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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2006.10.009 Byline: Diego Klabjan Keywords: Integer programming; Duality; Algorithms Abstract: Linear programming duality is well understood and the reduced cost of a column is frequently used in various algorithms. On the other hand, for integer programs it is not clear how to define a dual function even though the subadditive dual theory has been developed a long time ago. In this work we propose a family of computationally tractable subadditive dual functions for integer programs. We develop a solution methodology that computes an optimal primal solution and an optimal subadditive dual function. We present computational experiments, which show that the new algorithm is tractable. Author Affiliation: Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, United States Article History: Received 13 February 2006; Accepted 19 October 2006

Abstract In this work, we design a machine learning based method – online adaptive primal support vector regression (SVR) – to model the implied volatility surface (IVS). The algorithm proposed is the first derivation and implementation of an online primal kernel SVR. It features enhancements that allow efficient online adaptive learning by embedding the idea of local fitness and budget maintenance to dynamically update support vectors upon pattern drifts. For algorithm acceleration, we implement its most computationally intensive parts in a Field Programmable Gate Arrays hardware, where a 132x speedup over CPU is achieved during online prediction. Using intraday tick data from the E-mini S&P 500 options market, we show that the Gaussian kernel outperforms the linear kernel in regulating the size of support vectors, and that our empirical IVS algorithm beats two competing online methods with regards to model complexity and regression errors (the mean absolute percentage error of our algorithm is up to 13%). Best results are obtained at the center of the IVS grid due to its larger number of adjacent support vectors than the edges of the grid. Sensitivity analysis is also presented to demonstrate how hyper parameters affect the error rates and model complexity. [ABSTRACT FROM AUTHOR]

Disruptions such as adverse weather, flight delays and flight cancellations are a frequent occurrence in airport operations. A sophisticated gate assignment plan can be easily disrupted and serious consequences might be caused. Therefore, an efficient gate re-assignment methodology is of great importance for the airline industry. In this paper, we propose an efficient gate re-assignment methodology to deal with the disruptions, in which the objective function is to minimize the weighted sum of the total flight delays, the number of gate re-assignment operations and the number of missed passenger connections. Two multi-commodity network flow models are built for the pure gate re-assignment problem and the gate re-assignment problem with connecting passengers. Recognizing the inherent NP hard nature of the gate re-assignment problem, two heuristic algorithms are proposed to solve the models efficiently. The proposed models and algorithms are tested based on real-world data of a large U.S. carrier and computational results reveal that the proposed methodologies can provide high quality solutions within a short computational time. [ABSTRACT FROM AUTHOR]

Most recent machine learning research focuses on developing new classifiers for the sake of improving classification accuracy. With many well-performing state-of-the-art classifiers available, there is a growing need for understanding interpretability of a classifier necessitated by practical purposes such as to find the best diet recommendation for a diabetes patient. Inverse classification is a post modeling process to find changes in input features of samples to alter the initially predicted class. It is useful in many business applications to determine how to adjust a sample input data such that the classifier predicts it to be in a desired class. In real world applications, a budget on perturbations of samples corresponding to customers or patients is usually considered, and in this setting, the number of successfully perturbed samples is key to increase benefits. In this study, we propose a new framework to solve inverse classification that maximizes the number of perturbed samples subject to a per-feature-budget limits and favorable classification classes of the perturbed samples. We design algorithms to solve this optimization problem based on gradient methods, stochastic processes, Lagrangian relaxations, and the Gumbel trick. In experiments, we find that our algorithms based on stochastic processes exhibit an excellent performance in different budget settings and they scale well. The relative improvement of the proposed stochastic algorithms over an existing method with a traditional formulation is 15% in the real-world dataset and 21% in two public datasets on average. • A new framework to solve inverse classification is developed. • It obtains successfully perturbed samples within a per-feature budget. • Algorithms are designed based on a gradient method and the Gumbel trick. • Real data from an industrial partner and two healthcare public datasets are used. • The stochastic approaches perform great on various budget scenarios, and they scale. [ABSTRACT FROM AUTHOR]

We consider the single item lot sizing problem with minimum order quantity where each period has an additional constraint on minimum production quantity. We study special cases of the general problem from the algorithmic and mathematical programming perspective. We exhibit a polynomial case when capacity is constant and minimum order quantities are non-increasing in time. Linear programming extended formulations are provided for various cases with constant minimum order quantity. [ABSTRACT FROM AUTHOR]

Abstract: Deplaning naturally occurs row by row down the length of an aircraft. Using simulation and optimization, we design deplaning strategies (e.g., deplane by group and/or column) that significantly reduce the overall unstructured deplaning time. The evaluations derived from a combination of optimization and simulation were tested across several equipment types using data gathered through field observations for calibration. [Copyright &y& Elsevier]

Abstract: Driven by a real-world application in the beverage industry, this paper provides a design of a new VNS variant to tackle the annual production budget problem. The problem consists of assigning and scheduling production lots in a multi-plant environment, where each plant has a set of filling lines that bottle and pack drinks. Plans also consider final product transfers between the plants. Our algorithm fixes setup variables for family of products and determines production, inventory and transfer decisions by solving a linear programming (LP) model. As we are dealing with very large problem instances, it is inefficient and unpractical to search the entire neighborhood of the incumbent solution at each iteration of the algorithm. We explore the sensitivity analysis of the LP to guide the partial neighborhood search. Dual-reoptimization is also used to speed-up the solution procedure. Tests with instances from our case study have shown that the algorithm can substantially improve the current business practice, and it is more competitive than state-of-the-art commercial solvers and other VNS variants. [Copyright &y& Elsevier]