Search results for "Shortest path problem"
showing 10 items of 32 documents
Scalable implementation of measuring distances in a Riemannian manifold based on the Fisher Information metric
2019
This paper focuses on the scalability of the Fisher Information manifold by applying techniques of distributed computing. The main objective is to investigate methodologies to improve two bottlenecks associated with the measurement of distances in a Riemannian manifold formed by the Fisher Information metric. The first bottleneck is the quadratic increase in the number of pairwise distances. The second is the computation of global distances, approximated through a fully connected network of the observed pairwise distances, where the challenge is the computation of the all sources shortest path (ASSP). The scalable implementation for the pairwise distances is performed in Spark. The scalable…
Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems
2016
Mixed integer optimal compensation deals with optimization problems with integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls could lead to intractability in problems of large dimensions. To address this challenge, we introduce a decomposition method which turns the original n-dimensional optimization problem into n independent scalar problems of lot sizing form. Each of these problems can be viewed as a two-player zero-sum game, which introduces some element of conservatism. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon, a step that mirro…
Stabilized branch-and-price algorithms for vector packing problems
2018
Abstract This paper considers packing and cutting problems in which a packing/cutting pattern is constrained independently in two or more dimensions. Examples are restrictions with respect to weight, length, and value. We present branch-and-price algorithms to solve these vector packing problems (VPPs) exactly. The underlying column-generation procedure uses an extended master program that is stabilized by (deep) dual-optimal inequalities. While some inequalities are added to the master program right from the beginning (static version), other violated dual-optimal inequalities are added dynamically. The column-generation subproblem is a multidimensional knapsack problem, either binary, boun…
Branch-price-and-cut algorithms for the pickup and delivery problem with time windows and multiple stacks
2016
Abstract This paper proposes models and algorithms for the pickup and delivery vehicle routing problem with time windows and multiple stacks. Each stack is rear-loaded and is operated in a last-in-first-out (LIFO) fashion, meaning that when an item is picked up, it is positioned at the rear of a stack. An item can only be delivered if it is in that position. This problem arises in the transportation of heavy or dangerous material where unnecessary handling should be avoided, such as in the transportation of cars between car dealers and the transportation of livestock from farms to slaughterhouses. To solve this problem, we propose two different branch-price-and-cut algorithms. The first sol…
Asymmetry matters: Dynamic half-way points in bidirectional labeling for solving shortest path problems with resource constraints faster
2017
Abstract With their paper “Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints” [Discrete Optimization 3, 2006, pp. 255–273] Righini and Salani introduced bounded bidirectional dynamic programming (DP) as an acceleration technique for solving variants of the shortest path problem with resource constraints (SPPRC). SPPRCs must be solved iteratively when vehicle routing and scheduling problems are tackled via Lagrangian relaxation or column-generation techniques. Righini and Salani and several subsequent works have shown that bounded bidirectional DP algorithms are often superior to their monodirectional counterparts, s…
Two shortest path metrics on well-formed parentheses strings
1996
We present an analysis of two transformations on well-formed parentheses strings. Using a lattice approach, the corresponding least-move distances are computable, the first in linear time and the second in quadratic time.
Implementation of algorithms forK shortest loopless paths
1986
Implementations of loopless k shortest path algorithms are examined. Efficient storage structures for a large number of paths are given. A fast algorithm for determining the shortest paths in Yen's method is developed. Timing experiments show that a hybrid of Clarke's and Yen's methods is generally the fastest, although not significantly. Using upper bounds for the lengths of paths essentially improves all methods.
Feature selection with Ant Colony Optimization and its applications for pattern recognition in space imagery
2016
This paper presents a feature selection (FS) algorithm using Ant Colony Optimization (ACO). It is inspired by the particular behavior of real ants, namely by the fact that they are capable of finding the shortest path between a food source and the nest. There are considered two ACO-FS model applications for pattern recognition in remote sensing imagery: ACO Band Selection (ACO-BS) and ACO Training Label Purification (ACO-TLP). The ACO-BS reduces dimensionality of an input multispectral image data by selecting the “best” subset of bands to accomplish the classification task. The ACO-TLP selects the most informative training samples from a given set of labeled vectors in order to optimize the…
The computational complexity of the relative robust shortest path problem with interval data
2004
Abstract The paper deals with the relative robust shortest path problem in a directed arc weighted graph, where arc lengths are specified as intervals containing possible realizations of arc lengths. The complexity status of this problem has been unknown in the literature. We show that the problem is NP -hard.
A class of label-correcting methods for the K shortest paths problem
2001
In this paper we deal with the problem of finding the first K shortest paths from a single origin node to all other nodes of a directed graph. In particular, we define the necessary and sufficient conditions for a set of distance label vectors, on the basis of which we propose a class of methods which can be viewed as an extension of the generic label-correcting method for solving the classical single-origin all-destinations shortest path problem. The data structure used is characterized by a set of K lists of candidate nodes, and the proposed methods differ in the strategy used to select the node to be extracted at each iteration. The computational results show that: 1. some label-correct…