Duty Scheduling in Public Transit

This article is about adaptive column generation techniques for the solution of duty scheduling problems in public transit. The current optimization status is exploited in an adaptive approach to guide the subroutines for duty generation, LP resolution, and schedule construction toward relevant parts of 9. large problem. Computational results for three European scenarios are reported

Solução exacta de problemas de corte unidimensional usando o método de partição e avaliação sucessivas e geração diferida de colunas

Quando se pretende obter uma solução inteira para o problema de corte unidimensional, depois de se ter resolvido a sua relaxação linear, é frequente recorrer, quer a técnicas de arredondamento de soluções, quer a diversos tipos de heurísticas. Estas dificuldades decorrem do facto de não ser viável enumerar todas as variáveis estruturais do problema, cujo número pode ser da ordem dos milhões. Neste artigo, apresenta se uma formulação em que o número de variáveis e restrições é uma função polinomial da largura do stock e do número de pedidos. Para algumas classes de problemas, é possível enumerar todas as variáveis e obter a solução óptima usando o método da partição e avaliação sucessivas. Para instâncias de maiores dimensões, apresenta se um procedimento que combina a geração diferida de colunas e o método da partição e avaliação sucessivas. Define se o subproblema e o modo como é modificado durante a fase de partição e avaliação sucessivas. São apresentados resultados de testes computacionais para diversos problemas de teste.If an integer solution to the one-dimensional cutting stock problem is required, after solving the linear programming relaxation, one frequently resorts to heuristics based on rounding up and down the continuos solution, or other heuristics similar type. The difficulties arise from the fact that it may not be practically possible to enumerate all the structural variables of the problem, whose number may be in the order of millions, even for instances of moderate size. In this article we present a formulation with a number of variables and constraints that is polinomial with respect to the width of the stock and the number of orders. For some classes of instances, it is possible to enumerate completely all the variables and to obtain an integer optional solution using a branch-and-bound method. For larger instances, we present a procedure that combines column generation and branch-and-bound. We define the subproblem, and the way it is modified during the branch-and-bound phase. Computational results are presented for several test problems

Large-scale optimization with the primal-dual column generation method

The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant allows to obtain suboptimal and well-centered dual solutions which naturally stabilizes the column generation. As recently presented in the literature, reductions in the number of calls to the oracle and in the CPU times are typically observed when compared to the standard column generation, which relies on extreme optimal dual solutions. However, these results are based on relatively small problems obtained from linear relaxations of combinatorial applications. In this paper, we investigate the behaviour of the PDCGM in a broader context, namely when solving large-scale convex optimization problems. We have selected applications that arise in important real-life contexts such as data analysis (multiple kernel learning problem), decision-making under uncertainty (two-stage stochastic programming problems) and telecommunication and transportation networks (multicommodity network flow problem). In the numerical experiments, we use publicly available benchmark instances to compare the performance of the PDCGM against recent results for different methods presented in the literature, which were the best available results to date. The analysis of these results suggests that the PDCGM offers an attractive alternative over specialized methods since it remains competitive in terms of number of iterations and CPU times even for large-scale optimization problems.Comment: 28 pages, 1 figure, minor revision, scaled CPU time

Integer Programming Algorithms: A Framework and State-of-the-Art Survey

A unifying framework is developed to facilitate the understanding of most known computational approaches to integer programming. A number of currently operational algorithms are related to this framework, and prospects for future progress are assessed.

A Mixed-Integer Programming Approach to Air Cargo Fleet Planning

This paper deals with the mathematical programming aspects of a long range planning study done for the Flying Tiger Line, an all-cargo airline. The study addressed two strategic problems: the design of the service network and the selection and deployment of the aircraft fleet. We show how the concept of a spider graph provides a natural building block for network design and present a mixed-integer programming model that enables the planner to evaluate any network constructed from spider graphs by determining the most profitable selection of aircraft and routing of cargo.integer programming application, air transportation