A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.

Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.

Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.

We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and obtains a direct approximation of the posterior density. Compared to Markov Chain Monte Carlo (MCMC) based sampling approaches, the VB approach achieves enhanced computational efficiency without sacrificing estimation accuracy. In the simulation study conducted here, the proposed VB approach detects various types of proper active structures for dynamic network models. Compared to the alternative approach, the proposed method achieves similar or better accuracy, and its computational time is halved. In a real data analysis scenario of day-ahead natural gas flow prediction in the German gas transmission network with 51 nodes between October 2013 and September 2015, the VB approach delivers promising forecasting accuracy along with clearly detected structures in terms of dynamic dependence.

Mixed-Integer Linear Programming (MILP) is concerned with the modelling and solving of problems from discrete optimisation. These problems can represent real-world scenarios, where discrete decisions can be appropriately captured and modelled by the integer variables. In real-world scenarios a MILP model is rarely solved only once. More frequently, the same model is used with varying data to describe different instances of the same problem which are solved on a regular basis. This holds true in particular for decision support systems, which can utilise MILP to provide real-time optimal decisions on a continual basis, see [4] and [40] for examples in nurse scheduling and vehicle routing. The MILPs that these decision support systems solve have identical structure due to both their underlying application and cyclical nature, and thus often have similar optimal solutions. Our aim is to exploit this repetitive structure, and create generative neural networks that generate binary decision encodings for subsets of important variables. These encodings can then be used in a primal heuristic by solving the induced sub-problem following variable fixations. Additionally, the then result of the primal heuristic can be used in a warm-start context to help improve solver performance in a globally optimal context.

AAAI's 2015 Workshop Program was held Sunday and Monday, January 25–26, 2015 at the Hyatt Regency Austin Hotel in Austion, Texas, USA. The AAAI-15 workshop program included 15 workshops covering a wide range of topics in artificial intelligence. Most workshops were held on a single day. The titles of the workshops included AI and Ethics, AI for Cities, AI for Transportation: Advice, Interactivity and Actor Modeling, Algorithm Configuration, Artificial Intelligence Applied to Assistive Technologies and Smart Environments, Beyond the Turing Test, Computational Sustainability, Computer Poker and Imperfect Information, Incentive and Trust in E-Communities, Multiagent Interaction without Prior Coordination, Planning, Search, and Optimization, Scholarly Big Data: AI Perspectives, Challenges, and Ideas, Trajectory-Based Behaviour Analytics, World Wide Web and Public Health Intelligence, Knowledge, Skill, and Behavior Transfer in Autonomous Robots, and Learning for General Competency in Video Games.

AAAI's 2015 Workshop Program was held Sunday and Monday, January 25–26, 2015 at the Hyatt Regency Austin Hotel in Austion, Texas, USA. The AAAI-15 workshop program included 15 workshops covering a wide range of topics in artificial intelligence. Most workshops were held on a single day. The titles of the workshops included AI and Ethics, AI for Cities, AI for Transportation: Advice, Interactivity and Actor Modeling, Algorithm Configuration, Artificial Intelligence Applied to Assistive Technologies and Smart Environments, Beyond the Turing Test, Computational Sustainability, Computer Poker and Imperfect Information, Incentive and Trust in E-Communities, Multiagent Interaction without Prior Coordination, Planning, Search, and Optimization, Scholarly Big Data: AI Perspectives, Challenges, and Ideas, Trajectory-Based Behaviour Analytics, World Wide Web and Public Health Intelligence, Knowledge, Skill, and Behavior Transfer in Autonomous Robots, and Learning for General Competency in Video Games.