Learning to Sparsify Travelling Salesman Problem Instances

CPAIOR 2021: 18th International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Vienna, Austria, 5 - 8 July 2021In order to deal with the high development time of exact and approximation algorithms for NP-hard combinatorial optimisation problems and the high running time of exact solvers, deep learning techniques have been used in recent years as an end-to-end approach to find solutions. However, there are issues of representation, generalisation, complex architectures, interpretability of models for mathematical analysis etc. using deep learning techniques. As a compromise, machine learning can be used to improve the run time performance of exact algorithms in a matheuristics framework. In this paper, we use a pruning heuristic leveraging machine learning as a pre-processing step followed by an exact Integer Programming approach. We apply this approach to sparsify instances of the classical travelling salesman problem. Our approach learns which edges in the underlying graph are unlikely to belong to an optimal solution and removes them, thus sparsifying the graph and significantly reducing the number of decision variables. We use carefully selected features derived from linear programming relaxation, cutting planes exploration, minimum-weight spanning tree heuristics and various other local and statistical analysis of the graph. Our learning approach requires very little training data and is amenable to mathematical analysis. We demonstrate that our approach can reliably prune a large fraction of the variables in TSP instances from TSPLIB/MATILDA (>85%) while preserving most of the optimal tour edges. Our approach can successfully prune problem instances even if they lie outside the training distribution, resulting in small optimality gaps between the pruned and original problems in most cases. Using our learning technique, we discover novel heuristics for sparsifying TSP instances, that may be of independent interest for variants of the vehicle routing problem.Science Foundation IrelandOpen access funding provided by SF

Advances in Branch-and-Fix methods to solve the Hamiltonian cycle problem in manufacturing optimization

159 p.Esta tesis parte del problema de la optimización de la ruta de la herramienta donde se contribuye con unsistema de soporte para la toma de decisiones que genera rutas óptimas en la tecnología de FabricaciónAditiva. Esta contribución sirve como punto de partida o inspiración para analizar el problema del cicloHamiltoniano (HCP). El HCP consiste en visitar todos los vértices de un grafo dado una única vez odeterminar que dicho ciclo no existe. Muchos de los métodos propuestos en la literatura sirven paragrafos no dirigidos y los que se enfocan en los grafos dirigidos no han sido implementados ni testeados.Uno de los métodos para resolver el problema es el Branch-and-Fix (BF), un método exacto que utiliza latranformación del HCP a un problema continuo. El BF es un algoritmo de ramificación que consiste enconstruir un árbol de decisión donde en cada vértice dos problemas lineales son resueltos. Este método hasido testeado en grafos de tamaño pequeño y por ello, no se ha estudiado en profundidad las limitacionesque puede presentar. Por ello, en esta tesis se proponen cuatro contribuciones metodológicasrelacionadas con el HCP y el BF: 1) mejorar la enficiencia del BF en diferentes aspectos, 2) proponer unmétodo de ramificación global, 3) proponer un método del BF colapsado, 4) extender el HCP a unescenario multi-objetivo y proponer un método para resolverlo

Topics in exact precision mathematical programming

The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.Ph.D.Committee Chair: Dr. William J. Cook; Committee Member: Dr. George Nemhauser; Committee Member: Dr. Robin Thomas; Committee Member: Dr. Santanu Dey; Committee Member: Dr. Shabbir Ahmed; Committee Member: Dr. Zonghao G

Extracting information from biological networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 175-194).Systems biology, the study of biological systems in a holistic manner, has been catalyzed by a dramatic improvement in experimental techniques, coupled with a constantly increasing availability of biological data. The representation and analysis of this heterogeneous data is facilitated by the powerful abstraction of biological networks. This thesis examines several types of these networks and looks in detail at the kind of information their analysis can yield. The first part discusses protein interaction networks. We introduce a new algorithm for the pairwise alignment of these networks. We show that these alignments can provide important clues to the function of proteins as well as insights into the evolutionary history of the species under examination. The second part discusses regulatory networks. We present an approach for validating putative drug targets based on the information contained in these networks. We show how this approach can also be used to discover drug targets. The third part discusses metabolic networks. We provide new insights into the structure of constraint-based models of cell metabolism and describe a methodology for performing a complete analysis of a metabolic network. We also present an implementation of this methodology and discuss its application to a variety of problems related to the metabolism of bacteria. The final part describes an application of our methodology to Mycobacterium tuberculosis, the pathogen responsible for almost 2 million deaths around the world every year. We introduce a method for reconciling metabolic network reconstructions and apply it to merge the two published networks for tuberculosis. We analyze the merged network and show how it can be refined based on available experimental data to improve its predictive power. We conclude with a list of potential drug targets.by Leonid Alexandrovich Chindelevitch.Ph.D

Computational automation for efficient design of acoustic metamaterials

Acoustic metamaterials (AMMs) are an exciting technology because they are capable of responding to vibrations in ways that are impossible to achieve with conventional materials. However, realization of AMMs requires engineering design to provide a connection between first-principles research and production of parts that perform as expected. Designing AMMs is a challenging endeavor because evaluating designs is costly and manufacturing metamaterials requires precise techniques with small minimum resolutions. To address these challenges, new computational tools are necessary to aid design. This work proposes three tasks that improve the capabilities of design for AMM while being extensible to other engineering design automation tasks. The first task is to develop a design exploration tool that improves the computational efficiency of identifying sets of high-performing designs in a design space that is sparse and comprises mixed discrete/continuous data. The second task is to develop a process for designers to evaluate manufacturability of difficult-to-manufacture parts and drive co-development of manufacturing methods and AMM. In the final task, a machine learning based method is developed to efficiently model AMM with heterogeneous arrangements of their microstructures such that strict homogenization is infeasible. The outcomes from completing these tasks will provide a significant and novel improvement over existing methods of designing AMMs.Mechanical Engineerin

XV Міжнародна конференція з математичної, природничо-наукової та технологічної освіти (ICon-MaSTEd 2022) 18-20 травня 2022 року, м. Кривий Ріг, Україна

Матеріали XV Міжнародної конференції з математичної, природничо-наукової та технологічної освіти (ICon-MaSTEd 2022) 18-20 травня 2022 року, м. Кривий Ріг, Україна.Proceedings of the XV International Conference on Mathematics, Science and Technology Education (ICon-MaSTEd 2022) 18-20 May 2022, Kryvyi Rih, Ukraine

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum