Andrea Lodi

Alexandra Schwartz

We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unif… (see more)ied viewpoint on the general problem classes and models, and give concrete examples from diverse application fields such as signal and image processing, portfolio selection, or machine learning. The paper discusses general-purpose modeling techniques and broadly applicable as well as problem-specific exact and heuristic solution approaches. While our perspective is that of mathematical optimization, a main goal of this work is to reach out to and build bridges between the different communities in which cardinality optimization problems are frequently encountered. In particular, we highlight that modern mixed-integer programming, which is often regarded as impractical due to commonly unsatisfactory behavior of black-box solvers applied to generic problem formulations, can in fact produce provably high-quality or even optimal solutions for cardinality optimization problems, even in large-scale real-world settings. Achieving such performance typically draws on the merits of problem-specific knowledge that may stem from different fields of application and, e.g., shed light on structural properties of a model or its solutions, or lead to the development of efficient heuristics; we also provide some illustrative examples.

2024-08-08

SIAM Review (published)

Assortment Optimization with Visibility Constraints

Théo Barré

Omar El Housni

2024-05-22

Integer Programming and Combinatorial Optimization (published)

Implementing a Hierarchical Deep Learning Approach for Simulating multilevel Auction Data

Marcelin Joanis

Igor Sadoune

2024-05-18

Computational Economics (published)

Increasing schedule reliability in the multiple depot vehicle scheduling problem with stochastic travel time

L'ea Ricard

Guy Desaulniers

Louis-Martin Rousseau

2024-04-01

Omega (published)

Reinforcement learning for freight booking control problems

Justin Dumouchelle

Emma Frejinger

2024-03-16

Journal of Revenue and Pricing Management (published)

Recovering Dantzig–Wolfe Bounds by Cutting Planes

Rui Chen

Oktay Günlük

Leveraging Dantzig–Wolfe Decomposition in the Original Variable Space for Mixed-Integer Programming Dantzig–Wolfe decomposition has been… (see more) extensively applied to solve large-scale mixed-integer programs with decomposable structures, leading to exact solution approaches, such as branch and price. However, these approaches would require solving the problem in an extended variable space and are not readily present in off-the-shelf solvers. In “Recovering Dantzig–Wolfe Bounds by Cutting Planes,” Chen, Günlük, and Lodi propose a computational effective approach for generating cutting planes from Dantzig–Wolfe decomposition to enhance branch and cut in the space of original variables. The proposed approach requires a relatively small number of cutting planes to recover the strength of the Dantzig–Wolfe dual bound and should be easy to implement in general-purpose mixed-integer programming solvers. The authors show that these cutting planes typically lead to a formulation with lower dual degeneracy and hence, a better computational performance than naïve approaches, such as the objective function cut.

2024-01-03

Operations Research (published)

An Exact Method for (Constrained) Assortment Optimization Problems with Product Costs

Markus Leitner

Roberto Roberti

Claudio Sole

2024-01-01

INFORMS J. Comput. (published)

An improved column-generation-based matheuristic for learning classification trees

Krunal Kishor Patel

Guy Desaulniers

2024-01-01

Comput. Oper. Res. (published)

Learning Tabu Search Algorithms: A Scheduling Application

Nazgol Niroumandrad

Nadia Lahrichi

. Metaheuristics are widely recognized as efficient approaches for many combinatorial problems. Studies to improve the performance of metahe… (see more)uristics have increasingly relied on the use of various methods either combining different metaheuristics or methods originating outside of the metaheuristic field. This paper presents a learning algorithm to improve tabu search by reducing its search space and the evaluation effort. We study the performance of a learning tabu search algorithm using classification methods in an attempt to select moves through the search space more wisely. The experimental results demonstrate the benefit of using a learning mechanism under deterministic and stochastic conditions.

2024-01-01

Comput. Oper. Res. (published)

Operational Research: methods and applications

Fotios Petropoulos

Gilbert Laporte

Emel Aktas

Sibel A. Alumur

Claudia Archetti

Hayriye Ayhan

Maria Battarra

Julia A. Bennell

Jean-Marie Bourjolly

John E. Boylan

Michèle Breton

David Canca

Laurent Charlin

Bo Chen

Cihan Tugrul Cicek

Louis Anthony Cox

Christine S.M. Currie

Erik Demeulemeester

Li Ding

Stephen M. Disney … (see 62 more)

Matthias Ehrgott

Martin J. Eppler

Güneş Erdoğan

Bernard Fortz

L. Alberto Franco

Jens Frische

Salvatore Greco

Amanda J. Gregory

Raimo P. Hämäläinen

Willy Herroelen

Mike Hewitt

Jan Holmström

John N. Hooker

Tuğçe Işık

Jill Johnes

Bahar Y. Kara

Özlem Karsu

Katherine Kent

Charlotte Köhler

Martin Kunc

Yong-Hong Kuo

Judit Lienert

Adam N. Letchford

Janny Leung

Dong Li

Haitao Li

Ivana Ljubić

Sebastián Lozano

Virginie Lurkin

Silvano Martello

Ian G. McHale

Gerald Midgley

John D.W. Morecroft

Akshay Mutha

Ceyda Oğuz

Sanja Petrovic

Ulrich Pferschy

Harilaos N. Psaraftis

Sam Rose

Lauri Saarinen

Said Salhi

Jing-Sheng Song

Dimitrios Sotiros

Kathryn E. Stecke

Arne K. Strauss

İstenç Tarhan

Clemens Thielen

Paolo Toth

Greet Vanden Berghe

Christos Vasilakis

Vikrant Vaze

Daniele Vigo

Kai Virtanen

Xun Wang

Rafał Weron

Leroy White

Tom Van Woensel

Mike Yearworth

E. Alper Yıldırım

Georges Zaccour

Xuying Zhao

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a … (see more)diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes.

2024-01-01

J. Oper. Res. Soc. (published)

When Nash Meets Stackelberg

Margarida Carvalho

Gabriele Dragotto

Felipe Feijoo