Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services

This study develops an online predictive optimization framework for dynamically operating a transit service in an area of crowd movements. The proposed framework integrates demand prediction and supply optimization to periodically redesign the service routes based on recently observed demand. To predict demand for the service, we use Quantile Regression to estimate the marginal distribution of movement counts between each pair of serviced locations. The framework then combines these marginals into a joint demand distribution by constructing a Gaussian copula, which captures the structure of correlation between the marginals. For supply optimization, we devise a linear programming model, which simultaneously determines the route structure and the service frequency according to the predicted demand. Importantly, our framework both preserves the uncertainty structure of future demand and leverages this for robust route optimization, while keeping both components decoupled. We evaluate our framework using a real-world case study of autonomous mobility in a university campus in Denmark. The results show that our framework often obtains the ground truth optimal solution, and can outperform conventional methods for route optimization, which do not leverage full predictive distributions.Comment: 34 pages, 12 figures, 5 table

Improving Optimization Bounds using Machine Learning: Decision Diagrams meet Deep Reinforcement Learning

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower bounds that can be significantly better than classical bounding mechanisms, such as linear relaxations. It is well known that the quality of the bounds achieved through this flexible bounding method is highly reliant on the ordering of variables chosen for building the diagram, and finding an ordering that optimizes standard metrics is an NP-hard problem. In this paper, we propose an innovative and generic approach based on deep reinforcement learning for obtaining an ordering for tightening the bounds obtained with relaxed and restricted DDs. We apply the approach to both the Maximum Independent Set Problem and the Maximum Cut Problem. Experimental results on synthetic instances show that the deep reinforcement learning approach, by achieving tighter objective function bounds, generally outperforms ordering methods commonly used in the literature when the distribution of instances is known. To the best knowledge of the authors, this is the first paper to apply machine learning to directly improve relaxation bounds obtained by general-purpose bounding mechanisms for combinatorial optimization problems.Comment: Accepted and presented at AAAI'1

Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose to learn a variable selection policy for branch-and-bound in mixed-integer linear programming, by imitation learning on a diversified variant of the strong branching expert rule. We encode states as bipartite graphs and parameterize the policy as a graph convolutional neural network. Experiments on a series of synthetic problems demonstrate that our approach produces policies that can improve upon expert-designed branching rules on large problems, and generalize to instances significantly larger than seen during training

A Survey on Reinforcement Learning for Combinatorial Optimization

This paper gives a detailed review of reinforcement learning in combinatorial optimization, introduces the history of combinatorial optimization starting in the 1960s, and compares it with the reinforcement learning algorithms in recent years. We explicitly look at a famous combinatorial problem known as the Traveling Salesperson Problem (TSP). We compare the approach of the modern reinforcement learning algorithms on TSP with an approach published in 1970. Then, we discuss the similarities between these algorithms and how the approach of reinforcement learning changes due to the evolution of machine learning techniques and computing power. We also mention the deep learning approach on the TSP, which is named Deep Reinforcement Learning. We argue that deep learning is a generic approach that can be integrated with traditional reinforcement learning algorithms and optimize the outcomes of the TSP.Comment: manuscript submitted to Management Scienc

Neural combinatorial optimization as an enabler technology to design real-time virtual network function placement decision systems

158 p.The Fifth Generation of the mobile network (5G) represents a breakthrough technology for thetelecommunications industry. 5G provides a unified infrastructure capable of integrating over thesame physical network heterogeneous services with different requirements. This is achieved thanksto the recent advances in network virtualization, specifically in Network Function Virtualization(NFV) and Software Defining Networks (SDN) technologies. This cloud-based architecture not onlybrings new possibilities to vertical sectors but also entails new challenges that have to be solvedaccordingly. In this sense, it enables to automate operations within the infrastructure, allowing toperform network optimization at operational time (e.g., spectrum optimization, service optimization,traffic optimization). Nevertheless, designing optimization algorithms for this purpose entails somedifficulties. Solving the underlying Combinatorial Optimization (CO) problems that these problemspresent is usually intractable due to their NP-Hard nature. In addition, solutions to these problems arerequired in close to real-time due to the tight time requirements on this dynamic environment. Forthis reason, handwritten heuristic algorithms have been widely used in the literature for achievingfast approximate solutions on this context.However, particularizing heuristics to address CO problems can be a daunting task that requiresexpertise. The ability to automate this resolution processes would be of utmost importance forachieving an intelligent network orchestration. In this sense, Artificial Intelligence (AI) is envisionedas the key technology for autonomously inferring intelligent solutions to these problems. Combining AI with network virtualization can truly transform this industry. Particularly, this Thesis aims at using Neural Combinatorial Optimization (NCO) for inferring endsolutions on CO problems. NCO has proven to be able to learn near optimal solutions on classicalcombinatorial problems (e.g., the Traveler Salesman Problem (TSP), Bin Packing Problem (BPP),Vehicle Routing Problem (VRP)). Specifically, NCO relies on Reinforcement Learning (RL) toestimate a Neural Network (NN) model that describes the relation between the space of instances ofthe problem and the solutions for each of them. In other words, this model for a new instance is ableto infer a solution generalizing from the problem space where it has been trained. To this end, duringthe learning process the model takes instances from the learning space, and uses the reward obtainedfrom evaluating the solution to improve its accuracy.The work here presented, contributes to the NCO theory in two main directions. First, this workargues that the performance obtained by sequence-to-sequence models used for NCO in the literatureis improved presenting combinatorial problems as Constrained Markov Decision Processes (CMDP).Such property can be exploited for building a Markovian model that constructs solutionsincrementally based on interactions with the problem. And second, this formulation enables toaddress general constrained combinatorial problems under this framework. In this context, the modelin addition to the reward signal, relies on penalty signals generated from constraint dissatisfactionthat direct the model toward a competitive policy even in highly constrained environments. Thisstrategy allows to extend the number of problems that can be addressed using this technology.The presented approach is validated in the scope of intelligent network management, specifically inthe Virtual Network Function (VNF) placement problem. This problem consists of efficientlymapping a set of network service requests on top of the physical network infrastructure. Particularly,we seek to obtain the optimal placement for a network service chain considering the state of thevirtual environment, so that a specific resource objective is accomplished, in this case theminimization of the overall power consumption. Conducted experiments prove the capability of theproposal for learning competitive solutions when compared to classical heuristic, metaheuristic, andConstraint Programming (CP) solvers

Machine Learning for Fluid Mechanics

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202