Optimising halting station of passenger railway lines

In many real life passenger railway networks, the types of stations and lines characterisethe halting stations of the train lines. Common types are Regional, Interregional or Intercity.This paper considers the problem of altering the halts of lines by both upgrading and downgrading stations, such that this results in less total travel time. We propose a combination of reduction methods, Lagrangian relaxation, and a problem-specific multiplier adjustment algorithm to solve the presented mixed integer linear programming formulation. A computational study of several real-life instances based on problem data of the Dutch passenger railway operator NS Reizigers is included.mathematical economics and econometrics ;

Fast and Compact Exact Distance Oracle for Planar Graphs

For a given a graph, a distance oracle is a data structure that answers distance queries between pairs of vertices. We introduce an $O(n^{5/3})$-space distance oracle which answers exact distance queries in $O(\log n)$ time for $n$-vertex planar edge-weighted digraphs. All previous distance oracles for planar graphs with truly subquadratic space i.e., space $O(n^{2 - \epsilon})$ for some constant $\epsilon > 0$) either required query time polynomial in $n$ or could only answer approximate distance queries. Furthermore, we show how to trade-off time and space: for any $S \ge n^{3/2}$, we show how to obtain an $S$-space distance oracle that answers queries in time $O((n^{5/2}/ S^{3/2}) \log n)$. This is a polynomial improvement over the previous planar distance oracles with $o(n^{1/4})$ query time

An auction algorithm for shortest paths

Caption title.Includes bibliographical references (p. 27-29).Research supported by the ARO. DAAL03-86-K-0171 Research supported by the NSF. DDM-8903385by Dimitri P. Bertsekas

A Computational study of branching rules for multi-commodity fixed-charged network flow problems

Branch and bound based algorithms are used by many commercial mixed integer programming solvers for solving complex optimization problems. In a branch and bound based method, a feasible region is divided into smaller sub-problems. This is called branching and various branching strategies have been developed to improve the performance of branch and bound based algorithms. However, their performance has primarily been studied on general mixed integer programs. Thus, in the first phase of this thesis, we study the performance of these branching strategies on a specific, structured mixed integer program, the capacitated multi-commodity fixed charge network flow (MCFCNF) problem. We also develop new branching strategies using the pool of available feasible solutions for solving the mixed integer program for MCFCNF. We present the computational results for testing various branching rules with four different variants of the network design problem studied with SCIP and GLPK mathematical solvers

Solving the optimum communication spanning tree problem

This paper presents an algorithm based on Benders decomposition to solve the optimum communication spanning tree problem. The algorithm integrates within a branch-and-cut framework a stronger reformulation of the problem, combinatorial lower bounds, in-tree heuristics, fast separation algorithms, and a tailored branching rule. Computational experiments show solution time savings of up to three orders of magnitude compared to state-of-the-art exact algorithms. In addition, our algorithm is able to prove optimality for five unsolved instances in the literature and four from a new set of larger instances.Peer ReviewedPostprint (author's final draft

Experiments in reduction techniques for linear and integer programming

This study consisted of evaluating the relative performance to a selection of the most promising size-reduction techniques. Experiments and comparisons were made among these techniques on a series of tested problems to determine their relative efficiency, efficiency versus time etc. Three main new methods were developed by modifying and extending the previous ones. These methods were also tested and their results are compared with the earlier methods

Polyhedral techniques in combinatorial optimization II: computations

Combinatorial optimization problems appear in many disciplines ranging from management and logistics to mathematics, physics, and chemistry. These problems are usually relatively easy to formulate mathematically, but most of them are computationally hard due to the restriction that a subset of the variables have to take integral values. During the last two decades there has been a remarkable progress in techniques based on the polyhedral description of combinatorial problems. leading to a large increase in the size of several problem types that can be solved. The basic idea behind polyhedral techniques is to derive a good linear formulation of the set of solutions by identifying linear inequalities that can be proved to be necessary in the description of the convex hull of feasible solutions. Ideally we can then solve the problem as a linear programming problem, which can be done efficiently. The purpose of this manuscript is to give an overview of the developments in polyhedral theory, starting with the pioneering work by Dantzig, Fulkerson and Johnson on the traveling salesman problem, and by Gomory on integer programming. We also present some modern applications, and computational experience