Column generation decomposition with the degenerate constraints in the subproblem

In this paper, we propose a new Dantzig–Wolfe decomposition for degenerate linear programs with the non degenerate constraints in the master problem and the degenerate ones in the subproblem. We propose three algorithms. The first one, where some set of variables of the original problem are added to the master problem, corresponds to the Improved Primal Simplex algorithm (IPS) presented recently by Elhallaoui et al. [7]. In the second one, some extreme points of the subproblem are added as columns in the master problem. The third algorithm is a mixed implementation that adds some original variables and some extreme points of a subproblem to the master problem. Experimental results on some degenerate instances show that the proposed algorithms yield computational times that are reduced by an average factor ranging from 3.32 to 13.16 compared to the primal simplex of CPLEX.     

Multi-phase dynamic constraint aggregation for set partitioning type problems

Dynamic constraint aggregation is an iterative method that was recently introduced to speed up the linear relaxation solution process of set partitioning type problems. This speed up is mostly due to the use, at each iteration, of an aggregated problem defined by aggregating disjoint subsets of constraints from the set partitioning model. This aggregation is updated when needed to ensure the exactness of the overall approach. In this paper, we propose a new version of this method, called the multi-phase dynamic constraint aggregation method, which essentially adds to the original method a partial pricing strategy that involves multiple phases. This strategy helps keeping the size of the aggregated problem as small as possible, yielding a faster average computation time per iteration and fewer iterations. We also establish theoretical results that provide some insights explaining the success of the proposed method. Tests on the linear relaxation of simultaneous bus and driver scheduling problems involving up to 2,000 set partitioning constraints show that the partial pricing strategy speeds up the original method by an average factor of 4.5.     

Integral simplex using decomposition with primal cutting planes

Mathematical Programming - This paper concentrates on the addition of cutting planes to the integral simplex using decomposition (ISUD) of Zaghrouti et al. (Oper Res 62(2):435–449,...     

2D-QSAR modeling,drug-likeness studies,ADMET prediction,and molecular docking for anti-lung cancer activity of 3-substituted-5-(phenylamino) indolone derivatives

Structural Chemistry - In this work, 2D-quantitative structure–activity relationship (QSAR) studies were performed on a set of 40 indolone derivative hybrids; the 40 indolone derivatives were...     

Integrated airline crew scheduling: A bi-dynamic constraint aggregation method using neighborhoods

The integrated crew scheduling (ICS) problem consists of determining, for a set of available crew members, least-cost schedules that cover all flights and respect various safety and collective agreement rules. A schedule is a sequence of pairings interspersed by rest periods that may contain days off. A pairing is a sequence of flights, connections, and rests starting and ending at the same crew base. Given its high complexity, the ICS problem has been traditionally tackled using a sequential two-stage approach, where a crew pairing problem is solved in the first stage and a crew assignment problem in the second stage. Recently, Saddoune et al. (2010b) developed a model and a column generation/dynamic constraint aggregation method for solving the ICS problem in one stage. Their computational results showed that the integrated approach can yield significant savings in total cost and number of schedules, but requires much higher computational times than the sequential approach. In this paper, we enhance this method to obtain lower computational times. In fact, we develop a bi-dynamic constraint aggregation method that exploits a neighborhood structure when generating columns (schedules) in the column generation method. On a set of seven instances derived from real-world flight schedules, this method allows to reduce the computational times by an average factor of 2.3, while improving the quality of the computed solutions.     

Flow-based integer linear programs to solve the weekly log-truck scheduling problem

Annals of Operations Research - In this paper we present the solution to a weekly log-truck scheduling problem (LTSP) integrating the routing and scheduling of trucks where all goods are...