithms for evaluation and optimization, and demonstrating superior performance on synthetic and real-world benchmarks.

Contribution

It develops the OPERA-MC method for efficient chance constraint evaluation and the NHILS hybrid evolutionary algorithm for better optimization in complex probabilistic knapsack problems.

Findings

NHILS outperforms existing methods in convergence and diversity.

OPERA-MC significantly reduces evaluation time for chance constraints.

The approach effectively handles real-world 5G network configuration problems.

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.