In urban areas, fluctuating road speeds due to traffic congestion and accidents significantly impact bus operations and stop connectivity. Current approaches cannot maintain public transport (PT) network stability during adaptation to changing road conditions, undermining both operations and passenger experience. This paper proposes a data sampling-based adjustment strategy to adapt the time-varying road conditions. The innovation lies in utilising limited network modifications to enhance the existing static PT network instead of considering reconstruction from scratch or minor adjustments (such as stop-skipping), aiming to minimise both passenger travel time degradation and the operational duration of each transit line. Our proposed multi-objective optimization model leverages historical traffic data samples and integrates route variation quantification with penalty mechanisms to enable real-time adaptive routing decisions. The case studies utilising Mandl’s network illustrate that our methodology can propose effective strategies for time-varying roads with any coefficient of variation. Experimental findings with high-variance samples indicate that our methodology decreases passenger travel time in roughly 80
The Traveling Salesman Problem (TSP) is a classic combinatorial optimization challenge with broad applications in logistics and transportation. While traditional heuristics remain dominant due to their efficiency and reliability, recent developments in Deep Reinforcement Learning (DRL) have introduced promising new directions for data-driven approaches to solving the TSP. Although DRL-based methods show promise, they often do not yet match classical heuristics in terms of computational efficiency and solution quality. One promising direction to bridging this gap is the integration of classical heuristics with learning-based methods. The Learn-to-Improve (L2I) framework follows this hybrid paradigm, combining heuristics with reinforcement learning to iteratively refine solutions. In this paper, we propose a novel multi-action sampling strategy that further enhances the L2I framework for solving TSP. The core idea is to improve solution quality by averaging rewards over multiple actions, which reduces bias and encourages more effective exploration compared to single-action strategies. During inference, multi-action sampling is applied in the later stages to explore diverse solution paths in parallel, helping to prevent premature convergence. Experimental results demonstrate that the proposed method outperforms existing L2I approaches while maintaining competitive computational efficiency.
The Unified Planning Framework (UPF) provides convenient access to automated planning technology. It allows for problem formulation independent of a planning engine and the utilization of planners available on the system. However, choosing a suitable parameter configuration of the planning engine for a given problem constitutes a significant challenge. Manually finding a high-quality configuration requires domain knowledge and a considerable time investment, contradicting the intended ease-of-use of the UPF. This issue is addressed by Algorithm Configuration (AC) techniques, which aim to automatically find high-quality configurations. Algorithm runtime as well as quality of solutions found by the parameterized algorithm have been shown to be improved by AC methods in wide-ranging problem settings, which includes planning. We integrate three state-of-the-art AC methods into the UPF and perform AC runs with planning engines which are integrated in the UPF. To this end, we perform AC in runtime, solution quality and anytime planning scenarios on problem instance sets from several International Planning Competitions (IPC). We demonstrate that AC methods provide performance improvements for the IPC.
This paper introduces a hybrid approach to address the Capacitated Vehicle Routing Problem with Time Windows by integrating quadratic unconstrained binary optimization (QUBO) hardware with deep learning-assisted heuristics. The proposed three-phase heuristic leverages the strengths of QUBO-solving hardware while mitigating its limitations, aiming at offering better scalability to larger problem instances. In the first phase, a deep learning-enhanced QUBO formulation is employed to partition the vertices into clusters. The second phase uses deep learning-assisted tree searches to generate candidate routes within each cluster. These candidate routes are combined in the third phase into a feasible global solution by solving a quadratic unconstrained binary set partition problem. This framework ensures compliance with capacity and time window constraints while maintaining computational efficiency. Computational results indicate that the hybrid approach is promising to potentially scale well for larger problem cases while respecting hardware limitations, offering a viable approach for leveraging quantum-inspired hardware in combination with advanced heuristics for solving complex combinatorial optimization problems.
This study examines the effectiveness of adversarial attacks in determining upper bounds for robustness distributions for neural networks. While complete neural network verification techniques can provide exact safety margins, their computational cost limits scalability. To address this, we evaluate multiple adversarial attack methods, including FGSM, PGD, AutoAttack and FAB, comparing them to a state-of-the-art verification technique, α , β -CROWN. Using the MNIST dataset, we demonstrate that adversarial attacks yield computationally efficient and tight upper bounds for robustness distributions. We assess the trade-offs between running time, accuracy and the quality of the bounds obtained through our approach. The results highlight complementarities between verification and attack methods: Attacks achieve near-optimal upper bounds at a significantly reduced computational cost. These findings open opportunities for large-scale robustness analysis while acknowledging limitations in safety guarantees inherent to the approximation techniques on which our approach is based.
We study a sequential decision-making problem for a profit-maximizing operator of an autonomous mobility-on-demand system. Optimizing a central operator’s vehicle-to-request dispatching policy requires efficient and effective fleet control strategies. To this end, we employ a multi-agent Soft Actor-Critic algorithm combined with weighted bipartite matching. We propose a novel vehicle-based algorithm architecture and adapt the critic’s loss function to appropriately consider coordinated actions. Furthermore, we extend our algorithm to incorporate rebalancing capabilities. Through numerical experiments, we show that our approach outperforms state-of-the-art benchmarks by up to 12.9
The disclosure of Artificial Intelligence to everyone is significantly pushing the need for resource – especially energy – efficient Machine Learning models. While it is well-established that Artificial Intelligence can enable and support sustainability in different application domains, its own sustainability is a critical concern and an open challenge for research and industry. The need for more accurate Machine Learning models clashes with the fact that a linear gain in accuracy requires exponentially larger resources: a more complex model, more training data and experiments, and consequently more computational resources, entailing a higher energy consumption. This paper proposes an energy efficient hyperparameter optimization algorithm – namely e ^2 HPO – integrating into a unique schema recent advances on both cost-aware and multiple information source Bayesian optimization. Experiments on three common Machine Learning algorithms whose core hyperparameters have been optimized on five different classification datasets empirically prove the benefits of the proposed algorithm. On the other hand, it turned out that some Machine Learning algorithms exhibit an intrinsic energy efficiency and this could lead e ^2 HPO – and similar approaches – to underperform with respect to more naive approaches.
Constraint Programming (CP) is a powerful approach to solving complex combinatorial problems. However, formulating combinatorial problems as CP models typically demands substantial expertise. Constraint acquisition (CA) seeks to assist in model building by deriving constraints from data. In passive learning, the system relies on a pre-labeled set of examples (solutions or non-solutions) to infer constraints, whereas active learning engages a domain expert or software system through targeted queries that classify newly proposed assignments to the variables of the problem. Hybrid CA frameworks that combine both strategies have also emerged to leverage the strengths of both approaches. However, when training data are scarce or noisy, passive methods may overfit the observed examples—appearing valid on the training set but failing to generalize to other, unseen solutions—and thereby introduce invalid constraints into the model. To address this issue that has been overlooked, we propose a new query-driven refinement approach that systematically challenges suspicious acquired constraints, using “violating assignments” designed to refute them while preserving all other constraints. Focusing on the AllDifferent constraint, we integrate this refinement into an existing hybrid CA system and experimentally demonstrate that our approach facilitates convergence to a correct final model.
In the last few years, deep learning has demonstrated significant potential in Operations Research across various tasks. In this work, we tackle the problem of repairing infeasible constraint satisfaction problems by introducing a novel deep reinforcement learning approach. Our method leverages graph deep learning to represent infeasible problems, utilizing a graph representation of Constraint Satisfaction Problems. By employing bipartite graph neural networks to encode the constraints of these problems, we train a deep learning agent to identify and extract a subset of constraints that restores feasibility solely from the reward signal, requiring no labeled data. We evaluate our approach using several bipartite graph neural network architectures and demonstrate its effectiveness in two domains: maximizing feasibility in Linear Programs and maximizing satisfiability in Boolean satisfiability problems. Our results show that the agent is competitive with existing heuristics in both solution quality and computational efficiency across these domains. An open source implementation of our methods is available at https://github.com/MehdiZouitine/Learning_to_repair_infeasible_problems_with_DRL_and_GNN .
Generative artificial intelligence (AI) models are advancing rapidly, and their ability to generate code has significant implications for software development. Their use in code generation raises concerns about plagiarism, malware generation and dataset contamination. Previous work proposed methods to address these issues, using developments from the field of natural language detection. However, due to the infancy of the field, there is a deficit in established benchmarks and datasets, making a comprehensive comparison between detection methods difficult. In this work, we investigated the efficacy of five existing zero-shot detection methods on AI-generated code. To do so, we used 17 large language models to generate and analyse 113 776 code samples from six common datasets and sources. By collecting new, previously unseen data with their respective time-stamps, we address the issue of data leakage, i.e., the exposure of LLMs to testing data during pre-training. Our proposed framework enables easy integration of new LLMs and datasets, facilitating the generation, detection and analysis of AI-generated code. Following this, we examined the impact of different hyperparameters used during code generation (such as the temperature) on detection performance. Our code is available under https://github.com/Progyo/Codetector .
Vector bin packing is a problem in combinatorial optimization that is particularly relevant in the area of cloud computing but also finds application in various areas of logistics. The problem deals with how to optimally place items into bins with constraints on multiple separate resource dimensions. We extend the problem to a cluster structure of bins, including variable bin sizes and cluster costs. The proposed extension of vector bin packing, which we term VCSCVBP, allows us to model a practical problem in the area of cloud computing, namely, the cloud capacity planning problem, where servers are organized in clusters. Optimizing data center capacity in terms of costs and fulfillment of customer demands in the form of virtual machines has become crucial due to the increasing demand for computing resources. We introduce several novel heuristics, called CS-P heuristics, consisting of a packing and a cluster selection step. The algorithms are evaluated with a benchmark based on practically relevant cloud computing data. Substantial runtime improvements are demonstrated by the computational experiments. For two out of three considered cost scenarios, only a slight deviation of the objective value obtained by the CS-P heuristics from the objective value obtained by the solver is observed. By exploiting cluster information and discarding certain cluster types through an additional procedure, this is also achieved for the third cost scenario.
Mixed-integer programming can handle optimization problems with complex constraints, but its computational cost often suffers from the combinatorial complexity of the problem. Decomposition-based matheuristics address this issue by splitting large-scale mixed-integer programs (MIPs) into smaller subproblems. Matheuristics typically exhibit hyperparameters that may affect their performance. An analysis of related work reveals that the optimization potential of hyperparameters is often left unexploited, leading to both inferior MIP-solutions and unnecessarily high computational costs. This paper studies a novel algorithmic approach to tune hyperparameters of matheuristics by Bayesian optimization. Fundamental properties of the algorithmic approach are examined by computational experiments with small- and large-scale instances of the use case. The results exhibit two natural and competing objectives of the tuning problem: optimizing the MIP-objective and the computational cost. While the two objectives can be optimized separately for small-scale instances, they need to be handled jointly for large-scale instances. In future research the multi-objective aspect of the hyperparameter tuning problem will be examined more deeply, and the single-instance approach will be extended to multiple instances.
We introduce new techniques for matched block design in multi-arm experiments. In matched block design, units with similar covariate values are grouped into blocks, with one unit per treatment in each block. Existing methods for unit-level block design often fail to produce optimal matches for multi-arm experiments. We present a mixed integer programming (MIP) formulation that guarantees optimal solutions for the general multi-arm matched blocking problem using a clique-based equipartitioning approach. For cases where the MIP is computationally infeasible, we introduce heuristics that decompose large problems into tractable subproblems while providing explicit quality-runtime tradeoffs. We demonstrate that our methods significantly outperform existing techniques on a diverse test suite, achieving consistent improvements in block balance quality. Additionally, we show how these methods can be adapted to improve covariate balance across treatment groups. We demonstrate that matched block design presents an interesting application area for metaheuristic and exact optimization methods.
Managing taxi fleets in large cities is challenging, especially when drivers operate independently. This study improves taxi repositioning by predicting demand and providing smart recommendations. Using real-world data from a Scandinavian taxi service, we employ neural networks with LSTM layers to forecast demand and test different strategies, like a simple greedy algorithm and a more structured matching-based approach, to guide taxis to high-demand areas. Since drivers ultimately decide whether to follow these suggestions, we also model their behavior using a probabilistic acceptance strategy. Through a simulation of a real day, we analyze how different approaches impact passenger wait times and overall efficiency. The results show that proactive re-positioning significantly reduces wait times but can increase total driving distance. The greedy algorithm tends to perform better in quickly getting taxis to passengers, while the matching model is more efficient in minimizing unnecessary travel. However, increased mobility comes at a cost, as rerouting leads to longer driving distances. Additionally, driver behavior plays a crucial role, with lower acceptance rates reducing the effectiveness of predictive recommendations. Overestimating demand in such cases helps mitigate inefficiencies.
Mixed-Integer Linear Programming (MILP) is a widely used method for modeling combinatorial optimization problems. Due to the NP-hard nature of many of these problems, efforts using machine-learning (ML) have been proposed to generate heuristics to speed up solvers, while maintaining optimality. While there is prior work on using graph neural networks (GNNs) to produce high-quality partial solutions, the methods used are non-auto-regressive which model the prediction of variables as conditionally independent due to concerns with solver runtimes. In this paper, we propose a novel auto-regressive reinforcement learning (RL) framework using GNNs which directly optimize for optimality and solver runtimes. Experimental results show our RL method outperforms the benchmark Predict-And-Search (PNS) method on harder real-world problems (55.7
Scholars in Operations Research have studied automated timetabling for the past sixty years, developing algorithms that assign students and teachers to courses and timeslots. In the Post-Enrollment Course Timetabling Problem (PECTP), we seek the optimal timetable that maximizes students getting enrolled in their requested courses. Given the complexity of the NP-complete PECTP, most high schools pre-assign teachers to each section of each course, and then build their Master Timetable. This action reduces the number of feasible timetables, since no teacher can be teaching two courses in the same timeslot, and most teachers are required to have a non-teaching timeslot every day. In this paper, we explain how we created the Master Timetable for a Canadian high school that intentionally does not pre-assign teachers to courses. Instead, each course has a set of possible teachers, and each teacher has a fixed number of courses they must be assigned. By providing flexible teacher assignments, this school increases the likelihood that all students get into the courses they select. Our final Master Timetable enrolls students in 99.8
Large language models (LLMs) have gained significant attention for their ability to solve complex tasks such as coding and reasoning. In this work, we aim to evaluate their ability to generate constraint programming (CP) models in a zero-shot setting, emphasizing model correctness and conformity to user-specified output formats. We propose a novel, iterative approach for zero-shot CP modeling that translates natural language problem descriptions into valid CP models and supports solution extraction to pre-defined output formats to facilitate effective adoption by domain experts and enable automated performance evaluation. To evaluate our approach, we introduce the Constraint Programming Evaluation (CPEVAL) benchmark (The CPEVAL benchmark and the proposed generation workflows are available at https://github.com/Yuliang795/LLMs-CP-CPEVAL .), derived from a diverse set of CP problems in CSPLib, coupled with an automated evaluation suite for large-scale assessment. We augment CPEVAL with paraphrased variants to assess robustness across linguistic variation and mitigate bias in the evaluation due to data memorization. Our extensive experiments across eight prominent LLMs and two CP modeling languages, MiniZinc and PyCSP3, show that our proposed iterative Two-Step method significantly enhances model correctness and conformity to user-specified output formats. Furthermore, we observe that larger LLMs demonstrate superior performance, with DeepSeek-R1 emerging as the top performer across both CP languages. We also observe that LLMs generally perform better in MiniZinc than in PyCSP3 .
We address the problem of automatic refutation of spectral graph theory conjectures with Monte Carlo methods. Usual ways are testing conjectures on an exhaustive database of graphs below a certain size, local search algorithms, or, more recently, deep reinforcement learning. We expand on previous works by finding smaller (and often sparser) counter-examples to spectral graph theory conjectures in seconds when it takes minutes or hours with other methods. We apply search algorithms (including state-of-the-art Monte Carlo Searches) to 68 automated conjectures already addressed by the deep cross-entropy method. In addition to the ones already disproved by deep cross-entropy, we refute 2 open conjectures until now. We highlight the efficiency of Monte Carlo Search algorithms compared to a state-of-the-art neural approach, and the advantages of the constructive method. Monte Carlo search can be used to automatically refute conjectures that are experimentally generated.
The Job Shop Scheduling Problem (JSSP) is a well-known NP-hard problem in combinatorial optimization, where the objective is to optimize job assignments across machines while minimizing a specific criterion such as makespan. Traditional mathematical and heuristic approaches struggle with scalability and handling complex precedence constraints. Recent advances in artificial intelligence, particularly deep reinforcement learning (DRL) and supervised learning, have shown promise but face challenges such as training instability and reliance on labeled data. To overcome these limitations, we propose SchedulExpert, a novel neural architecture based on a Mixture of Experts (MoE) framework with self-supervised learning. SchedulExpert integrates a Graph Attention Network (GAT) encoder, an attention-based routing mechanism, and multiple expert modules to enhance flexibility and efficiency in scheduling decisions. Experimental evaluations on benchmark JSSP instances demonstrate that SchedulExpert achieves competitive performance against state-of-the-art metaheuristic and neural-based methods, offering a scalable and effective solution for real-world scheduling challenges.
Industries are increasingly reliant on advanced process modeling techniques to improve development and operational efficiency. Utilising these models for optimisation holds the potential to significantly enhance performance, reduce costs, and ensure the highest standards of quality. However, when the underlying models become too complex or computationally expensive, surrogate-based optimisation offers a viable solution. In this work, we introduce a multi-target tree regression approach designed to address the complexities of multi-objective optimisation. The proposed methodology simultaneously handles multiple outputs, effectively captures nonlinear relationships, and enhances interpretability, making it a powerful tool for process optimisation. Additionally, we propose a novel methodology to mitigate the challenges of high dimensionality which is inherent in large datasets, enabling more efficient use of mathematical programming surrogates. By leveraging the developed methodologies, we aim to implement multi-objective optimisation to optimise key performance metrics like yield and purity in a real-world Active Pharmaceutical Ingredient Manufacturing Case Study, while deriving a Pareto curve to effectively illustrate the trade-off between competing objectives.
