arXiv subjects

Steven D. Prestwich

Publications and source records attributed to Steven D. Prestwich.

2 recordsLinked to original sources

arXiv2026

Mixed-Integer Linear Programming Approximations for the Stochastic Knapsack

We develop mathematical programming approximations to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select a subset of these items to be included into their knapsack. We study both static and dynamic variants of this problem: in the static setting, the decision about which items should be included in the knapsack is taken at the outset, before any random item value or weight is revealed; in the dynamic setting, items are received sequentially, and the decision about a particular item is made by taking into account previously observed values and weights. The knapsack has a given capacity, and if the total realised weight exceeds this capacity then a penalty cost is incurred for each unit of excess capacity utilised. The goal is to maximise the expected net profit. We tackle the case of normally distributed item weights and we show that our approach extends to the case in which item weights are correlated and follow a multivariate normal distribution. In addition, we show our approach represents an effective heuristic for the case in which item weights follow generic probability distributions. In an extensive computational study we demonstrate that our models are near-optimal and more scalable than other state-of-the-art approaches.

math.OC↗

arXiv2026

Grammar-Aware Literate Generative Mathematical Programming with Compiler-in-the-Loop

Mathematical programming is widely employed across various sectors - such as logistics, energy, and workforce planning - to model and solve industrial optimisation problems, but its use requires substantial domain expertise. Large language models offer a promising way to translate natural-language problem descriptions into optimisation models, yet existing approaches are costly and generally produce models written in general-purpose computer code (e.g. Python), which can be difficult to inspect, validate, and reuse. In this work, we introduce SyntAGM, a system that generates optimisation models in a readable algebraic modelling language through an iterative generate-compile-assess-revise loop. SyntAGM leverages PyOPL, an OPL-like modelling language compiler designed to provide actionable feedback for iterative model repair. To obtain a valid PyOPL model that matches the problem description, SyntAGM mobilises compiler feedback and an LLM-based alignment judge. In addition, it combines in-context exposure to the target language grammar, and few-shot retrieval of modelling exemplars. Across multiple benchmarks, SyntAGM achieves a more favourable cost-quality trade-off compared to established prompting baselines.

cs.PL↗