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Title: Conflict graphs in mixed-integer linear programming : preprocessing, heuristics and cutting planes.
Authors: Brito, Samuel Souza
metadata.dc.contributor.advisor: Santos, Haroldo Gambini
Keywords: Programação linear
Programação - computadores - processamento
Programação heurística
Issue Date: 2020
metadata.dc.contributor.referee: Santos, Haroldo Gambini
Fonseca, George Henrique Godim da
Mateus, Geraldo Robson
Aragão, Marcus Vinicius Soledade Poggi de
Toffolo, Túlio Ângelo Machado
Citation: BRITO, Samuel Souza. Conflict graphs in mixed-integer linear programming: preprocessing, heuristics and cutting planes. 110 f. 2020. Tese (Doutorado em Ciência da Computação) - Instituto de Ciências Exatas e Biológicas, Universidade Federal de Ouro Preto, Ouro Preto, 2020.
Abstract: This thesis addresses the development of con ict graph-based algorithms for MixedInteger Linear Programming, including: (i) an e cient infrastructure for the construction and manipulation of con ict graphs; (ii) a preprocessing routine based on a clique strengthening scheme that can both reduce the number of constraints and produce stronger formulations; (iii) a clique cut separator capable of obtaining dual bounds at the root node LP relaxation that are 19.65% stronger than those provided by the equivalent cut generator of a state-of-the-art commercial solver, 3.62 times better than those attained by the clique cut separator of the GLPK solver and 4.22 times stronger than the dual bounds obtained by the clique separation routine of the COIN-OR Cut Generation Library; (iv) an odd-cycle cut separator with a new lifting module to produce valid odd-wheel inequalities; (v) two diving heuristics capable of generating integer feasible solutions in restricted execution times. Additionally, we generated a new version of the COIN-OR Branch-and-Cut (CBC) solver by including our con ict graph infrastructure, preprocessing routine and cut separators. The average gap closed by this new version of CBC was up to four times better than its previous version. Moreover, the number of mixed-integer programs solved by CBC in a time limit of three hours was increased by 23.53%.
Description: Programa de Pós-Graduação em Ciência da Computação. Departamento de Ciência da Computação, Instituto de Ciências Exatas e Biológicas, Universidade Federal de Ouro Preto.
metadata.dc.rights.license: Autorização concedida ao Repositório Institucional da UFOP pelo(a) autor(a) em 17/06/2020 com as seguintes condições: disponível sob Licença Creative Commons 4.0 que permite copiar, distribuir e transmitir o trabalho desde que sejam citados o autor e o licenciante. Não permite o uso para fins comerciais.
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