The column generation technique is essential for solving linear programs with an exponential number of variables. Many important applications such as the vehicle routing problem (VRP) now require it. However, in practice, getting column generation to converge is challenging. It often ends up adding too many columns. In this work, we frame the problem of selecting which columns to add as one of sequential decisionmaking. We propose a neural column generation architecture that iteratively selects columns to be added to the problem. The architecture, inspired by stabilization techniques, first predicts the optimal duals. These predictions are then used to obtain the columns to add. We show using VRP instances that in this setting several machine learning models yield good performance on the task and that our proposed architecture learned using imitation learning outperforms a modern stabilization technique.

Building smart transportation services in urban cities has become a worldwide problem owing to the rapidly increasing global population and the development of Internet-of-Things applications. Traffic congestion and environmental concerns can be alleviated by sharing mobility, which reduces the number of vehicles on the road network. The taxi-parcel sharing problem has been considered as an efficient planning model for people and goods flows. In this paper, we enhance the functionality of a current people-parcel taxi sharing model. The adapted model analyzes the historical request data and predicts the current service demands. We then propose two novel online routing algorithms that construct optimal routes in real-time. The objectives are to maximize (as far as possible) both the parcel delivery requests and ride requests while minimizing the idle time and travel distance of the taxis. The proposed online routing algorithms are evaluated on instances adapted from real Cabspotting datasets. After implementing our routing algorithms, the total idle travel distance per day was 9.64% to 12.76% lower than that of the existing taxi-parcel sharing method. Our online routing algorithms can be incorporated into an efficient smart shared taxi system.

Kidney transplant is the preferred method of treatment for patients suffering from kidney failure. However, not all patients can find a donor which matches their physiological characteristics. Kidney exchange programs (KEPs) seek to match such incompatible patient-donor pairs together, usually with the main objective of maximizing the total number of transplants. Since selecting one optimal solution translates to a decision on who receives a transplant, it has a major effect on the lives of patients. The current practice in selecting an optimal solution does not necessarily ensure fairness in the selection process. In this paper, the existence of multiple optimal plans for a KEP is explored as a mean to achieve individual fairness. We propose the use of randomized policies for selecting an optimal solution in which patients' equal opportunity to receive a transplant is promoted. Our approach gives rise to the problem of enumerating all optimal solutions, which we tackle using a hybrid of constraint programming and linear programming. The advantages of our proposed method over the common practice of using the optimal solution obtained by a solver are stressed through computational experiments. Our methodology enables decision makers to fully control KEP outcomes, overcoming any potential bias or vulnerability intrinsic to a deterministic solver.

We present an extensive study of methods for exactly solving stochastic constraint (optimisation) problems (SCPs) in network analysis. These problems are prevalent in science, governance and industry. The first method we study is generic and decomposes stochastic constraints into a multitude of smaller local constraints that are solved using a constraint programming (CP) or mixed-integer programming (MIP) solver. However, many SCPs are formulated on probability distributions with a monotonic property, meaning that adding a positive decision to a partial solution to the problem cannot cause a decrease in solution quality. The second method is specifically designed for solving global stochastic constraints on monotonic probability distributions (SCMDs) in CP. Both methods use knowledge compilation to obtain a decision diagram encoding of the relevant probability distributions, where we focus on ordered binary decision diagrams (OBDDs). We discuss theoretical advantages and disadvantages of these methods and evaluate them experimentally. We observed that global approaches to solving SCMDs outperform decomposition approaches from CP, and perform complementarily to MIP-based decomposition approaches, while scaling much more favourably with instance size. Both methods have many alternative design choices, as both knowledge compilation and constraint solvers are used in a single pipeline. To identify which configurations work best, we apply programming by optimisation. Specifically, we show how an automated algorithm configurator can be used to find optimised configurations of our pipeline. After configuration, our global SCMD solving pipeline outperforms its closest competitor (a MIP-based decomposition pipeline) on all test sets we considered by up to two orders of magnitude in terms of PAR10 scores.

The combinatorial problems that constraint programming typically solves belong to the class of NP-hard problems. The AI planning community focuses on even harder problems: for example, classical planning is PSPACE-hard. A natural and well-known constraint programming approach to classical planning solves a succession of fixed plan-length problems, but with limited success. We revisit this approach in light of recent progress on general-purpose branching heuristics. We conduct an empirical comparison of our proposal against state-of-the-art planners.

Semi-supervised or constrained graph clustering incorporates prior information in order to improve clustering results. Pairwise constraints are often utilized to guide the clustering process. This work addresses a constrained graph clustering problem in biological networks where (1) subgraph connectivity constraints are strictly required to be satisfied and (2) clustering quality is assessed with respect to pairwise constraint violations. Existing constrained graph clustering methods often fail to fully satisfy connectivity constraints. This paper presents an iterated local search algorithm which aims to find the clustering with the highest quality in a short computing time. Experiments demonstrate how the proposed solutions are of good quality, often being optimal. Additionally, the proposed method significantly outperforms an existing branch-and-cut algorithm in terms of computational runtime and produces competitive results with regard to other local search techniques and graph clustering algorithms. Furthermore, a multilevel algorithm for clustering is designed to handle large-scale graphs. The performance of the overall scheme for a variety of coarsening methods from the literature is studied on a large number of biological networks exceeding 10,000 genes.

The problem of selecting a subset of nodes with greatest influence in a graph, commonly known as influence maximization, has been well studied over the past decade. This problem has real world applications which can potentially affect lives of individuals. Algorithmic decision making in such domains raises concerns about their societal implications. One of these concerns, which surprisingly has only received limited attention so far, is algorithmic bias and fairness. We propose a flexible framework that extends and unifies the existing works in fairness-aware influence maximization. This framework is based on an integer programming formulation of the influence maximization problem. The fairness requirements are enforced by adding linear constraints or modifying the objective function. Contrary to the previous work which designs specific algorithms for each variant, we develop a formalism which is general enough for specifying different notions of fairness. A problem defined in this formalism can be then solved using efficient mixed integer programming solvers. The experimental evaluation indicates that our framework not only is general but also is competitive with existing algorithms.

As machine learning is increasingly used to make real-world decisions, recent research efforts aim to define and ensure fairness in algorithmic decision making. Existing methods often assume a fixed set of observable features to define individuals, but lack a discussion of certain features not being observed at test time. In this paper, we study fairness of naive Bayes classifiers, which allow partial observations. In particular, we introduce the notion of a discrimination pattern, which refers to an individual receiving different classifications depending on whether some sensitive attributes were observed. Then a model is considered fair if it has no such pattern. We propose an algorithm to discover and mine for discrimination patterns in a naive Bayes classifier, and show how to learn maximum-likelihood parameters subject to these fairness constraints. Our approach iteratively discovers and eliminates discrimination patterns until a fair model is learned. An empirical evaluation on three real-world datasets demonstrates that we can remove exponentially many discrimination patterns by only adding a small fraction of them as constraints.

Compared to most other computational approaches to solving combinatorial problems, Constraint Programming's distinctive feature has been its very high-level modeling primitives which expose much of the combinatorial substructures of a problem. Weighted counting on these substructures (i.e. constraints) can be used to compute beliefs about certain variable-value assignments occurring in a solution to the given constraint. A recent proposal generalizes the propagation mechanism of constraint programming to one sharing such beliefs between constraints. These beliefs, even if not computed exactly, can be very revealing for search. In this paper we investigate how best to guide combinatorial search in this cp-based belief propagation framework. We empirically evaluate branching heuristics on a wide set of benchmark constraint satisfaction problems.

Reduction to a sequence of SAT problems has been a main approach for solving parallel planning problems for a long time. However, attempts at using constraint programming (CP) solvers for this purpose have witnessed relatively limited success. We show that existing CP formulations can deliver competitive results when a lazy clause generation solver (which is a hybrid of SAT and CP) is employed. This suggests promise for future cross-fertilization in SAT, CP, and AI planning.

Not all patients who need kidney transplant can find a donor with compatible characteristics. Kidney exchange programs (KEPs) seek to match such incompatible patient-donor pairs together, usually with the objective of maximizing the total number of transplants. We propose a randomized policy for selecting an optimal solution in which patients’ equity of opportunity to receive a transplant is promoted. Our approach gives rise to the problem of enumerating all optimal solutions, which we tackle using a hybrid of constraint programming and linear programming. We empirically demonstrate the advantages of our proposed method over the common practice of using the first optimal solution obtained by a solver.

A number of data mining problems on probabilistic networks can be modeled as Stochastic Constraint Optimization and Satisfaction Problems, i.e., problems that involve objectives or constraints with a stochastic component. Earlier methods for solving these problems used Ordered Binary Decision Diagrams (OBDDs) to represent constraints on probability distributions, which were decomposed into sets of smaller constraints and solved by Constraint Programming (CP) or Mixed Integer Programming (MIP) solvers. For the specific case of monotonic distributions, we propose an alternative method: a new propagator for a global OBDD-based constraint. We show that this propagator is (sub-)linear in the size of the OBDD, and maintains domain consistency. We experimentally evaluate the effectiveness of this global constraint in comparison to existing decomposition-based approaches, and show how this propagator can be used in combination with another data mining specific constraint present in CP systems. As test cases we use problems from the data mining literature.

AI and machine learning tools are being used with increasing frequency for decision making in domains that affect peoples’ lives such as employment, education, policing and financial qualifications. These uses raise concerns about biases of algorithmic discrimination and have motivated the development of fairness-aware machine learning. However, existing fairness approaches are based solely on attributes of individuals. In many cases, discrimination is much more complex, and taking into account the social, organizational, and other connections between individuals is important. We introduce new notions of fairness that are able to capture the relational structure in a domain. We use first-order logic to provide a flexible and expressive language for specifying complex relational patterns of discrimination. Furthermore, we extend an existing statistical relational learning framework, probabilistic soft logic (PSL), to incorporate our definition of relational fairness. We refer to this fairness-aware framework FairPSL. FairPSL makes use of the logical definitions of fairnesss but also supports a probabilistic interpretation. In particular, we show how to perform maximum a posteriori (MAP) inference by exploiting probabilistic dependencies within the domain while avoiding violations of fairness guarantees. Preliminary empirical evaluation shows that we are able to make both accurate and fair decisions.

Factored stochastic constraint programming (FSCP) is a formalism to represent multi-stage decision making problems under uncertainty. FSCP models support factorized probabilistic models and involve constraints over decision and random variables. These models have many applications in real-world problems. However, solving these problems requires evaluating the best course of action for each possible outcome of the random variables and hence is computationally challenging. FSCP problems often involve repeated subproblems which ideally should be solved once. In this paper we show how identifying and exploiting these identical subproblems can simplify solving them and leads to a compact representation of the solution. We compile an And-Or search tree to a compact decision diagram. Preliminary experiments show that our proposed method significantly improves the search efficiency by reducing the size of the problem and outperforms the existing methods.

This paper proposes an adaptive segmentation method as a market clearing mechanism for peer-to-peer（P2P） energy trading scheme with large number of market players. In the proposed method, market players participate in the market by announcing their bids. In the first step,players are assigned to different segments based on their features, where the balanced k-means clustering method is implemented to form segments. These segments are formed based on the similarity between players, where the amount of energy for trade and its corresponding price are considered as features of players. In the next step, a distributed method is employed to clear the market in each segment without any need to private information of players. The novelty of this paper relies on developing an adaptive algorithm for dividing large number of market players into multiple segments to enhance scalability of the P2P trading by reducing data exchange and communication overheads.The proposed approach can be used along with any distributed method for market clearing. In this paper, two different structures including community-based market and decentralized bilateral trading market are used to demonstrate the efficacy of the proposed method. Simulation results show the beneficial properties of the proposed segmentation method.

Statistical relational learning models are powerful tools that combine ideas from first-order logic with probabilistic graphical models to represent complex dependencies. Despite their success in encoding large problems with a compact set of weighted rules, performing inference over these models is often challenging. In this paper, we show how to effectively combine two powerful ideas for scaling inference for large graphical models. The first idea, lifted inference, is a wellstudied approach to speeding up inference in graphical models by exploiting symmetries in the underlying problem. The second idea is to frame Maximum a posteriori (MAP) inference as a convex optimization problem and use alternating direction method of multipliers (ADMM) to solve the problem in parallel. A well-studied relaxation to the combinatorial optimization problem defined for logical Markov random fields gives rise to a hinge-loss Markov random field (HLMRF) for which MAP inference is a convex optimization problem. We show how the formalism introduced for coloring weighted bipartite graphs using a color refinement algorithm can be integrated with the ADMM optimization technique to take advantage of the sparse dependency structures of HLMRFs. Our proposed approach, lifted hinge-loss Markov random fields (LHL-MRFs), preserves the structure of the original problem after lifting and solves lifted inference as distributed convex optimization with ADMM. In our empirical evaluation on real-world problems, we observe up to a three times speed up in inference over HL-MRFs.

A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component. Building on the recently proposed language SC-ProbLog for modeling SCOPs, we propose a new method for solving these problems. Earlier methods used Probabilistic Logic Programming (PLP) techniques to create Ordered Binary Decision Diagrams (OBDDs), which were decomposed into smaller constraints in order to exploit existing constraint programming (CP) solvers. We argue that this approach has as drawback that a decomposed representation of an OBDD does not guarantee domain consistency during search, and hence limits the efficiency of the solver. For the specific case of monotonic distributions, we suggest an alternative method for using CP in SCOP, based on the development of a new propagator; we show that this propagator is linear in the size of the OBDD, and has the potential to be more efficient than the decomposition method, as it maintains domain consistency.

AI and machine learning tools are being used with increasing frequency for decision making in domains that affect peoples' lives such as employment, education, policing and loan approval. These uses raise concerns about biases of algorithmic discrimination and have motivated the development of fairness-aware machine learning. However, existing fairness approaches are based solely on attributes of individuals. In many cases, discrimination is much more complex, and taking into account the social, organizational, and other connections between individuals is important. We introduce new notions of fairness that are able to capture the relational structure in a domain. We use first-order logic to provide a flexible and expressive language for specifying complex relational patterns of discrimination. Furthermore, we extend an existing statistical relational learning framework, probabilistic soft logic (PSL), to incorporate our definition of relational fairness. We refer to this fairness-aware framework FairPSL. FairPSL makes use of the logical definitions of fairnesss but also supports a probabilistic interpretation. In particular, we show how to perform maximum a posteriori(MAP) inference by exploiting probabilistic dependencies within the domain while avoiding violation of fairness guarantees. Preliminary empirical evaluation shows that we are able to make both accurate and fair decisions.

Complex multi-stage decision making problems often involve uncertainty, for example, regarding demand or processing times. Stochastic constraint programming was proposed as a way to formulate and solve such decision problems, involving arbitrary constraints over both decision and random variables. What stochastic constraint programming still lacks is support for the use of factorized probabilistic models that are popular in the graphical model community. We show how a state-of-the-art probabilistic inference engine can be integrated into standard constraint solvers. The resulting approach searches over the And-Or search tree directly, and we investigate tight bounds on the expected utility objective. This significantly improves search efficiency and outperforms scenario-based methods that ground out the possible worlds.