Uma abordagem para a resolução do problema de transporte com custo fixo

Orientador : Prof. Dr. Arinei Carlos Lindbeck da SilvaCoorientador : Prof. Dr. Gustavo Valentim LochTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 20/06/2017Inclui referências : f. 69-78Resumo: O Problema de Transporte com Custo Fixo (PTCF) é uma classe da Programação Linear (PL), em que o custo total de envio de um produto, de uma origem para um destino, é composto por um custo unitário de transporte, proporcional à quantidade de itens enviados, e um custo fixo, associado à abertura da rota. O PTCF é NP-hard e além disso possui uma característica que à medida que a diferença entre o valor do custo unitário e o do custo fixo aumenta, o tempo computacional sofre alteração, piorando o desempenho. A base de problemas gerada por Sun, em 1998, foi adotada para realizar os testes computacionais. Após revisar alguns métodos da literatura, as heurísticas HEUR-1, HEUR-2, KOWA e HEUR-3 foram desenvolvidas e implementadas, utilizando estrutura de árvores e com otimização em relação ao cálculo das variáveis duais. Após realizar os testes computacionais, os métodos desenvolvidos foram comparados entre si constatando-se a superioridade de HEUR-3. A seguir, HEUR-3 foi comparado com BT, GIP, CORE2 e CORE3, que são métodos da literatura utilizados para resolver o PTCF além de comparar o desempenho com o solver Gurobi. Para todos os testes foi definido como critério de parada o tempo limite de 120 segundos. Cabe ressaltar que HEUR-3 e BT são heurísticas puras enquanto GIP, CORE2 e CORE3 fazem uso de um solver em determinado momento da rotina. Os valores obtidos para o PTCF em cada método da literatura e solver aqui citados, juntamente com HEUR-3, são analisados e discutidos parte a parte. A conclusão dessa tese mostra que HEUR-3 é superior quando comparado ao solver GUROBI e aos métodos BT, CORE2 e CORE3, o que não ocorre apenas com relação à técnica GIP. Palavras-chave: Heurística, implementação computacional, Gurobi.Abstract: The Fixed Charge Transportation Problem (FCTP) is a Linear Programming (LP) class, whereby the total shipping cost of a product, from a source to a destination, consists of a unit transportation cost, proportional to the amount of sent items and a fixed charge associated with the opening of the route. The FCTP is NP-hard and has a characteristic in which, as far as the difference between the value of the unit cost and the fixed charge increases, the computational time changes, worsening the performance. The base of problems generated by Sun, in 1998, was adopted to perform the computational tests. Following the review of some literature methods, the heuristics HEUR-1, HEUR-2, KOWA and HEUR-3 were developed and implemented, using a tree structure and with optimization in relation to the calculation of dual variables. After executing the computational tests, the developed methods were compared to each other, confirming the superiority of HEUR-3. Next, HEUR-3 was compared to BT, GIP, CORE2 and CORE3, which are literature methods used to solve the FCTP, in addition to compare the performance with the Gurobi solver. For all tests, the timeout of 120 seconds was set as stop criterion. It should be noted that HEUR-3 and BT are pure heuristics while GIP, CORE2 and CORE3 make use of a solver at a given moment of the routine. The values obtained for the FCTP in each of the literature methods and solver listed here, together with HEUR-3, are analyzed and discussed side by side. The conclusion of this thesis shows that HEUR-3 is superior when compared to the GUROBI solver and with BT, CORE2 and CORE3 methods, which does not only occur merely to the GIP technique. Keywords: Heuristic, computational implementation, Gurobi

Processing of Erroneous and Unsafe Data

Statistical offices have to overcome many problems before they can publish reliable data. Two of these problems are examined in this thesis. The first problem is the occurrence of errors in the collected data. Due to these errors publication figures cannot be directly based on the collected data. Before publication the errors in the data have to be localised and corrected. In this thesis we focus on the localisation of errors in a mix of categorical and numerical data. The problem is formulated as a mathematical optimisation problem. Several new algorithms for solving this problem are proposed, and computational results of the most promising algorithms are compared to each other. The second problem that is examined in this thesis is the occurrence of unsafe data, i.e. data that would reveal too much sensitive information about individual respondents. Before publication of data, such unsafe data need to be protected. In the thesis we examine various aspects of the protection of unsafe data.Statistische bureaus dienen tal van problemen te overwinnen voordat zij de resultaten van hun onderzoeken kunnen publiceren. In het proefschrift wordt ingegaan op twee van deze problemen. Het eerste probleem is dat verzamelde gegevens foutief kunnen zijn. Door de mogelijke aanwezigheid van fouten in de gegevens moeten deze gegevens eerst worden gecontroleerd en indien nodig worden gecorrigeerd voordat tot publicatie van resultaten wordt overgegaan. In het proefschrift wordt vooral aandacht besteed aan het opsporen van de foutieve gegevens. Door te veronderstellen dat er zo min mogelijk fouten zijn gemaakt kan het opsporen van de foutieve waarden als een wiskundig optimaliseringsprobleem worden geformuleerd. In het proefschrift wordt een aantal methoden ontwikkeld om dit complexe probleem efficient op te lossen. Het tweede probleem dat in het proefschrift onderzocht wordt is dat geen gegevens gepubliceerd mogen worden die de privacy van individuele respondenten of kleine groepen respondenten schaden. Om gegevens van individuele of kleine groepen respondenten te beschermen moeten beveiligingsmaatregelen, zoals het niet publiceren van bepaalde informatie, worden getroffen. In het proefschrift wordt ingegaan op de wiskundige problemen die het beveiligen van gevoelige gegevens met zich mee brengt. Voor een aantal problemen, zoals het berekenen van het informatieverlies ten gevolge van het beveiligen van gevoelige gegevens en het minimaliseren van de informatie die niet gepubliceerd wordt, worden oplossingen beschreven