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

Boxstep : a new strategy for large scale mathematical programming

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Crew Planning at Flying Tiger: A Successful Application of Integer Programming

This paper presents a successful application of integer programming to the scheduling of flight crews for a cargo airline. The crew planning process is discussed, the role of the set partitioning model is explained, and representative computational experience is reported. The success of this application is shown to rest upon improved problem conceptualization and decomposition rather than on any advances in solution techniques.crew scheduling, integer programming applications