Chance-Constrained Multiple-Choice Knapsack Problem: Model, Algorithms, and Applications

TL;DR

This paper introduces a new chance-constrained variant of the multiple-choice knapsack problem with unknown weight distributions, proposing a data-driven local search algorithm that performs well on synthetic and real-world benchmarks.

Contribution

It formulates CCMCKP with unknown distributions, develops the DDALS algorithm, and provides benchmark datasets, advancing solution methods for this complex problem.

Findings

DDALS outperforms baseline algorithms on benchmarks.

The algorithm remains effective with limited sample data.

Open-sourced benchmarks facilitate future research.

Abstract

The multiple-choice knapsack problem (MCKP) is a classic NP-hard combinatorial optimization problem. Motivated by several significant real-world applications, this work investigates a novel variant of MCKP called chance-constrained multiple-choice knapsack problem (CCMCKP), where the item weights are random variables. In particular, we focus on the practical scenario of CCMCKP, where the probability distributions of random weights are unknown but only sample data is available. We first present the problem formulation of CCMCKP and then establish two benchmark sets. The first set contains synthetic instances and the second set is devised to simulate a real-world application scenario of a certain telecommunication company. To solve CCMCKP, we propose a data-driven adaptive local search (DDALS) algorithm. The main novelty of DDALS lies in its data-driven solution evaluation approach that can effectively handle unknown probability distributions of item weights. Moreover, in cases with unknown distributions, high intensity of chance constraints, limited amount of sample data and large-scale problems, it still exhibits good performance. Experimental results demonstrate the superiority of DDALS over other baselines on the two benchmarks. Additionally, ablation studies confirm the effectiveness of each component of the algorithm. Finally, DDALS can serve as the baseline for future research, and the benchmark sets are open-sourced to further promote research on this challenging problem.