Constraint Programming Based Column Generation Research Articles

Network Migration Problem: A Hybrid Logic-Based Benders Decomposition Approach

Telecommunication networks frequently face technological advancements and need to upgrade their infrastructure. Adapting legacy networks to the latest technology requires synchronized technicians responsible for migrating the equipment. The goal of the network migration problem is to find an optimal plan for this process. This is a defining step in the customer acquisition of telecommunications service suppliers, and its outcome directly impacts the network owners’ purchasing behavior. We propose the first exact method for the network migration problem, a logic-based Benders decomposition approach that benefits from a hybrid constraint programming–based column generation in its master problem and a constraint programming model in its subproblem. This integrated solution technique is applicable to any integer programming problem with similar structure, most notably the vehicle routing problem with node synchronization constraints. Comprehensive evaluation of our method over instances based on six real networks demonstrates the computational efficiency of the algorithm in obtaining quality solutions. We also show the merit of each incorporated optimization paradigm in achieving this performance. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by Mitacs. SciNet is funded by the Canada Foundation for Innovation, the Government of Ontario, Ontario Research Fund–Research Excellence, and the University of Toronto. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2023.1280 .

A constraint programming based column generation approach for crew scheduling: A case study for the Kayseri railway

Although railway systems have been widely used in public transportation for several years, crew scheduling research focuses on airline operations. Since the crew costs constitute the critical part of the operational costs in railway public transportation, the crew scheduling problem gains more importance. Crew scheduling aims to assign all trips to duty packages in a timeline while satisfying several labour working rules, company requirements, and operational restrictions. Because of the complexity of real-world conditions, crew scheduling problems are NP-complete. In this study, the crew scheduling problem was addressed, and a constraint programming based column generation algorithm was proposed as a solution approach. A column generation algorithm was employed to solve problems having a considerable number of variables. In this study, the master problem was designed as a set partitioning problem that aimed to assign all trips to duty while minimizing the cost. In the subproblem, new column(s) satisfying all constraints were generated and added to the master problem to reduce the cost. To analyse the performance of the proposed approach, an integer programming model of the problem was developed. An extensive computational study is presented to compare the results of these two modelling approaches via different real-life problem instances.

Mixed-integer linear programming, constraint programming and column generation approaches for operating room planning under block strategy

The planning of operating rooms under block strategy is addressed in this study. The decisions are about opening the operating rooms and assigning specialties and surgeons to blocks at the tactical level, and sequencing the surgeries at the operational level. This problem aims to minimize the costs of opening the operating rooms and their overtime, the waiting costs of patients, and the surgeons' idle costs. We propose two mixed-integer linear programming models, a constraint programming (CP) model and a constraint programming-based column generation (CPCG) method for handling the problem. The performance of the models is evaluated by random test instances. The results indicate that CP and CPCG models are more efficient than the linear programming models in terms of computational time, and the number of variables and constraints. The proposed method CPCG generates optimal solutions for problem instances of up to 30 surgeries in less than 4 min. The CP model finds the optimal solutions in about one minute but proving the optimality of the found solutions is time-consuming in some instances. The maximum optimality gap for the proposed two-step linear programming model is 2%, while its run time is less than 20 s. A sensitivity analysis is done on the main parameters of the problem like objectives' weights, opening cost of ORs, unit waiting cost of patients, and the maximum available time in surgery blocks. Among the three objectives, the unit waiting cost of patients has the most sensitivity to variations of the objective function weights.

Constraint Programming-based Column Generation

This paper surveys recent applications and advances of the Constraint Programming-based Column Generation framework, where the master subproblem is solved by traditional OR techniques, while the pricing subproblem is solved by Constraint Programming. This framework has been introduced to solve crew assignment problems, where complex regulations make the pricing subproblem demanding for traditional techniques, and then it has been applied to other contexts. The main benefits of using Constraint Programming are the expressiveness of its modeling language and the flexibility of its solvers. Recently, the Constraint Programming-based Column Generation framework has been applied to many other problems, ranging from classical combinatorial problems such as graph coloring and two dimensional bin packing, to application oriented problems, such as airline planning and resource allocation in wireless ad-hoc networks.

A constraint programming based column generation approach to nurse rostering problems

This paper presents our investigations on a hybrid constraint programming based column generation (CP–CG) approach to nurse rostering problems. We present a complete model to formulate all the complex real-world constraints in several benchmark nurse rostering problems. The hybrid CP–CG approach is featured with not only the effective relaxation and optimality reasoning of linear programming but also the powerful expressiveness of constraint programming in modeling the complex logical constraints in nurse rostering problems. In solving the CP pricing subproblem, we propose two strategies to generate promising columns which contribute to the efficiency of the CG procedure. A Depth Bounded Discrepancy Search is employed to obtain diverse columns. A cost threshold is adaptively tightened based on the information collected during the search to generate columns of good quality. Computational experiments on a set of benchmark nurse rostering problems demonstrate a faster convergence by the two strategies and justify the effectiveness and efficiency of the hybrid CP–CG approach.

Constraint programming-based column generation

This paper surveys recent applications and advances of the constraint programming-based column generation framework, where the master subproblem is solved by traditional OR techniques, while the pricing subproblem is solved by constraint programming (CP). This framework has been introduced to solve crew assignment problems, where complex regulations make the pricing subproblem demanding for traditional techniques, and then it has been applied to other contexts. The main benefits of using CP are the expressiveness of its modeling language and the flexibility of its solvers. Recently, the CP-based column generation framework has been applied to many other problems, ranging from classical combinatorial problems such as graph coloring and two dimensional bin packing, to application oriented problems, such as airline planning and resource allocation in wireless ad hoc networks.

Solving VRPTWs with Constraint Programming Based Column Generation

Constraint programming based column generation is a hybrid optimization framework recently proposed (Junker et al., 1999) that uses constraint programming to solve column generation subproblems. In the past, this framework has been used to solve scheduling problems where the associated graph is naturally acyclic and has done so very efficiently. This paper attempts to solve problems whose graph is cyclic by nature, such as routing problems, by solving the elementary shortest path problem with constraint programming. We also introduce new redundant constraints which can be useful in the general framework. The experimental results are comparable to those of the similar method in the literature (Desrochers, Desrosiers, and Solomon, 1992) but the proposed method yields a much more flexible approach.

Constraint Programming Based Column Generation for Crew Assignment

Airline crew assignment problems are large-scale optimization problems which can be adequately solved by column generation. The subproblem is typically a so-called constrained shortest path problem and solved by dynamic programming. However, complex airline regulations arising frequently in European airlines cannot be expressed entirely in this framework and limit the use of pure column generation. In this paper, we formulate the subproblem as a constraint satisfaction problem, thus gaining high expressiveness. Each airline regulation is encoded by one or several constraints. An additional constraint which encapsulates a shortest path algorithm for generating columns with negative reduced costs is introduced. This constraint reduces the search space of the subproblem significantly. Resulting domain reductions are propagated to the other constraints which additionally reduces the search space. Numerical results based on data of a large European airline are presented and demonstrate the potential of our approach.