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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

[pt] ALGORITMO PRICE-AND-CUT COM 3-SRCS E ENUMERAÇÃO DE COLUNAS PARA O PROBLEMA DE ALOCAÇÃO GENERALIZADA / [en] PRICE-AND-CUT ALGORITHM WITH 3-SRCS CUTS AND COLUMN ENUMERATION FOR THE GENERALIZED ASSIGNMENT PROBLEM

RAFAEL AZEVEDO MOSCOSO SILVA CRUZ 15 June 2021 (has links)
[pt] Esta dissertação estuda formulações, algoritmos e métodos exatos para resolver instâncias do Problema de Alocação Generalizada (PAG) com uma separação de desigualdades (3, 0.5)-SRC que viabilize a enumeração de colunas. Este trabalho é motivado pela perspectiva de alcançar o estado-da-arte com resultados competitivos comparáveis às melhores soluções encontradas na literatura por Avella (2010) e Michelon (2012). A pesquisa abrange métodos exatos e heurísticas, com ênfase no estudo que aborda a decomposição de Dantzig-Wolfe, o algoritmo de geração de colunas, a estabilização de colunas por meio da ponderação de duais proposto por Wentges (1997) e a enumeração de colunas habilitada pela minimização do gap decorrente do algoritmo de price-and-cut. O algoritmo de price-and-cut desenvolvido recorre à geração de colunas (pricing) aliada à separação de (3, 0.5)-SRCs para aumentar o lower bound gerado, assim minimizando o gap. A geração de colunas implementada é inspirada no algoritmo de Savelsbergh (1997); e a separação de (3, 0.5)-SRCs é motivada pelo trabalho de Jepsen (2008) e pelo algoritmo branch-cut-andprice proposto por Poggi e Uchoa (2016) para o CVRP. De acordo com os experimentos computacionais, as desigualdades adotadas são capazes de reduzir o gap suficientemente para viabilizar a enumeração de colunas em diversas instâncias do PAG com até 200 tarefas e 20 máquinas. O método utilizado obteve resultados compatíveis às melhores soluções conhecidas, enumerando todas as colunas necessárias para cobrir o gap determinado pelo price-and-cut. Esse resultado incentiva futuras pesquisas para estender a aplicação do algoritmo a instâncias maiores e mais difíceis. / [en] This dissertation deals with formulations, algorithms and exact methods for solving the well-known Generalized Assignment Problem (GAP) through a price-and-cut approach with the separation of (3, 0.5)-SRC inequalities in order to improve column enumeration feasibility and efficiency. This work is motivated by the perspective of reaching state-of-the-art performance, attaining competitive results which are comparable with the best known solutions found in the literature by Avella (2010) and Michelon (2012). This research was build on exact methods and some heuristics with emphasis on the Dantzig- Wolfe decomposition, the column generation algorithm, the stabilization through weighted Dantzig-Wolfe decomposition proposed byWentges (1997) and finally the column enumeration motivated by the gap minimization reached through the price-and-cut algorithm. The price-and-cut algorithm proposed here resort to column generation (pricing) combined with the separation of (3, 0.5)-SRC cuts in order to increase the generated lower bound, thus minimizing the attained gap. This column generation algorithm follows the work of Savelsbergh (1997); and the separation of (3, 0.5)-SRCs is formulated by Jepsen (2008) and motivated by the branch-cut-and-price algorithm proposed by Poggi and Uchoa (2016) for the CVRP. According to computational experiments, the adopted inequalities are capable of sufficiently reducing the gap, assuring the feasibility of column enumeration for several GAP instances with up to 200 tasks and 20 machines. This method achieved expressive results, compatible with the best known solutions, enumerating all the necessary columns to cover the gap found by the price-and-cut. Therefore, these results motivate future research towards the extension of the method s applicability to larger and more complex instances.

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