Integrating Column Generation and Large Neighborhood Search for Bus Driver Scheduling with Complex Break Constraints

The Bus Driver Scheduling Problem (BDSP) is a combinatorial optimization problem with the goal to design shifts to cover prearranged bus tours. The objective takes into account the operational cost as well as the satisfaction of drivers. This problem is heavily constrained due to strict legal rules and collective agreements. The objective of this article is to provide state-of-the-art exact and hybrid solution methods that can provide high-quality solutions for instances of different sizes. This work presents a comprehensive study of both an exact method, Branch and Price (B&P), as well as a Large Neighborhood Search (LNS) framework which uses B&P or Column Generation (CG) for the repair phase to solve the BDSP. It further proposes and evaluates a novel deeper integration of B&P and LNS, storing the generated columns from the LNS subproblems and reusing them for other subproblems, or to find better global solutions. The article presents a detailed analysis of several components of the solution methods and their impact, including general improvements for the B&P subproblem, which is a high-dimensional Resource Constrained Shortest Path Problem (RCSPP), and the components of the LNS. The evaluation shows that our approach provides new state-of-the-art results for instances of all sizes, including exact solutions for small instances, and low gaps to a known lower bound for mid-sized instances. Conclusions: We observe that B&P provides the best results for small instances, while the tight integration of LNS and CG can provide high-quality solutions for larger instances, further improving over LNS which just uses CG as a black box. The proposed methods are general and can also be applied to other rule sets and related optimization problems

SPOT: Spatio-Temporal Pattern Mining and Optimization for Load Consolidation in Freight Transportation Networks

Freight consolidation has significant potential to reduce transportation costs and mitigate congestion and pollution. An effective load consolidation plan relies on carefully chosen consolidation points to ensure alignment with existing transportation management processes, such as driver scheduling, personnel planning, and terminal operations. This complexity represents a significant challenge when searching for optimal consolidation strategies. Traditional optimization-based methods provide exact solutions, but their computational complexity makes them impractical for large-scale instances and they fail to leverage historical data. Machine learning-based approaches address these issues but often ignore operational constraints, leading to infeasible consolidation plans. This work proposes SPOT, an end-to-end approach that integrates the benefits of machine learning (ML) and optimization for load consolidation. The ML component plays a key role in the planning phase by identifying the consolidation points through spatio-temporal clustering and constrained frequent itemset mining, while the optimization selects the most cost-effective feasible consolidation routes for a given operational day. Extensive experiments conducted on industrial load data demonstrate that SPOT significantly reduces travel distance and transportation costs (by about 50% on large terminals) compared to the existing industry-standard load planning strategy and a neighborhood-based heuristic. Moreover, the ML component provides valuable tactical-level insights by identifying frequently recurring consolidation opportunities that guide proactive planning. In addition, SPOT is computationally efficient and can be easily scaled to accommodate large transportation networks.

PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planning

This paper considers how to fuse Machine Learning (ML) and optimization to solve large-scale Supply Chain Planning (SCP) optimization problems. These problems can be formulated as MIP models which feature both integer (non-binary) and continuous variables, as well as flow balance and capacity constraints. This raises fundamental challenges for existing integrations of ML and optimization that have focused on binary MIPs and graph problems. To address these, the paper proposes PROPEL, a new framework that combines optimization with both supervised and Deep Reinforcement Learning (DRL) to reduce the size of search space significantly. PROPEL uses supervised learning, not to predict the values of all integer variables, but to identify the variables that are fixed to zero in the optimal solution, leveraging the structure of SCP applications. PROPEL includes a DRL component that selects which fixed-at-zero variables must be relaxed to improve solution quality when the supervised learning step does not produce a solution with the desired optimality tolerance. PROPEL has been applied to industrial supply chain planning optimizations with millions of variables. The computational results show dramatic improvements in solution times and quality, including a 60% reduction in primal integral and an 88% primal gap reduction, and improvement factors of up to 13.57 and 15.92, respectively.

Conformal Prediction with Upper and Lower Bound Models

This paper studies a Conformal Prediction (CP) methodology for building prediction intervals in a regression setting, given only deterministic lower and upper bounds on the target variable. It proposes a new CP mechanism (CPUL) that goes beyond post-processing by adopting a model selection approach over multiple nested interval construction methods. Paradoxically, many well-established CP methods, including CPUL, may fail to provide adequate coverage in regions where the bounds are tight. To remedy this limitation, the paper proposes an optimal thresholding mechanism, OMLT, that adjusts CPUL intervals in tight regions with undercoverage. The combined CPUL-OMLT is validated on large-scale learning tasks where the goal is to bound the optimal value of a parametric optimization problem. The experimental results demonstrate substantial improvements over baseline methods across various datasets.

Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow

The nonlinear, non-convex AC Optimal Power Flow (AC-OPF) problem is fundamental for power systems operations. The intrinsic complexity of AC-OPF has fueled a growing interest in the development of optimization proxies for the problem, i.e., machine learning models that predict high-quality, close-to-optimal solutions. More recently, dual conic proxy architectures have been proposed, which combine machine learning and convex relaxations of AC-OPF, to provide valid certificates of optimality using learning-based methods. Building on this methodology, this paper proposes, for the first time, a dual conic proxy architecture for the semidefinite (SDP) relaxation of AC-OPF problems. Although the SDP relaxation is stronger than the second-order cone relaxation considered in previous work, its practical use has been hindered by its computational cost. The proposed method combines a neural network with a differentiable dual completion strategy that leverages the structure of the dual SDP problem. This approach guarantees dual feasibility, and therefore valid dual bounds, while providing orders of magnitude of speedups compared to interior-point algorithms. The paper also leverages self-supervised learning, which alleviates the need for time-consuming data generation and allows to train the proposed models efficiently. Numerical experiments are presented on several power grid benchmarks with up to 500 buses. The results demonstrate that the proposed SDP-based proxies can outperform weaker conic relaxations, while providing several orders of magnitude speedups compared to a state-of-the-art interior-point SDP solver.

Optimization Learning

This article introduces the concept of optimization learning, a methodology to design optimization proxies that learn the input/output mapping of parametric optimization problems. These optimization proxies are trustworthy by design: they compute feasible solutions to the underlying optimization problems, provide quality guarantees on the returned solutions, and scale to large instances. Optimization proxies are differentiable programs that combine traditional deep learning technology with repair or completion layers to produce feasible solutions. The article shows that optimization proxies can be trained end-to-end in a self-supervised way. It presents methodologies to provide performance guarantees and to scale optimization proxies to large-scale optimization problems. The potential of optimization proxies is highlighted through applications in power systems and, in particular, real-time risk assessment and security-constrained optimal power flow.

Confidence-Aware Deep Learning for Load Plan Adjustments in the Parcel Service Industry

This study develops a deep learning-based approach to automate inbound load plan adjustments for a large transportation and logistics company. It addresses a critical challenge for the efficient and resilient planning of E-commerce operations in presence of increasing uncertainties. The paper introduces an innovative data-driven approach to inbound load planning. Leveraging extensive historical data, the paper presents a two-stage decision-making process using deep learning and conformal prediction to provide scalable, accurate, and confidence-aware solutions. The first stage of the prediction is dedicated to tactical load-planning, while the second stage is dedicated to the operational planning, incorporating the latest available data to refine the decisions at the finest granularity. Extensive experiments compare traditional machine learning models and deep learning methods. They highlight the importance and effectiveness of the embedding layers for enhancing the performance of deep learning models. Furthermore, the results emphasize the efficacy of conformal prediction to provide confidence-aware prediction sets. The findings suggest that data-driven methods can substantially improve decision making in inbound load planning, offering planners a comprehensive, trustworthy, and real-time framework to make decisions. The initial deployment in the industry setting indicates a high accuracy of the proposed framework.

Differential Privacy Overview and Fundamental Techniques

This chapter is meant to be part of the book "Differential Privacy in Artificial Intelligence: From Theory to Practice" and provides an introduction to Differential Privacy. It starts by illustrating various attempts to protect data privacy, emphasizing where and why they failed, and providing the key desiderata of a robust privacy definition. It then defines the key actors, tasks, and scopes that make up the domain of privacy-preserving data analysis. Following that, it formalizes the definition of Differential Privacy and its inherent properties, including composition, post-processing immunity, and group privacy. The chapter also reviews the basic techniques and mechanisms commonly used to implement Differential Privacy in its pure and approximate forms.

Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems

The integration of renewable energy sources (RES) into power grids presents significant challenges due to their intrinsic stochasticity and uncertainty, necessitating the development of new techniques for reliable and efficient forecasting. This paper proposes a method combining probabilistic forecasting and Gaussian copula for day-ahead prediction and scenario generation of load, wind, and solar power in high-dimensional contexts. By incorporating weather covariates and restoring spatio-temporal correlations, the proposed method enhances the reliability of probabilistic forecasts in RES. Extensive numerical experiments compare the effectiveness of different time series models, with performance evaluated using comprehensive metrics on a real-world and high-dimensional dataset from Midcontinent Independent System Operator (MISO). The results highlight the importance of weather information and demonstrate the efficacy of the Gaussian copula in generating realistic scenarios, with the proposed weather-informed Temporal Fusion Transformer (WI-TFT) model showing superior performance.

Learning Joint Models of Prediction and Optimization

The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from exogenous features before solving. This setting is common to many real-world decision processes, and recently it has been shown that decision quality can be substantially improved by solving and differentiating the optimization problem within an end-to-end training loop. However, this approach requires significant computational effort in addition to handcrafted, problem-specific rules for backpropagation through the optimization step, challenging its applicability to a broad class of optimization problems. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models. The approach is generic, and based on an adaptation of the Learning-to-Optimize paradigm, from which a rich variety of existing techniques can be employed. Experimental evaluations show the ability of several Learning-to-Optimize methods to provide efficient and accurate solutions to an array of challenging Predict-Then-Optimize problems.