Improving the Cooperation Between the Master Problem and the Subproblem in Constraint Programming Based Column Generation

• Published in: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems pp. 217 - 227
• Main Authors: Gendron, Bernard, Lebbah, Hocine, Pesant, Gilles
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Exact sciences and technology; Learning and adaptive systems; Mathematical programming; Operational research and scientific management; Operational research. Management science; Search strategy; Coordination; Customization; Pricing; Scheduling; Set partitioning; Tariffication; Combinatorial optimization; Artificial intelligence; Constrained optimization; Mathematical programming
• ISBN: 9783540261520; 3540261524
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11493853_17

Constraint programming (CP) based column generation uses CP to solve the pricing subproblem. We consider a set partitioning formulation with a huge number of variables, each of which can be generated by solving a CP subproblem. We propose two customized search strategies to solve the CP subproblem, which aim to improve the coordination between the master problem and the subproblem. Specifically, these two strategies attempt to generate more promising columns for the master problem in order to counter the effect of slow convergence and the difficulty of reaching integer solutions. The first strategy uses the dual variables to direct the search towards columns that drive the relaxed master problem faster to optimality. The second strategy exploits the structure of the constraints in the master problem to generate columns that help to reach integer solutions more quickly. We use a physician scheduling problem to test the strategies.