Search

The crew-pairing problem (CPP) is solved in the first step of the crew-scheduling process. It consists of creating a set of pairings (sequence of flights, connections, and rests forming one or multiple days of work for an anonymous crew member) that covers a given set of flights at minimum cost. Those pairings are assigned to crew members in a subsequent crew-rostering step. In this paper, we propose a new integral column-generation algorithm for the CPP, called improved integral column generation with prediction ([Formula: see text]), which leaps from one integer solution to another until a near-optimal solution is found. Our algorithm improves on previous integral column-generation algorithms by introducing a set of reduced subproblems. Those subproblems only contain flight connections that have a high probability of being selected in a near-optimal solution and are, therefore, solved faster. We predict flight-connection probabilities using a deep neural network trained in a supervised framework. We test [Formula: see text] on several real-life instances and show that it outperforms a state-of-the-art integral column-generation algorithm as well as a branch-and-price heuristic commonly used in commercial airline planning software, in terms of both solution costs and computing times. We highlight the contributions of the neural network to [Formula: see text].

The exact solution and heuristic solution have their own strengths and weaknesses on solving the Vehicle Routing Problems with Time Windows (VRPTW). This paper proposes a hybrid Column Generation Algorithm with Metaheuristic Optimization (CGAMO) to overcome their weaknesses. Firstly, a Modified Labelling Algorithm (MLA) in the sub-problem of path searching is analysed. And a search strategy in CGAMO based on the demand of sub-problem is proposed to improve the searching efficiency. While putting the paths found in the sub-problem into the main problems of CGAMO, the iterations may fall into endless loops. To avoid this problem and keep the main problems in a reasonable size, two conditions on saving the old paths in the main problem are used. These conditions enlarge the number of constraints considered in the iterations to strengthen the limits of dual variables. Through analysing the sub-problem, we can find many useless paths that have no effect on the objective function. Secondly, in order to reduce the number of useless paths and improve the efficiency, this paper proposes a heuristic optimization strategy of CGAMO for dual variables. It is supposed to accelerate the solving speed from the view of on the dual problem. Finally, extensive experiments show that CGAMO achieves a better performance than other state-of-the-art methods on solving VRPTW. The comparative experiments also present the parameters sensitivity analysis, including the different effects of MLA in the different path selection strategies, the characteristics and the applicable scopes of the two pathkeeping conditions in the main problem. First published online:25 Oct 2013

We present a new column generation algorithm for the determination of a classifier in the two classes LAD (Logical Analysis of Data) model. Unlike existing algorithms who seek a classifier that at the same time maximizes the margin of correctly classified observations and minimizes the amount of violations of incorrectly classified observations, we fix the margin to a difficult-to-achieve target and minimize a piecewise convex linear function of the violation of incorrectly classified observations. Moreover a part of the training set, called control set, is reserved to select, among all feasible classifiers found by the algorithm, the one with highest performance on that set. One advantage of the proposed algorithm is that it essentially does not require any calibration. Computational results are presented that show the effectiveness of this approach.

Flight disruptions disturb airlines’ routine, causing a lot of troubles to passengers as well as bringing on huge economic losses to airlines. So the irregular flight recovery is made to solve this problem. Irregular flight recovery is a large-scale and integer programming problem, which has complex variables and constraints. In this research, we model in terms of real situation and a column generation algorithm combined with Bellman-Ford algorithm is presented to release the influences resulted from disruptions. Computational experiments show that the proposed algorithm is feasible. Keywords-flight disruptions; airlines;column generation; network optimation

An exact column generation algorithm for integer programs with a large (implicit) number of columns is presented. The family of problems that can be treated includes not only standard partitioning problems such as bin packing and certain vehicle routing problems in which the columns generated have 0 - 1 components and a right hand side vector of 1 's, but also the cutting stock problem in which the columns and right hand side are nonnegative integer vectors. We develop a combined branching and subproblem modification scheme that generalizes existing approaches, and also describe the use of lower bounds to reduce tailing-off effects.

We develop a set-covering type formulation for a crew planning problem that determines the minimum sufficient crew size for a region over a finite planning horizon where the periodic repeatability of crew schedules is considered as well. The resulting problem formulation cannot be solved with a traditional column generation algorithm. We propose a column-and-row generation algorithm and present preliminary computational results.

In this paper we present a novel column generation (CG) formulation and a branch-and-price (BP) algorithm for the Vehicle Routing Problem with Cross-Docking (VRPCD). Our BP algorithm is compared with a previous algorithm to solve the VRPCD and the computational results show that our approach dominates the other in terms of the quality of lower and upper bounds and also can evaluate optimal solutions faster.

When a dual-based procedure is used to solve a geometric programming problem, the presence of inactive constraints at the primal optimum reduces the amount of information available about the relationship between the optimal primal and dual vectors. In certain situations one must resort to solving one or more subsidiary problems to recover solution from the dual optimum. This paper reviews such situations and presents an alternative formulation of the dual as a generalized linear program, along with a column generation algorithm based on the same. The algorithm avoids subsidiary problems, and the formulation provides more information than the traditional dual when recovering the primal optimum.

The solution strategy known as the column generation principle—and its dual counterpart, constraint generation—is one of the standard tools of mathematical programming. Since the pioneering work on the maximum multi-commodity network flow problem by Ford and Fulkerson [FoF58, FoF62] in the late 50’s, column generation methods have been developed and applied in a variety of contexts. With no doubt, the most famous column generation method is the Dantzig-Wolfe decomposition method for specially structured linear programs ([DaW60, DaW61]), in which the column generation is based on the pricingout mechanism of the simplex method. [Another famous column generation technique is the one for cutting stock problems, where the column generation is based on the solution of knapsack problems ([GiG61, GiG63, GiG65]).]

Cutting plane and column generation algorithms are known to be dual in a certain sense. In this paper, a general cutting plane algorithm of Kelley type for convex programs and a general column generation algorithm of Dantzig-Wolfe type for Wolfe's generalized program are described. These two algorithms are shown to be dual. An estimation of the optimal value known for Dantzig-Wolfe methods is carried over to cutting plane methods.

In a previous paper, Appelgren (Appelgren, L. 1969. A column generation algorithm for a ship scheduling problem. Trans. Sci. 3 53–68.), a decomposition algorithm for a class of vessel scheduling problems was presented. In some problems, the algorithm gives fractional solutions that cannot be interpreted as feasible schedules. This paper treats two integer programming methods that can be used to resolve these cases. The cutting plane method that was first tested was abandoned because it was not able to solve all the test problems. The second method is a branch-and-bound algorithm, where the branching is performed on one of the “essential” fractional variables and where the bounds are obtained by the decomposition algorithm. All fractional problems that have been found by simulation or in regular use of the algorithm have been solved, mostly with one branching only. There are fundamental difficulties in combining these integer programming methods with the Dantzig-Wolfe decomposition, since the constraints generated in the master program have to be taken into account in the solution of the subprograms. The success in this case is due to the simple structure of the master LP problem.