An integer programming column generation principle for heuristic search methods

Column Generation for Linear and Integer Programming

Column generation refers to linear programming (LP) algorithms designed to solve problems in which there are a huge number of variables compared to the number of constraints and the simplex algorithm step of determining whether the current basic solution is optimal or finding a variable to enter the basis is done by solving an optimization problem rather than by enumeration. To the best of my k...

Methods and Applications in Integer Programming: All-Integer Column Generation and Nurse Scheduling

Integer programming can be used to provide solutions to complex decision and planning problems occurring in a wide variety of situations. Applying integer programming to a real life problem basically involves a first phase where a mathematical model is constructed, and a second phase where the problem described by the model is solved. While the nature of the challenges involved in the respectiv...

Advances in shortest path based column generation for integer programming

Improved Integer Programming Models and Heuristic Search for AI Planning

Motivated by the requirements of many real-life applications, recent research in AI planning has shown a growing interest in tackling problems that involve numeric constraints and complex optimization objectives. Applying Integer Programming (IP) to such domains seems to have a significant potential, since it can naturally accommodate their representational requirements. In this paper we explor...

An Evolutionary Algorithm for Column Generation in Integer Programming: An Effective Approach for 2D Bin Packing

We consider the 3-stage two-dimensional bin packing problem, which occurs in real-world problems such as glass cutting. For it, we present a new integer linear programming formulation and a branch and price algorithm. Column generation is performed by applying either a greedy heuristic or an Evolutionary Algorithm (EA). Computational experiments show the benefits of the EA-based approach. The h...