Ted K. Ralphs This paper introduces interdiction branching, a new branching method for binary integer programs that is designed to overcome the difficulties encountered in solving problems for which branching on variables is inherently weak. Unlike traditional methods, selection of the disjunction in interdiction branching takes into account the best feasible solution found so far. In particular, the … Read more
We investigate the multi-trip elementary shortest path problem (MESPPRC) with resource constraints in which the objective is to find a shortest path between a source node and a sink node such that nodes other than the specified replenishment node are visited at most once and resource constraints are not violated. After each visit to the … Read more
Branching is an important component of branch-and-bound algorithms for solving mixed integer linear programs. We consider the problem of selecting, at each iteration of the branch-and-bound algorithm, a general branching disjunction of the form $“\pi x \leq \pi_0 \vee \pi x \geq \pi_0 + 1”$, where $\pi, \pi_0$ are integral. We show that the problem … Read more
This paper studies location routing and scheduling problems, a class of problems in which the decisions of facility location, vehicle routing, and route assignment are optimized simultaneously. For a version with capacity and time restrictions, two formulations are presented, one graph-based and one set-partitioning-based. For the set-partitioning-based formulation, valid inequalities are identified and their effectiveness … Read more
We investigate the problem of simultaneously determining the location of facilities and the design of vehicle routes to serve customer demands under vehicle and facility capacity restrictions. We present a set-partitioning-based formulation of the problem and study the relationship between his formulation and the graph-based formulations that have been used in previous studies of this … Read more
Branching is an important component of the branch-and-cut algorithm for solving mixed integer linear programs. Most solvers branch by imposing a disjunction of the form“$x_i \leq k \vee x_i \geq k+1$” for some integer $k$ and some integer-constrained variable $x_i$. A generalization of this branching scheme is to branch by imposing a more general disjunction … Read more
We describe a rudimentary branch-and-cut algorithm for solving integer bilevel linear programs that extends existing techniques for standard integer linear programs to this very challenging computational setting. The algorithm improves on the branch-and-bound algorithm of Moore and Bard in that it uses cutting plane techniques to produce improved bounds, does not require specialized branching strategies, … Read more
The value function of a mixed-integer linear program (MILP) is a function that returns the optimal solution value as a function of the right-hand side. In this paper, we analyze the structure of the value function of a MILP with a single constraint. We show that the value function is uniquely determined by a finite … Read more
We present a suite of tools for visualizing the status and progress of branch-and-bound algorithms for mixed integer programming. By integrating these tools with the open-source codes CBC, SYMPHONY, and GLPK, we demonstrate the potential usefulness of visual representations in helping a user predict future progress of the algorithm or analyzing the algorithm’s performance. We … Read more
In this paper, we discuss the challenges that arise in parallelizing algorithms for solving mixed integer linear programs and introduce a software framework that aims to address these challenges. The framework was designed specifically with support for implementation of relaxation-based branch-and-bound algorithms in mind. Achieving efficiency for such algorithms is particularly challenging and involves a … Read more