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Andre A. Cire

Bio: Andre A. Cire is an academic researcher from University of Toronto. The author has contributed to research in topics: Constraint programming & Solver. The author has an hindex of 18, co-authored 65 publications receiving 855 citations. Previous affiliations of Andre A. Cire include State University of Campinas & Carnegie Mellon University.


Papers
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Book
16 Jun 2018
TL;DR: This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology.
Abstract: This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming."Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world." [Pascal Van Hentenryck]

123 citations

Journal ArticleDOI
TL;DR: A general branch-and-bound algorithm for discrete optimization in which binary decision diagrams play the role of the traditional linear programming relaxation, in which relaxed BDD representations of the problem provide bounds and guidance for branching, and restricted BDDs supply a primal heuristic.
Abstract: We propose a general branch-and-bound algorithm for discrete optimization in which binary decision diagrams (BDDs) play the role of the traditional linear programming relaxation. In particular, relaxed BDD representations of the problem provide bounds and guidance for branching, and restricted BDDs supply a primal heuristic. Each problem is given a dynamic programming model that allows one to exploit recursive structure, even though the problem is not solved by dynamic programming. A novel search scheme branches within relaxed BDDs rather than on values of variables. Preliminary testing shows that a rudimentary BDD-based solver is competitive with or superior to a leading commercial integer programming solver for the maximum stable set problem, the maximum cut problem on a graph, and the maximum 2-satisfiability problem. Specific to the maximum cut problem, we tested the BDD-based solver on a classical benchmark set and identified tighter relaxation bounds than have ever been found by any technique, nearl...

95 citations

Posted Content
TL;DR: This work proposes a general and hybrid approach, based on DRL and CP, for solving combinatorial optimization problems, and experimentally shows that the framework introduced outperforms the stand-alone RL and CP solutions, while being competitive with industrial solvers.
Abstract: Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces with combinatorial optimization is the state-space explosion problem: the number of possibilities grows exponentially with the problem size, which makes solving intractable for large problems. In the last years, deep reinforcement learning (DRL) has shown its promise for designing good heuristics dedicated to solve NP-hard combinatorial optimization problems. However, current approaches have two shortcomings: (1) they mainly focus on the standard travelling salesman problem and they cannot be easily extended to other problems, and (2) they only provide an approximate solution with no systematic ways to improve it or to prove optimality. In another context, constraint programming (CP) is a generic tool to solve combinatorial optimization problems. Based on a complete search procedure, it will always find the optimal solution if we allow an execution time large enough. A critical design choice, that makes CP non-trivial to use in practice, is the branching decision, directing how the search space is explored. In this work, we propose a general and hybrid approach, based on DRL and CP, for solving combinatorial optimization problems. The core of our approach is based on a dynamic programming formulation, that acts as a bridge between both techniques. We experimentally show that our solver is efficient to solve two challenging problems: the traveling salesman problem with time windows, and the 4-moments portfolio optimization problem. Results obtained show that the framework introduced outperforms the stand-alone RL and CP solutions, while being competitive with industrial solvers.

70 citations

Book ChapterDOI
30 Dec 2013
TL;DR: This work proposes a new approach for solving sequencing problems based on multivalued decision diagrams (MDDs), which are compact graphical representations of Boolean functions, originally introduced for applications in circuit design by Lee and widely studied and applied in computer science.
Abstract: Sequencing problems are among the most widely studied problems in operations research. Specific variations of sequencing problems include single machine scheduling, the traveling salesman problem with time windows, and precedence-constrained machine scheduling. In this work we propose a new approach for solving sequencing problems based on multivalued decision diagrams (MDDs). Decision diagrams are compact graphical representations of Boolean functions, originally introduced for applications in circuit design by Lee [7], and widely studied and applied in computer science. They have been recently used to represent the feasible set of discrete optimization problems, as demonstrated in [2] and [3, 4]. This is done by perceiving the constraints of a problem as a Boolean function f(x) representing whether a solution x is feasible. Nonetheless, such MDDs can grow exponentially large, which makes any practical computation prohibitive in general.

52 citations

Book ChapterDOI
28 May 2012
TL;DR: It is found experimentally that orderings that result in smaller exact B DDs have a strong tendency to produce tighter bounds in relaxation BDDs, and it is shown that the width of an exact BDD can be given a theoretical upper bound for certain classes of graphs.
Abstract: The ordering of variables can have a significant effect on the size of the reduced binary decision diagram (BDD) that represents the set of solutions to a combinatorial optimization problem. It also influences the quality of the objective function bound provided by a limited-width relaxation of the BDD. We investigate these effects for the maximum independent set problem. By identifying variable orderings for the BDD, we show that the width of an exact BDD can be given a theoretical upper bound for certain classes of graphs. In addition, we draw an interesting connection between the Fibonacci numbers and the width of exact BDDs for general graphs. We propose variable ordering heuristics inspired by these results, as well as a k-layer look-ahead heuristic applicable to any problem domain. We find experimentally that orderings that result in smaller exact BDDs have a strong tendency to produce tighter bounds in relaxation BDDs.

49 citations


Cited by
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01 Jan 2007
TL;DR: Minimum Cardinality Matrix Decomposition into Consecutive-Ones Matrices: CP and IP Approaches and Connections in Networks: Hardness of Feasibility Versus Optimality.
Abstract: Minimum Cardinality Matrix Decomposition into Consecutive-Ones Matrices: CP and IP Approaches.- Connections in Networks: Hardness of Feasibility Versus Optimality.- Modeling the Regular Constraint with Integer Programming.- Hybrid Local Search for Constrained Financial Portfolio Selection Problems.- The "Not-Too-Heavy Spanning Tree" Constraint.- Eliminating Redundant Clauses in SAT Instances.- Cost-Bounded Binary Decision Diagrams for 0-1 Programming.- YIELDS: A Yet Improved Limited Discrepancy Search for CSPs.- A Global Constraint for Total Weighted Completion Time.- Computing Tight Time Windows for RCPSPWET with the Primal-Dual Method.- Necessary Condition for Path Partitioning Constraints.- A Constraint Programming Approach to the Hospitals / Residents Problem.- Best-First AND/OR Search for 0/1 Integer Programming.- A Position-Based Propagator for the Open-Shop Problem.- Directional Interchangeability for Enhancing CSP Solving.- A Continuous Multi-resources cumulative Constraint with Positive-Negative Resource Consumption-Production.- Replenishment Planning for Stochastic Inventory Systems with Shortage Cost.- Preprocessing Expression-Based Constraint Satisfaction Problems for Stochastic Local Search.- The Deviation Constraint.- The Linear Programming Polytope of Binary Constraint Problems with Bounded Tree-Width.- On Boolean Functions Encodable as a Single Linear Pseudo-Boolean Constraint.- Solving a Stochastic Queueing Control Problem with Constraint Programming.- Constrained Clustering Via Concavity Cuts.- Bender's Cuts Guided Large Neighborhood Search for the Traveling Umpire Problem.- A Large Neighborhood Search Heuristic for Graph Coloring.- Generalizations of the Global Cardinality Constraint for Hierarchical Resources.- A Column Generation Based Destructive Lower Bound for Resource Constrained Project Scheduling Problems.

497 citations

31 Dec 1994
TL;DR: A partially enumerative algorithm is presented for the maximum clique problem which is very simple to implement and Computational results for an efficient implementation on an IBM 3090 computer are provided.
Abstract: We present an exact partial enumerative algorithm for the maximum clique problem. The pruning device used is derived from graph colorings. Pruning of the search tree is accomplished not only by the number of colors used to color a tree subproblem but also by using information gained in the process of coloring. This leads to increased pruning which translates into improved computational performance. Experimental results on test problems are presented.

467 citations

Journal ArticleDOI
TL;DR: This survey explores the synergy between the CO and RL frameworks, which can become a promising direction for solving combinatorial problems.

247 citations

Book ChapterDOI
26 Jun 2018
TL;DR: The neural combinatorial optimization framework is extended to solve the traveling salesman problem (TSP) and the performance of the proposed framework alone is generally as good as high performance heuristics (OR-Tools).
Abstract: The aim of the study is to provide interesting insights on how efficient machine learning algorithms could be adapted to solve combinatorial optimization problems in conjunction with existing heuristic procedures. More specifically, we extend the neural combinatorial optimization framework to solve the traveling salesman problem (TSP). In this framework, the city coordinates are used as inputs and the neural network is trained using reinforcement learning to predict a distribution over city permutations. Our proposed framework differs from the one in [1] since we do not make use of the Long Short-Term Memory (LSTM) architecture and we opted to design our own critic to compute a baseline for the tour length which results in more efficient learning. More importantly, we further enhance the solution approach with the well-known 2-opt heuristic. The results show that the performance of the proposed framework alone is generally as good as high performance heuristics (OR-Tools). When the framework is equipped with a simple 2-opt procedure, it could outperform such heuristics and achieve close to optimal results on 2D Euclidean graphs. This demonstrates that our approach based on machine learning techniques could learn good heuristics which, once being enhanced with a simple local search, yield promising results.

242 citations