École Polytechnique de Montréal

About: École Polytechnique de Montréal is a education organization based out in Montreal, Quebec, Canada. It is known for research contribution in the topics: Finite element method & Computer science. The organization has 8015 authors who have published 18390 publications receiving 494372 citations.

A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows

Abstract: The vehicle routing problem with time windows VRPTW is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service. In this paper, we present the development of a new optimization algorithm for its solution. The LP relaxation of the set partitioning formulation of the VRPTW is solved by column generation. Feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming. The LP solution obtained generally provides an excellent lower bound that is used in a branch-and-bound algorithm to solve the integer set partitioning formulation. Our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark VRPTW test problems. The algorithm was capable of optimally solving 100-customer problems. This problem size is six times larger than any reported to date by other published research.

Recovering traceability links between code and documentation

Abstract: Software system documentation is almost always expressed informally in natural language and free text. Examples include requirement specifications, design documents, manual pages, system development journals, error logs, and related maintenance reports. We propose a method based on information retrieval to recover traceability links between source code and free text documents. A premise of our work is that programmers use meaningful names for program items, such as functions, variables, types, classes, and methods. We believe that the application-domain knowledge that programmers process when writing the code is often captured by the mnemonics for identifiers; therefore, the analysis of these mnemonics can help to associate high-level concepts with program concepts and vice-versa. We apply both a probabilistic and a vector space information retrieval model in two case studies to trace C++ source code onto manual pages and Java code to functional requirements. We compare the results of applying the two models, discuss the benefits and limitations, and describe directions for improvements.

Large Population Stochastic Dynamic Games: Closed-Loop McKean-Vlasov Systems and the Nash Certainty Equivalence Principle

Abstract: We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the so-called Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis. The McKean-Vlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent (or particle) at the microscopic level and the mass of individuals (or particles) at the macroscopic level. The overall game is decomposed into (i) an optimal control problem whose Hamilton-Jacobi-Bellman (HJB) equation determines the optimal control for each individual and which involves a measure corresponding to the mass effect, and (ii) a family of McKean-Vlasov (M-V) equations which also depend upon this measure. We designate the NCE Principle as the property that the resulting scheme is consistent (or soluble), i.e. the prescribed control laws produce sample paths which produce the mass effect measure. By construction, the overall closed-loop behaviour is such that each agent’s behaviour is optimal with respect to all other agents in the game theoretic Nash sense.

Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$ -Nash Equilibria

Abstract: We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property. A stability property of the mass behavior is established, and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques.