Paratransit services are vital for individuals who cannot use fixed-route public transit, including those with disabilities. Optimizing these services is essential for transit agencies to deliver high-quality service efficiently. This paper introduces a Constraint Programming (CP) model to jointly optimize route planning and shift scheduling for paratransit operations, along with practical guidance for real-world implementation. A case study in Savannah, Georgia, demonstrates that the new approach is competitive with a recently proposed, highly effective AI-accelerated column generation framework, and significantly increases the number of requests served compared to current practices. The method is also easier to implement and provides an inherently practical solution for transportation planners. CP further provides the flexibility to optimize schedules without requiring shifts to start exactly on the hour, yielding an additional 5% improvement in the number of requests served.

Background: 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. Objectives: 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. Methods: 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. Results: 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.

Most US school districts draw geographic "attendance zones" to assign children to schools based on their home address, a process that can replicate existing neighborhood racial/ethnic and socioeconomic status (SES) segregation in schools. Redrawing boundaries can reduce segregation, but estimating expected rezoning impacts is often challenging because families can opt-out of their assigned schools. This paper seeks to alleviate this societal problem by developing a joint redistricting and choice modeling framework, called redistricting with choices (RWC). The RWC framework is applied to a large US public school district to estimate how redrawing elementary school boundaries might realistically impact levels of socioeconomic segregation. The main methodological contribution of RWC is a contextual stochastic optimization model that aims to minimize district-wide segregation by integrating rezoning constraints with a machine learning-based school choice model. The study finds that RWC yields boundary changes that might reduce segregation by a substantial amount (23%) -- but doing so might require the re-assignment of a large number of students, likely to mitigate re-segregation that choice patterns could exacerbate. The results also reveal that predicting school choice is a challenging machine learning problem. Overall, this study offers a novel practical framework that both academics and policymakers might use to foster more diverse and integrated schools.

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 costeffective 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.

This paper analyzes the privacy of traditional Statistical Disclosure Control (SDC) systems under a differential privacy interpretation. SDCs, such as cell suppression and swapping, promise to safeguard the confidentiality of data and are routinely adopted in data analyses with profound societal and economic impacts. Through a formal analysis and empirical evaluation of demographic data from real households in the U.S., the paper shows that widely adopted SDC systems not only induce vastly larger privacy losses than classical differential privacy mechanisms, but, they may also come at a cost of larger accuracy and fairness.

As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the necessary background in quantum computing to comprehend the problem. While this is a well-studied problem, optimization models that minimize the true objective have only been explored recently. This paper introduces a new optimization model and symmetry-breaking constraints that improve solving time by up to two orders of magnitude compared to earlier work when a Constraint Programming solver is used. Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits, obtained by any method, for well-known benchmarks. Several in-depth analyses are presented to validate the effectiveness of the symmetry-breaking constraints from multiple perspectives. Finally, an extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with optimality guarantees.

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.

The Bus Driver Scheduling Problem (BDSP) is a combinatorial optimisation problem with high practical relevance. The aim is to assign bus drivers to predetermined routes while minimising a specified objective function that considers operating costs as well as employee satisfaction. Since we must satisfy several rules from a collective agreement and European regulations, the BDSP is highly constrained. Hence, using exact methods to solve large real-life-based instances is computationally too expensive, while heuristic methods still have a considerable gap to the optimum. Our paper presents a Large Neighbourhood Search (LNS) approach to solve the BDSP. We propose several novel destroy operators and an approach using column generation to repair the sub-problem. We analyse the impact of the destroy and repair operators and investigate various possibilities to select them, including adaptivity. The proposed approach improves all the upper bounds for larger instances that exact methods cannot solve, as well as for some mid-sized instances, and outperforms existing heuristic approaches for this problem on all benchmark instances.

Recent years have witnessed increasing interest in optimization proxies, i.e., machine learning models that approximate the input-output mapping of parametric optimization problems and return near-optimal feasible solutions. Following recent work by (Nellikkath & Chatzivasileiadis, 2021), this paper reconsiders the optimality verification problem for optimization proxies, i.e., the determination of the worst-case optimality gap over the instance distribution. The paper proposes a compact formulation for optimality verification and a gradient-based primal heuristic that brings significant computational benefits to the original formulation. The compact formulation is also more general and applies to non-convex optimization problems. The benefits of the compact formulation are demonstrated on large-scale DC Optimal Power Flow and knapsack problems.

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies. DLL leverages conic duality and the representation power of ML models to provide high-duality, dual-feasible solutions, and therefore valid Lagrangian dual bounds, for linear and nonlinear conic optimization problems. The paper introduces a systematic dual completion procedure, differentiable conic projection layers, and a self-supervised learning framework based on Lagrangian duality. It also provides closed-form dual completion formulae for broad classes of conic problems, which eliminate the need for costly implicit layers. The effectiveness of DLL is demonstrated on linear and nonlinear conic optimization problems. The proposed methodology significantly outperforms a state-of-the-art learning-based method, and achieves 1000x speedups over commercial interior-point solvers with optimality gaps under 0.5\% on average.

This paper reconsiders the On-Demand Multimodal Transit Systems (ODMTS) Design with Adoptions problem (ODMTS-DA) to capture the latent demand in on-demand multimodal transit systems. The ODMTS-DA is a bilevel optimization problem, for which Basciftci and Van Hentenryck proposed an exact combinatorial Benders decomposition. Unfortunately, their proposed algorithm only finds high-quality solutions for medium-sized cities and is not practical for large metropolitan areas. The main contribution of this paper is to propose a new path-based optimization model, called P-Path, to address these computational difficulties. The key idea underlying P-Path is to enumerate two specific sets of paths which capture the essence of the choice model associated with the adoption behavior of riders. With the help of these path sets, the ODMTS-DA can be formulated as a single-level mixed-integer programming model. In addition, the paper presents preprocessing techniques that can reduce the size of the model significantly. P-Path is evaluated on two comprehensive case studies: the midsize transit system of the Ann Arbor – Ypsilanti region in Michigan (which was studied by Basciftci and Van Hentenryck) and the large-scale transit system for the city of Atlanta. The experimental results show that P-Path solves the Michigan ODMTS-DA instances in a few minutes, bringing more than two orders of magnitude improvements compared with the existing approach. For Atlanta, the results show that P-Path can solve large-scale ODMTS-DA instances (about 17 millions variables and 37 millions constraints) optimally in a few hours or in a few days. These results show the tremendous computational benefits of P-Path which provides a scalable approach to the design of on-demand multimodal transit systems with latent demand. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was partially supported by National Science Foundation Leap-HI [Grant 1854684] and the Tier 1 University Transportation Center (UTC): Transit - Serving Communities Optimally, Responsively, and Efficiently (T-SCORE) from the U.S. Department of Transportation [69A3552047141]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0014 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0014 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory’s Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0233 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0233 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Many special events, including sports games and concerts, often cause surges in demand and congestion for transit systems. Therefore, it is important for transit providers to understand their impact on disruptions, delays, and fare revenues. Ridership after large sporting events is distinct from many other ridership patterns due to the high density of ridership localized to a few nearby stations. This paper provides the following novel methodology for long-term planning of large-event, post-game ridership by 1) predicting the total post-game ridership; 2) combining the total prediction with historical trends to forecast the passenger flow curve at nearby stations after the game; and 3) estimating the required train frequencies to serve these customers with minimal passengers left behind by each train. Additionally, this paper proposes a suite of data-driven techniques that together create a data-driven pipeline to exploit Automated Fare Collection (AFC) data for evaluating, anticipating, and managing the performance of transit systems. This paper includes a case study where the proposed pipeline is used to generate an adjusted train schedule for the post-game period and simulated with the rail ridership data from the Metropolitan Atlanta Rapid Transit Authority (MARTA). The simulation results highlight how the proposed schedules based on the estimated required post-game train frequencies could significantly improve post-game congestion and wait time. Furthermore, the results show that the long-term post-game demand forecasts could be an effective tool for tactical planning decisions such as the number of additional trains and operators that are needed during post-game periods compared to the regularly scheduled timetables.

This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must balance optimality and feasibility conditions. Supervised learning methods often approach this challenge by training the model on a large collection of pre-solved instances. This paper takes a different route and proposes the idea of Primal-Dual Learning (PDL), a self-supervised training method that does not require a set of pre-solved instances or an optimization solver for training and inference. Instead, PDL mimics the trajectory of an Augmented Lagrangian Method (ALM) and jointly trains primal and dual neural networks. Being a primal-dual method, PDL uses instance-specific penalties of the constraint terms in the loss function used to train the primal network. Experiments show that, on a set of nonlinear optimization benchmarks, PDL typically exhibits negligible constraint violations and minor optimality gaps, and is remarkably close to the ALM optimization. PDL also demonstrated improved or similar performance in terms of the optimality gaps, constraint violations, and training times compared to existing approaches.

The Autonomous Transfer Hub Network (ATHN) is one of the most promising ways to adapt self-driving trucks for the freight industry. These networks use autonomous trucks for the middle mile, while human drivers perform the first and last miles. This paper extends previous work on optimizing ATHN operations by including transfer hub capacities, which are crucial for labor planning and policy design. It presents a Constraint Programming (CP) model that shifts an initial schedule produced by a Mixed Integer Program to minimize the hub capacities. The scalability of the CP model is demonstrated on a case study at the scale of the United States, based on data provided by Ryder System, Inc. The CP model efficiently finds optimal solutions and lowers the necessary total hub capacity by 42%, saving $15.2M in annual labor costs. The results also show that the reduced capacity is close to a theoretical (optimistic) lower bound.

A critical concern in data-driven processes is to build models whose outcomes do not discriminate against some protected groups. In learning tasks, knowledge of the group attributes is essential to ensure non-discrimination, but in practice, these attributes may not be available due to legal and ethical requirements. To address this challenge, this paper studies a model that protects the privacy of individuals’ sensitive information while also allowing it to learn non-discriminatory predictors. A key feature of the proposed model is to enable the use of off-the-shelves and non-private fair models to create a privacy-preserving and fair model. The paper analyzes the relation between accuracy, privacy, and fairness, and assesses the benefits of the proposed models on several prediction tasks. In particular, this proposal allows both scalable and accurate training of private and fair models for very large neural networks.

Idle vehicle relocation is crucial for addressing demand-supply imbalance that frequently arises in the ride-hailing system. Current mainstream methodologies - optimization and reinforcement learning - suffer from obvious computational drawbacks. Optimization models need to be solved in real-time and often trade off model fidelity (hence quality of solutions) for computational efficiency. Reinforcement learning is expensive to train and often struggles to achieve coordination among a large fleet. This paper designs a hybrid approach that leverages the strengths of the two while overcoming their drawbacks. Specifically, it trains an optimization proxy, i.e., a machine-learning model that approximates an optimization model, and refines the proxy with reinforcement learning. This Reinforcement Learning from Optimization Proxy (RLOP) approach is efficient to train and deploy, and achieves better results than RL or optimization alone. Numerical experiments on the New York City dataset show that the RLOP approach reduces both the relocation costs and computation time significantly compared to the optimization model, while pure reinforcement learning fails to converge due to computational complexity.

The Jobs Shop Scheduling problem (JSP) is a canonical combinatorial optimization problem that is routinely solved for a variety of industrial purposes. It models the optimal scheduling of multiple sequences of tasks, each under a fixed order of operations, in which individual tasks require exclusive access to a predetermined resource for a specified processing time. The problem is NP-hard and computationally challenging even for medium-sized instances. Motivated by the increased stochasticity in production chains, this paper explores a deep learning approach to deliver efficient and accurate approximations to the JSP. In particular, this paper proposes the design of a deep neural network architecture to exploit the problem structure, its integration with Lagrangian duality to capture the problem constraints, and a post-processing optimization, to guarantee solution feasibility. The resulting method, called JSP-DNN, is evaluated on hard JSP instances from the JSPLIB benchmark library and is shown to produce JSP approximations of high quality at negligible computational costs.

This paper surveys the recent work in the intersection of differential privacy (DP) and fairness. It focuses on surveying the work observing that DP systems may exacerbate bias and disparate impacts for different groups of individuals. The survey reviews the conditions under which privacy and fairness may be aligned or contrasting goals, analyzes how and why DP exacerbates bias and unfairness in decision problems and learning tasks, and reviews the available solutions to mitigate the fairness issues arising in DP systems. The survey provides a unified understanding of the main challenges and potential risks arising when deploying privacy-preserving machine learning or decisions making tasks under a fairness lens.

Post-processing immunity is a fundamental property of differential privacy: it enables arbitrary data-independent transformations to differentially private outputs without affecting their privacy guarantees. Post-processing is routinely applied in data-release applications, including census data, which are then used to make allocations with substantial societal impacts. This paper shows that post-processing causes disparate impacts on individuals or groups and analyzes two critical settings: the release of differentially private datasets and the use of such private datasets for downstream decisions, such as the allocation of funds informed by US Census data. In the first setting, the paper proposes tight bounds on the unfairness for traditional post-processing mechanisms, giving a unique tool to decision makers to quantify the disparate impacts introduced by their release. In the second setting, this paper proposes a novel post-processing mechanism that is (approximately) optimal under different fairness metrics, either reducing fairness issues substantially or reducing the cost of privacy. The theoretical analysis is complemented with numerical simulations on Census data.

The learning-to-rank problem aims at ranking items to maximize exposure of those most relevant to a user query. A desirable property of such ranking systems is to guarantee some notion of fairness among specified item groups. While fairness has recently been considered in the context of learning-to-rank systems, current methods cannot provide guarantees on the fairness of the predicted rankings. This paper addresses this gap and introduces Smart Predict and Optimize for Fair Ranking (SPOFR), an integrated optimization and learning framework for fairness-constrained learning to rank. The end-to-end SPOFR framework includes a constrained optimization sub-model and produces ranking policies that are guaranteed to satisfy fairness constraints, while allowing for fine control of the fairness-utility tradeoff. SPOFR is shown to significantly improve on current state-of-the-art fair learning-to-rank systems with respect to established performance metrics.

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications, such as pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel optimization problems in which the upper level problem features some integer variables and the lower level problem enjoys strong duality. We propose a dedicated Benders decomposition method for solving this class of bilevel problems, which decomposes the Benders subproblem into two more tractable, sequentially solvable problems that can be interpreted as the upper and lower level problems. We show that the Benders subproblem decomposition carries over to an interesting extension of bilevel problems, which connects the upper level solution with the lower level dual solution, and discuss some special cases of bilevel problems that allow sequence-independent subproblem decomposition. Several novel schemes for generating numerically stable cuts, finding a good incumbent solution, and accelerating the search tree are discussed. A computational study demonstrates the computational benefits of the proposed method over a state-of-the-art, bilevel-tailored, branch-and-cut method; a commercial solver; and the standard Benders method on standard test cases and the motivating applications in sequential energy markets.

Idle vehicle relocation is crucial for addressing demand-supply imbalance that frequently arises in the ride-hailing system. Current mainstream methodologies - optimization and reinforcement learning - suffer from obvious computational drawbacks. Optimization models need to be solved in real-time and often trade off model fidelity (hence quality of solutions) for computational efficiency. Reinforcement learning is expensive to train and often struggles to achieve coordination among a large fleet. This paper designs a hybrid approach that leverages the strengths of the two while overcoming their drawbacks. Specifically, it trains an optimization proxy, i.e., a machine-learning model that approximates an optimization model, and then refines the proxy with reinforcement learning. This Reinforcement Learning from Optimization Proxy (RLOP) approach is computationally efficient to train and deploy, and achieves better results than RL or optimization alone. Numerical experiments on the New York City dataset show that the RLOP approach reduces both the relocation costs and computation time significantly compared to the optimization model, while pure reinforcement learning fails to converge due to computational complexity.

We present a novel framework for modeling traffic congestion events over road networks. Using multi-modal data by combining count data from traffic sensors with police reports that report traffic incidents, we aim to capture two types of triggering effect for congestion events. Current traffic congestion at one location may cause future congestion over the road network, and traffic incidents may cause spread traffic congestion. To model the non-homogeneous temporal dependence of the event on the past, we use a novel attention-based mechanism based on neural networks embedding for point processes. To incorporate the directional spatial dependence induced by the road network, we adapt the “tail-up” model from the context of spatial statistics to the traffic network setting. We demonstrate our approach’s superior performance compared to the state-of-the-art methods for both synthetic and real data.

A critical concern in data-driven decision making is to build models whose outcomes do not discriminate against some demographic groups, including gender, ethnicity, or age. To ensure non-discrimination in learning tasks, knowledge of the sensitive attributes is essential, while, in practice, these attributes may not be available due to legal and ethical requirements. To address this challenge, this paper studies a model that protects the privacy of the individuals’ sensitive information while also allowing it to learn non-discriminatory predictors. The method relies on the notion of differential privacy and the use of Lagrangian duality to design neural networks that can accommodate fairness constraints while guaranteeing the privacy of sensitive attributes. The paper analyses the tension between accuracy, privacy, and fairness and the experimental evaluation illustrates the benefits of the proposed model on several prediction tasks.

This paper presents a Branch and Price approach for a real-life Bus Driver Scheduling problem with a complex set of break constraints. The column generation uses a set partitioning model as master problem and a resource constrained shortest path problem as subproblem. Due to the complex constraints, the branch and price algorithm adopts several novel ideas to improve the column generation in the presence of a high-dimensional subproblem, including exponential arc throttling and a dedicated two-stage dominance algorithm. Evaluation on a publicly available set of benchmark instances shows that the approach provides the first provably optimal solutions for small instances, improving best-known solutions or proving them optimal for 48 out of 50 instances, and yielding an optimality gap of less than 1% for more than half the instances.

Post-processing immunity is a fundamental property of differential privacy: it enables the application of arbitrary data-independent transformations to the results of differentially private outputs without affecting their privacy guarantees. When query outputs must satisfy domain constraints, post-processing can be used to project them back onto the feasibility region. Moreover, when the feasible region is convex, a widely adopted class of post-processing steps is also guaranteed to improve accuracy. Post-processing has been applied successfully in many applications including census data, energy systems, and mobility. However, its effects on the noise distribution is poorly understood: It is often argued that post-processing may introduce bias and increase variance. This paper takes a first step towards understanding the properties of post-processing. It considers the release of census data and examines, both empirically and theoretically, the behavior of a widely adopted class of post-processing functions.

Many agencies release datasets and statistics about groups of individuals that are used as input to a number of critical decision processes. To conform with privacy and confidentiality requirements, these agencies are often required to release privacy-preserving versions of the data. This paper studies the release of differentially private datasets and analyzes their impact on some critical resource allocation tasks under a fairness perspective. The paper shows that, when the decisions take as input differentially private data, the noise added to achieve privacy disproportionately impacts some groups over others. The paper analyzes the reasons for these disproportionate impacts and proposes guidelines to mitigate these effects. The proposed approaches are evaluated on critical decision problems that use differentially private census data.

This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning architectures. These approaches hold the promise to develop new hybrid machine learning and optimization methods to predict fast, approximate, solutions to combinatorial problems and to enable structural logical inference. This paper presents a conceptual review of the recent advancements in this emerging area.

When demand increases beyond the system capacity, riders in ride-hailing/ride-sharing systems often experience long waiting time, resulting in poor customer satisfaction. This paper proposes a spatio-temporal pricing framework (AP-RTRS) to alleviate this challenge and shows how it naturally complements state-of-the-art dispatching and routing algorithms. Specifically, the pricing optimization model regulates demand to ensure that every rider opting to use the system is served within reason-able time: it does so either by reducing demand to meet the capacity constraints or by prompting potential riders to postpone service to a later time. The pricing model is a model-predictive control algorithm that works at a coarser temporal and spatial granularity compared to the real-time dispatching and routing, and naturally integrates vehicle relocations. Simulation experiments indicate that the pricing optimization model achieves short waiting times without sacrificing revenues and geographical fairness.

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for large-scale instances. Machine learning frameworks that learn to approximate solutions to such hard optimization problems are a potentially promising avenue to address these difficulties, particularly when many closely related problem instances must be solved repeatedly. Supervised learning frameworks can train a model using the outputs of pre-solved instances. However, when the outputs are themselves approximations, when the optimization problem has symmetric solutions, and/or when the solver uses randomization, solutions to closely related instances may exhibit large differences and the learning task can become inherently more difficult. This paper demonstrates this critical challenge, connects the volatility of the training data to the ability of a model to approximate it, and proposes a method for producing (exact or approximate) solutions to optimization problems that are more amenable to supervised learning tasks. The effectiveness of the method is tested on hard non-linear nonconvex and discrete combinatorial problems.

Abstract In zone‐based evacuation planning, the region to evacuate is divided into zones, and each zone must be assigned a path to safety and departure times along the path. Zone‐based evacuations are highly desirable in practice because they allow emergency services to communicate evacuation orders and to control the evacuation more precisely. Zone‐based evacuations may also be combined with contraflows (to maximize the network capacities) and may impose additional constraints on the evacuation path (e.g., path convergence) and the departure times (e.g., non‐preemption). This paper synthesizes existing models and algorithms for large‐scale zone‐based evacuation planning and complements them with some new ones to fill some of the gaps in the design space. Each model and algorithm is also extended to accommodate contraflows. A companion paper evaluates them on a real, large‐scale case study, both from a macroscopic standpoint and through microscopic simulations under a variety of assumptions.

Abstract A companion paper introduces models and algorithms for large‐scale zone‐based evacuation planning in which each evacuation zone is assigned a path to safety and a departure time. It also shows how to combine zone‐based evacuations with contraflows and impose additional path‐convergence and nonpreemptive constraints. This paper evaluates these algorithms on a real, large‐scale case study, both from a macroscopic standpoint and through microscopic simulations under a variety of assumptions. The results quantify, for the first time, the benefits and limitations of contraflows, convergent plans, and nonpreemption, providing unique perspectives on how to deploy these algorithms in practice. They also highlight the approaches best suited to capture each of these design features and the computational burden they impose. The paper also suggests new directions for future research in zone‐based evacuation planning and beyond in order to address the fundamental challenges by emergency services around the world.

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often solved repeatedly under various conditions, either in real-time or in large-scale studies. This need is further exacerbated by the increasing stochasticity of power systems due to renewable energy sources in front and behind the meter. To address these challenges, this paper presents a deep learning approach to the OPF. The learning model exploits the information available in the similar states of the system (which is commonly available in practical applications), as well as a dual Lagrangian method to satisfy the physical and engineering constraints present in the OPF. The proposed model is evaluated on a large collection of realistic medium-sized power systems. The experimental results show that its predictions are highly accurate with average errors as low as 0.2%. Additionally, the proposed approach is shown to improve the accuracy of the widely adopted linear DC approximation by at least two orders of magnitude.

Many applications of machine learning and optimization operate on sensitive data streams, posing significant privacy risks for individuals whose data appear in the stream. Motivated by an application in energy systems, this paper presents OptStream, a novel algorithm for releasing differentially private data streams under the w-event model of privacy. The procedure ensures privacy while guaranteeing bounded error on the released data stream. OptStream is evaluated on a test case involving the release of a real data stream from the largest European transmission operator. Experimental results show that OptStream may not only improve the accuracy of state-of-the-art methods by at least one order of magnitude but also support accurate load forecasting on the privacy-preserving data.

This paper introduces a differentially private (DP) mechanism to protect the information exchanged during the coordination of sequential and interdependent markets. This coordination represents a classic Stackelberg game and relies on the exchange of sensitive information between the system agents. The paper is motivated by the observation that the perturbation introduced by traditional DP mechanisms fundamentally changes the underlying optimization problem and even leads to unsatisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stackelberg Mechanism (PPSM), a framework that enforces the notions of feasibility and fidelity (i.e. near-optimality) of the privacy-preserving information to the original problem objective. PPSM complies with the notion of differential privacy and ensures that the outcomes of the privacy-preserving coordination mechanism are close-to-optimality for each agent. Experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the proposed approach. A full version of this paper [Fioretto et al., 2020b] contains complete proofs and additional discussion on the motivating application.

This paper considers the dispatching of large-scale real-time ride-sharing systems to address congestion issues faced by many cities. The goal is to serve all customers (service guarantees) with a small number of vehicles while minimizing waiting times under constraints on ride duration. This paper proposes an end-to-end approach that tightly integrates a state-of-the-art dispatching algorithm, a machine-learning model to predict zone-to-zone demand over time, and a model predictive control optimization to relocate idle vehicles. Experiments using historic taxi trips in New York City indicate that this integration decreases average waiting times by about 30% over all test cases and reaches close to 55% on the largest instances for high-demand zones.

Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances. Therefore it becomes important to study how best to place them on the grid in order to meet a resiliency criteria, while minimizing costs and capturing their dependencies on the associated communication systems that sustain their distributed operations. This paper introduces the Optimal Resilient Design Problem for Distribution and Communication Systems (ORDPDC) to address this need. The ORDPDC is formulated as a two-stage stochastic mixed-integer program that captures the physical laws of distribution systems, the communication connectivity of the smart grid components, and a set of scenarios that specifies which components are affected by potential disasters. The paper proposes an exact branch-and-price algorithm for the ORDPDC that features a strong lower bound and a variety of acceleration schemes to address degeneracy. The ORDPDC model and branch-and-price algorithm were evaluated on a variety of test cases with varying disaster intensities and network topologies. The results demonstrate the significant impact of the network topologies on the expansion plans and costs, as well as the computational benefits of the proposed approach.

The paper studies how to release data about a critical infrastructure network (e.g., a power network or a transportation network) without disclosing sensitive information that can be exploited by malevolent agents, while preserving the realism of the network. It proposes a novel obfuscation mechanism that combines several privacy-preserving building blocks with a bi-level optimization model to significantly improve accuracy. The obfuscation is evaluated for both realism and privacy properties on real energy and transportation networks. Experimental results show the obfuscation mechanism substantially reduces the potential damage of an attack exploiting the released data to harm the real network.

The growing dependence of electric power systems on gas-fired generators to balance fluctuating and intermittent production by renewable energy sources has increased the variation and volume of flows withdrawn from natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these dynamic conditions requires optimization methods that account for substantial intraday transients and can rapidly compute solutions in reaction to generator re-dispatch. Here, we present a computationally efficient method for minimizing gas compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flows. The optimization method uses a simplified representation of gas flow physics, provides a choice of discretization schemes in time and space, and exploits a two-stage approach to minimize energy costs and ensure smooth and physically meaningful solutions. The resulting large-scale NLPs are solved using an interior point method. The optimization scheme is validated by comparing the solutions with an integration of the dynamic equations using an adaptive timestepping differential equation solver, as well as a different, recently proposed optimal control scheme. The comparison shows that solutions to the discretized problem are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme produces at least an order of magnitude reduction in computation time relative to the state of the art and scales to large gas transmission networks with more than 6,000 kilometers of total pipeline. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0821 .

Many applications of machine learning and optimization operate on data streams. While these datasets are fundamental to fuel decision-making algorithms, often they contain sensitive information about individuals, and their usage poses significant privacy risks. Motivated by an application in energy systems, this paper presents OptStream, a novel algorithm for releasing differentially private data streams under the w-event model of privacy. OptStream is a 4-step procedure consisting of sampling, perturbation, reconstruction, and post-processing modules. First, the sampling module selects a small set of points to access in each period of interest. Then, the perturbation module adds noise to the sampled data points to guarantee privacy. Next, the reconstruction module re-assembles non-sampled data points from the perturbed sample points. Finally, the post-processing module uses convex optimization over the privacy-preserving output of the previous modules, as well as the privacy-preserving answers of additional queries on the data stream, to improve accuracy by redistributing the added noise. OptStream is evaluated on a test case involving the release of a real data stream from the largest European transmission operator. Experimental results show that OptStream may not only improve the accuracy of state-of-the-art methods by at least one order of magnitude but also supports accurate load forecasting on the privacy-preserving data.

This paper explores Community-Based Trip Sharing which uses the structure of communities and commuting patterns to optimize car or ride sharing for urban communities. It introduces the Commuting Trip Sharing Problem (CTSP) and proposes an optimization approach to maximize trip sharing. The optimization method, which exploits trip clustering, shareability graphs, and mixed-integer programming, is applied to a dataset of 9000 daily commuting trips from a mid-size city. Experimental results show that community-based trip sharing reduces daily car usage by up to 44%, thus producing significant environmental and traffic benefits and reducing parking pressure. The results also indicate that daily flexibility in pairing cars and passengers has significant impact on the benefits of the approach, revealing new insights on commuting patterns and trip sharing.

Social influence has been shown to create a Matthew effect in online markets, increasing inequalities and leading to “winner-take-all” phenomena. Matthew effects have been observed for numerous market policies, including when the products are presented to consumers by popularity or quality. This paper studies how to reduce Matthew effects, while keeping markets efficient and predictable when social influence is used. It presents a market strategy based on randomization and segmentation, that ensures that the best products, if they are close in quality, will have reasonably close market shares. The benefits of this market strategy is justified both theoretically and empirically and the loss in market efficiency is shown to be acceptable.

Unpredictability is often portrayed as an undesirable outcome of social influence in cultural markets. Unpredictability stems from the "rich get richer" effect, whereby small fluctuations in the market share or popularity of products are amplified over time by social influence. In this paper, we report results of an experimental study that shows that unpredictability is not an inherent property of social influence. We investigate strategies for creating markets in which the popularity of products is better-and more predictably-aligned with their underlying quality. For our study, we created a cultural market of science stories and conducted randomized experiments on different policies for presenting the stories to study participants. Specifically, we varied how the stories were ranked, and whether or not participants were shown the ratings these stories received from others. We present a policy that leverages social influence and product positioning to help distinguish the product's market share (popularity) from underlying quality. Highlighting products with the highest estimated quality reduces the "rich get richer" effect highlighting popular products. We show that this policy allows us to more robustly and predictably identify high quality products and promote blockbusters. The policy can be used to create more efficient online cultural markets with a better allocation of resources to products.

Modeling and predicting the popularity of online content is a significant problem for the practice of information dissemination, advertising, and consumption. Recent work analyzing massive datasets advances our understanding of popularity, but one major gap remains: To precisely quantify the relationship between the popularity of an online item and the external promotions it receives. This work supplies the missing link between exogenous inputs from public social media platforms, such as Twitter, and endogenous responses within the content platform, such as YouTube. We develop a novel mathematical model, the Hawkes intensity process, which can explain the complex popularity history of each video according to its type of content, network of diffusion, and sensitivity to promotion. Our model supplies a prototypical description of videos, called an endo-exo map. This map explains popularity as the result of an extrinsic factor -- the amount of promotions from the outside world that the video receives, acting upon two intrinsic factors -- sensitivity to promotion, and inherent virality. We use this model to forecast future popularity given promotions on a large 5-months feed of the most-tweeted videos, and found it to lower the average error by 28.6% from approaches based on popularity history. Finally, we can identify videos that have a high potential to become viral, as well as those for which promotions will have hardly any effect.

With rapid population growth and urbanization, emergency services in various cities around the world worry that the current transportation infrastructure is no longer adequate for large-scale evacuations. This paper considers how to mitigate this issue through infrastructure upgrades, such as the additions of lanes to road segments and the raising of bridges and roads. The paper proposes a MIP model for deciding the most effective infrastructure upgrades as well as a Benders decomposition approach where the master problem jointly plans the upgrades and evacuation routes and the subproblem schedules the evacuation itself. Experimental results demonstrate the practicability of the approach on a real case study, filling a significant need for emergencies services.

This paper considers prescriptive evacuation planning for a region threatened by a natural disaster such a flood, a wildfire, or a hurricane. It proposes a Benders decomposition that generalizes the two-stage approach proposed in earlier work for convergent evacuation plans. Experimental results show that Benders decomposition provides significant improvements in solution quality in reasonable time: It finds provably optimal solutions to scenarios considered in prior work, closing these instances, and increases the number of evacuees by 10 to 15% on average on more complex flood scenarios.

Conservation is an ethic of sustainable use of natural resources which focuses on the preservation of biodiversity, i.e., the degree of variation of life. Conservation planning seeks to reach this goal by means of deliberate actions, aimed at the protection (or restoration) of biodiversity features. In this paper we present an intelligent system to assist conservation managers in planning habitat restoration actions, with focus on the activities to be carried out in the islands of the Great Barrier Reef (QLD) and the Pilbara (WA) regions of Australia. In particular, we propose a constrained optimisation formulation of the habitat restoration planning (HRP) problem, capturing aspects such as population dynamics and uncertainty. We show that the HRP is NP-hard, and develop a constraint programming (CP) model and a large neighbourhood search (LNS) procedure to generate activity plans under budgeting constraints.

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the nonconvex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solutions.

Evacuation planning is a critical aspect of disaster preparedness and response to minimize the number of people exposed to a threat. Controlled evacuations aim at managing the flow of evacuees as efficiently as possible and have been shown to produce significant benefits compared to self-evacuations. However, existing approaches do not capture the delays introduced by diverging and crossing evacuation routes, although evidence from actual evacuations highlights that these can lead to significant congestion. This paper introduces the concept of convergent evacuation plans to tackle this issue. It presents a MIP model to obtain optimal convergent evacuation plans which, unfortunately, does not scale to realistic instances. The paper then proposes a two-stage approach that separates the route design and the evacuation scheduling. Experimental results on a real case study show that the two-stage approach produces better primal bounds than the MIP model and is two orders of magnitude faster; It also produces dual bounds stronger than the linear relaxation of the MIP model. Finally, simulations of the evacuation demonstrate that convergent evacuation plans outperform existing approaches for realistic driver behaviors.

We address the problem of power system restoration after a significant blackout. Prior work focus on optimization methods for finding high-quality restoration plans. Optimal solutions consist in a sequence of grid repairs and corresponding steady states. However, such approaches lack formal guarantees on the transient stability of restoration actions, a key property to avoid additional grid damage and cascading failures. In this paper, we show how to integrate transient stability in the optimization procedure by capturing the rotor dynamics of power generators. Our approach reasons about the differential equations describing the dynamics and their underlying transient states. The key contribution lies in modeling and solving optimization problems that return stable generators dispatch minimizing the difference with respect to steady states solutions. Computational efficiency is increased using preprocessing procedures along with traditional reduction techniques. Experimental results on existing benchmarks confirm the feasibility of the new approach.

Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. This led to general modelling techniques and generic propagators, often based on deterministic finite automata (DFA) and their extensions. We consider counter-DFAs (cDFA), which provide concise models for regular counting constraints, that is constraints over the number of times a regular-language pattern occurs in a sequence. We show how to enforce domain consistency in polynomial time for at-most and at-least regular counting constraints based on the frequent case of a cDFA with only accepting states and a single counter that can be increased by transitions. We also show that the satisfaction of exact regular counting constraints is NP-hard and that an incomplete propagator for exact regular counting constraints is faster and provides more pruning than the existing propagator from (Beldiceanu, Carlsson, and Petit 2004). Finally, by avoiding the unrolling of the cDFA used by COSTREGULAR, the space complexity reduces from O(n · |Σ| · |Q|) to O(n · (|Σ| + |Q|)), where Σ is the alphabet and Q the state set of the cDFA.

Evacuations are a critical aspect of disaster management, and generally the first prevention measure to ensure the safety of the population under threat. Designing evacuation plans is a complex task that requires to take into account multiple factors in order to limit congestion and ensure that all evacuees reach safety in time. This paper proposes a conflict-based path-generation algorithm for evacuation planning and a web-based intelligent system targeted at local authorities and emergency services. The key contribution of this paper is to propose the first scalable approach to produce actionable evacuation plans that simultaneously schedules the evacuation and selects contraflow roads. The benefits of the approach are illustrated on two large-scale case studies. The resulting optimization model is integrated in NICTA EVACUATION PLANNER, a tool to model, plan, and simulate evacuations.

The practice of discrete optimization involves modeling and solving complex combinatorial problems which have never been encountered before and for which no universal computational paradigm exists. Teaching such skills is challenging: Students must learn, not only the core technical skills, but also an ability to think creatively in order to select and adapt a paradigm to solve the problem at hand. This paper explores the question of whether the teaching of such creative skills translates to massive open online courses (MOOCs). It first describes a methodology for teaching discrete optimization that has been successful on campus over fifteen years. It then discusses how to adapt the campus format to a MOOC version. The success of the approach is evaluated through extensive data analytics enabled by the wealth of information produced by MOOCs.

Linear active-power-only power flow approximations are pervasive in the planning and control of power systems. However, AC power systems are governed by a system of nonlinear nonconvex power flow equations. Existing linear approximations fail to capture key power flow variables, including reactive power and voltage magnitudes, both of which are necessary in many applications that require voltage management and AC power flow feasibility. This paper proposes novel linear-programming models (the LPAC models) that incorporate reactive power and voltage magnitudes in a linear power flow approximation. The LPAC models are built on a polyhedral relaxation of the cosine terms in the AC equations as well as Taylor approximations of the remaining nonlinear terms. Experimental comparisons with AC solutions on a variety of standard IEEE and Matpower benchmarks show that the LPAC models produce accurate values for active and reactive power, phase angles, and voltage magnitudes. The potential benefits of the LPAC models are illustrated on two “proof-of-concept” studies in power restoration and capacitor placement.

This paper considers the restoration of multiple interdependent infrastructures after a man-made or natural disaster. Modern infrastructures feature complex cyclic interdependencies and require a holistic restoration process. This paper presents the first scalable approach for the last-mile restoration of the joint electrical power and gas infrastructures. It builds on an earlier three-stage decomposition for restoring the power network that decouples the restoration ordering and the routing aspects. The key contributions of the paper are (1) mixed-integer programming models for finding a minimal restoration set and a restoration ordering and (2) a randomized adaptive decomposition to obtain high-quality solutions within the required time constraints. The approach is validated on a large selection of benchmarks based on the United States infrastructures and state-of-the-art weather and fragility simulation tools. The results show significant improvements over current field practices.

This paper considers matrix models, a class of CSPs which generally exhibit significant symmetries. It proposed the idea of LexLeader feasibility checkers that verify, during search, whether the current partial assignment can be extended into a canonical solution. The feasibility checkers are based on a novel result by [Katsirelos et al., 2010] on how to check efficiently whether a solution is canonical. The paper generalizes this result to partial assignments, various variable orderings, and value symmetries. Empirical results on 5 standard benchmarks shows that feasibility checkers may bring significant performance gains, when jointly used with DOUBLELEX or SNAKELEX.

Protein structure prediction is regarded as a highly challenging problem both for the biology and for the computational communities. In recent years, many approaches have been developed, moving to increasingly complex lattice models and off-lattice models. This paper presents a Large Neighborhood Search (LNS) to find the native state for the Hydrophobic-Polar (HP) model on the Face-Centered Cubic (FCC) lattice or, in other words, a self-avoiding walk on the FCC lattice having a maximum number of H-H contacts. The algorithm starts with a tabu-search algorithm, whose solution is then improved by a combination of constraint programming and LNS. The flexible framework of this hybrid algorithm allows an adaptation to the Miyazawa-Jernigan contact potential, in place of the HP model, thus suggesting its potential for tertiary structure prediction. Benchmarking statistics are given for our method against the hydrophobic core threading program HPstruct, an exact method which can be viewed as complementary to our method.

The availability of commodity multicore and multiprocessor machines and the inherent parallelism in constraint programming search offer significant opportunities for constraint programming. These opportunities also present a fundamental challenge: how to exploit parallelism transparently to speed up constraint programs. This paper shows how to parallelize constraint programs transparently without changes to the sequential code. The main technical idea consists of automatically lifting a sequential exploration strategy into its parallel counterpart, allowing workers to share and steal subproblems. Experimental results show that the parallel implementation may produce significant speedups on multicore machines.

Constraint programming is a success story for artificial intelligence. It quickly moved from research laboratories to industrial applications and is in daily use to solve complex optimization throughout the world. At the same time, constraint programming continued to evolve, addressing new needs and opportunities. This talk reviews some recent progress in constraint programming, including its hybridization with other optimization approaches, the quest for more autonomous search, and its applications in a variety of nontraditional areas.

The introduction of edge-finding techniques was a significant development in constraint-based scheduling. Today, edge finders are still the state of the art in the disjunctive case and a technique of interest in cumulative scheduling. This paper reconsiders edge-finding algorithms for cumulative scheduling and shows that Nuijten's edge finder, and its derivatives, are incomplete because they use an invalid dominance rule. We then present a correct cumulative edge finder running in time O(n2k), where n is the number of tasks and k the number of different capacity requirements of the tasks. The new algorithm is organized in two phases and first uses dynamic programming to precompute the innermost maximization in the edge-finder specification. The paper also proposes the first extended edge-finding algorithms that run in time O(n2k), improving the running time of available algorithms. Finally, the paper discusses how to speed up the algorithm in practice and how the first phase can be used to improve algorithms based on energetic reasoning.

Finding Golomb rulers is an extremely challenging optimization problem (with many practical applications) that has been approached by a variety of search methods in recent years. This paper presents a hybrid evolutionary algorithm to find near-optimal Golomb rulers in reasonable time. The algorithm, which is conceptual simple and uses a natural modeling, focuses on feasibility, finding near-optimal rulers indirectly. It significantly outperforms earlier (hybrid) evolutionary algorithms and compares favorably with hybridizations of local search and constraint programming. In particular, the algorithm quickly finds optimal rulers with up to 11 marks and isolates optimal rulers with up to 14 marks in reasonable time. It also finds near-optimal rulers for up to 16 marks quickly.

Mathematical-modeling and constraint-programming languages have orthogonal strengths in stating combinatorial optimization problems. Modeling languages typically feature high-level set and algebraic notations, while constraint-programming languages provide a rich constraint language and the ability to specify search procedures. This paper shows that many of the functionalities typically found in modeling languages can be integrated elegantly in constraint-programming libraries without defining a specific language or preprocessor. In particular, it presents the design of Modeler, a C++ modeling layer for constraint programming which demonstrates how to enhance the expressiveness of constraint-programming libraries and to bridge much of the gap between libraries and modeling languages.

Search strategies, that is, strategies that describe how to explore search trees, have raised much interest for constraint satisfaction in recent years. In particular, limited discrepancy search and its variations have been shown to achieve significant improvements in efficiency over depth-first search for some classes of applications.This article reconsiders the implementation of discrepancy search, and of search strategies in general, for applications where the search procedure is dynamic, randomized, and/or generates global cuts (or nogoods) that apply to the remaining search. It illustrates that recomputation-based implementations of discrepancy search are not robust with respect to these extensions and require special care which may increase the memory requirements significantly and destroy the genericity of the implementation.To remedy these limitations, the article proposes a novel implementation scheme based on problem decomposition, which combines the efficiency of the recomputation-based implementations with the robustness of traditional iterative implementations. Experimental results on job-shop scheduling problems illustrate the potential of this new implementation scheme, which, surprisingly, may significantly outperform recomputation-based schemes.

Combinatorial optimization problems are ubiquitous in numerous practical applications. Yet most of them are challenging, both from computational complexity and programming standpoints. Local search is one of the main approaches to address these problems. However, it often requires sophisticated incremental algorithms and data structures, and considerable experimentation. This paper proposes a constraint-based, object-oriented, architecture to reduce the development time of local search algorithms significantly. The architecture consists of declarative and search components. The declarative component includes invariants, which maintain complex expressions incrementally, and differentiable objects, which maintain properties that can be queried to evaluate the effect of local moves. Differentiable objects are high-level modeling concepts, such as constraints and functions, that capture combinatorial substructures arising in many applications. The search component supports various abstractions to specify heuristics and meta-heuristics. We illustrate the architecture with the language Comet and several applications, such as car sequencing and the progressive party problem. The applications indicate that the architecture allows for very high-level modeling of local search algorithms, while preserving excellent performance.

In recent years, it has been increasingly recognized that constraint and integer programming have orthogonal and complementary strengths in stating and solving combinatorial optimization applications. In addition, their integration has become an active research topic. The optimization programming language OPL was a first attempt at integrating these technologies both at the language and at the solver levels. In particular, OPL is a modeling language integrating the rich language of constraint programming and the ability to specify search procedures at a high level of abstraction. Its implementation includes both constraint and mathematical programming solvers, as well as some cooperation schemes to make them collaborate on a given problem. The purpose of this paper is to illustrate, using OPL, the constraint-programming approach to combinatorial optimization and the complementary strengths of constraint and integer programming.

Abstract interpretation is a general methodology for systematic development of program analyses. An abstract interpretation framework is centered around a parametrized non-standard semantics that can be instantiated by various domains to approximate different program properties. Many abstract interpretation frameworks and analyses for Prolog have been proposed, which seek to extract information useful for program optimization. Although motivated by practical considerations, notably making Prolog competitive with imperative languages, such frameworks fail to capture some of the control structures of existing implementations of the language. In this paper, we propose a novel framework for the abstract interpretation of Prolog which handles the depth-first search rule and the cut operator. It relies on the notion of substitution sequence to model the result of the execution of a goal. The framework consists of (i) a denotational concrete semantics, (ii) a safe abstraction of the concrete semantics defined in terms of a class of post-fixpoints, and (iii) a generic abstract interpretation algorithm. We show that traditional abstract domains of substitutions may easily be adapted to the new framework, and provide experimental evidence of the effectiveness of our approach. We also show that previous work on determinacy analysis, that was not expressible by existing abstract interpretation frameworks, can be seen as an instance of our framework. The ideas developed in this paper can be applied to other logic languages, notably to constraint logic languages, and the theoretical approach should be of general interest for the analysis of many non-deterministic programming languages.

OPL is a modeling language for mathematical programming and combinatorial optimization. It is the first language to combine high-level algebraic and set notations from mathematical modeling languages with a rich constraint language and the ability to specify search procedures and strategies that are the essence of constraint programming. This paper describes the facilities available in OPL to specify search procedures. It describes the abstractions of OPL to specify both the search tree (search) and how to explore it (strategies). The paper also illustrates how to use these high-level constructs to implement traditional search procedures in constraint programming and scheduling.

Local search is a traditional technique to solve combinatorial search problems and has raised much interest in recent years. The design and implementation of local search algorithms is not an easy task in general and may require considerable experimentation and programming effort. However, contrary to global search, little support is available to assist the design and implementation of local search algorithms. This paper is an attempt to support the implementation of local search. It presents the preliminary design of LOCALIZER, a modeling language which makes it possible to express local search algorithms in a notation close to their informal descriptions in scientific papers. Experimental results on our first implementation show the feasibility of the approach.

This paper examines the role of dependence analysis in defimng bindingtime analyses (BTAs) for imperative programs and in establishing that such BTAs are safe.In particular, we are concerned with characterizing safety conditions under which a program specialize that uses the results of a BTA is guaranteed to terminate.Our safety conditions are formalized wa semantic characterizations of the statements in a program along two dimensions: srartc versus dynamic, and finite versus injinife.This permits us to give a semantic definition of "static-infinite computation", a concept that has not been previously formalized.To illustrate the concepts, we present three different BTAs for an imperative language, we show that two of them me safe in the absence of "static-infinite computations".In developing these notions, we make use of program represenrarion graphs, which are a program representation similar to the dependence graphs used in parallelizing and vectorizing compilers.In operational terms, our BTAs are related to the operation ofprogrrrm slicing, which can be implemented using such graphs.

Type analysis of Prolog is of primary importance for high-performance compilers, since type information may lead to better indexing and to sophisticated specializations of unification and built-in predicates to name a few. However, these optimizations often require a sophisticated type inference system capable of inferring disjunctive and recursive types and hence expensive in computation time.

Constraint logic programming (CLP) is a generalization of logic programming where unification is replaced by constraint solving as the basic operation of the language. The combination of constraint solving and nondeterminism (approximated by backtracking) makes these languages appealing for a variety of combinatorial search problems. Existing CLP languages support backtracking by generalizing traditional Prolog implementations: modifications to the constraint system are trailed and restored on backtracking. Although simple and efficient, trailing may be very demanding in memory space, since the constraint system may potentially be saved at each choice point. This paper proposes a fundamentally new implementation scheme for backtracking in CLP languages over linear (rational or real) arithmetic. The new scheme, called semantic backtracking, does not use trailing but rather exploits the semantics of the constraints to undo the effect of newly added constraints. Semantic backtracking reduces the space complexity by an order of magnitude compared to implementations based on trailing and makes space complexity essentially independent of the number of choice points. In addition, semantic backtracking introduces negligible space and time overhead on deterministic programs. The price for this improvement is an increase in backtracking time, although constraint-solving time may actually decrease. The scheme has been implemented as part of a complete CLP system CLP(RLin) and compared analytically and experimentally with an optimized trailing implementation. Experimental results indicate that semantic backtracking produces significant reduction in memory space, while keeping the time overhead reasonably small.

Abstract interpretation [7] is a systematic methodology to design static program analysis which has been studied extensively in the logic programming community, because of the potential for optimizations in logic programming compilers and the sophistication of the analyses which require conceptual support. With the emergence of efficient generic abstract interpretation algorithms for logic programming, the main burden in building an analysis is the abstract domain which gives a safe approximation of the concrete domain of computation. However, accurate abstract domains for logic programming are often complex because of the variety of analyses to perform their interdependence, and the need to maintain structural information. The purpose of this paper is to propose conceptual and software support for the design of abstract domains. It contains two main contributions: the notion of open product and a generic pattern domain. The open product is a new way of combining abstract domains allowing each combined domain to benefit from information from the other components through the notions of queries and open operations. The open product is general-purpose and can be used for other programming paradigms as well. The generic pattern domain Pat (R)automatically upgrades a domain D with structural information yielding a more accurate domain Pat (D) without additional design or implementation cost. The two contributions are orthogonal and can be combined in various ways to obtain sophisticated domains while imposing minimal requirements on the designer. Both contributions are characterized theoretically and experimentally and were used to design very complex abstract domains such as PAT(OProp⊗OMode⊗OPS) which would be very difficult to design otherwise. On this last domain, designers need only contribute about 20% (about 3,400 lines) of the complete system (about 17,700 lines).

Abstract interpretation of PROLOG programs has attracted many researchers in recent years, partly because of the potential for optimization in PROLOG compilers and partly because of the declarative nature of logic programming languages that make them more amenable to optimization than procedural languages. Most of the work, however, has remained at the theoretical level, focusing on the developments of frameworks and the definition of abstract domains. This paper reports our effort to verify experimentally the practical value of this area of research. It describes the design and implementation of the generic abstract interpretation algorithm GAIA that we originally proposed in Le Charlier et al. [1991], its instantiation to a sophisticated abstract domain (derived from Bruynooghe and Janssens [1988]) containing modes, types, sharing, and aliasing, and its evaluation both in terms of performance and accuracy. The overall implementation (over 5000 lines of Pascal) has been systematically analyzed on a variety of programs and compared with the complexity analysis of Le Charlie et al. [1991] and the specific analysis systems of Hickey and Mudambi [1989], Taylor [1989; 1990], Van Roy and Despain [1990], and Warren et al. [1988].

Combinatorial search problems are ubiquitous in computer science and appears in many application areas, including operations research, hardware design, computational geometry, and finance. I take the position that constraint programming languages will play an increasingly important role in the development of these applications. The basic motivation behind these languages is to support well established paradigms and constraint solving techniques inside programming languages to: reduce the development time of these applications significantly; and preserve most of the efficiency of specialized algorithms.

The domain Prop [22,8] is a conceptually simple and elegant abstract domain to compute groundness information for Prolog programs. In particular, abstract substitutions are represented by Boolean functions built using the logical connectives ⇔, ∨, ∧. Prop has raised much theoretical interest recently but little is known about the practical accuracy and efficiency of this domain.In this paper, we describe an implementation of Prop and we use it to instantiate a generic abstract interpretation algorithm [14, 10, 17, 15]. A key feature of the implementation is the use of ordered binary decision graphs. The implementation has been compared systematically to two other abstract domains, Mode and Pattern, from the point of view of groundness analysis.The experimental results indicate that (1)Prop is very accurate to infergroundness information; (2) this domain is quite practical in terms of efficiency, although it is theoretically exponential (in the number of clause variables).

Abstract The efficient implementation of generic abstract interpretation algorithms for Prolog is reconsidered after References 1 and 2. Two new optimization techniques are proposed and applied to the original algorithm of Reference 1: dependency on clause prefixes and caching of operations. The first improvement avoids re‐evaluating a clause prefix when no abstract value which it depends on has been updated. The second improvement consists of caching all operations on substitutions and reusing the results whenever possible. The algorithm and the two optimization techniques have been implemented in C (about 8000 lines of code each), tested on a large number of Prolog programs, and compared with the original implementation on an abstract domain containing modes, types and sharing. In conjunction with refinements of the domain algorithms, they produce an average reduction of more than 58 per cent is computation time. Extensive experimental results on the programs are given, including computation times, memory consumption, hit ratios for the caches, the number of operations performed, and the time distribution. As a main result, the improved algorithms exhibit the same efficiency as the specific tools of References 3 and 4, despite the fact that our abstract domain is more sophisticated and accurate. The abstract operations also take 90 per cent of the computation time, indicating that the overhead of the control is very limited. Results on a simpler domain are also given and show that even extremely basic domains can benefit from the optimizations. The general‐purpose character of the optimizations is also discussed.