Research on the Shortest Path Problem Based on Green Transportation

2014 ◽  
Vol 1010-1012 ◽  
pp. 1858-1861
Author(s):  
Bao You Liu ◽  
Ya Ru Liu
Keyword(s):  
Shortest Path ◽  
Operations Research ◽  
Optimization Problem ◽  
Daily Life ◽  
Mathematical Optimization ◽  
Shortest Path Problem ◽  
Hebei Province ◽  
Research Knowledge ◽  
Green Transportation ◽  
Mathematical Optimization Problem

The shortest path problem is a typical mathematical optimization problem which often encountered in the production field and daily life. From the perspective of green transportation, in this paper, the shortest path problem in Hebei Province was put forward that applied the operations research knowledge, and solved the analysis by lingo11.0. The results showed that the shortest path is 2230.00 km that started from Shijiazhuang through each prefecture-level city, then back to Shijiazhuang. The shortest path from Shijiazhuang to Qinhuangdao is 589.00 km.

An Approach for the Fast Calculation Method of Pareto Solutions of a Two-objective Network

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Natsumi Takahashi ◽  
Tomoaki Akiba ◽  
Shuhei Nomura ◽  
Hisashi Yamamoto
Keyword(s):  
Shortest Path ◽  
Optimization Problem ◽  
Computing Time ◽  
Search Space ◽  
Shortest Path Problem ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Fast Calculation ◽  
Multi Objective ◽  
Other Information

The shortest path problem is a kind of optimization problem and its aim is to find the shortest path connecting two specific nodes in a network, where each edge has its distance. When considering not only the distances between the nodes but also some other information, the problem is formulated as a multi-objective shortest path problem that involves multiple conflicting objective functions. The multi-objective shortest path problem is a kind of optimization problem of multi-objective network. In the general cases, multi-objectives are rarely optimized by a solution. So, to solve the multi-objective shortest path problem leads to obtaining Pareto solutions. An algorithm for this problem has been proposed by using the extended Dijkstra's algorithm. However, this algorithm for obtaining Pareto solutions has many useless searches for paths. In this study, we consider two-objective shortest path problem and propose efficient algorithms for obtaining the Pareto solutions. Our proposed algorithm can reduce more search space than existing algorithms, by solving a single-objective shortest path problem. The results of the numerical experiments suggest that our proposed algorithms reduce the computing time and the memory size for obtaining the Pareto solutions.

scholarly journals Heuristic Function Influence to the Global Optimum Value in Shortest Path Problem

2017 ◽  
Author(s):  
Andysah Putera Utama Siahaan
Keyword(s):  
Shortest Path ◽  
Search Algorithm ◽  
Daily Life ◽  
Global Optimum ◽  
Shortest Path Problem ◽  
Manhattan Distance ◽  
Evaluation Function ◽  
Heuristic Function ◽  
Optimum Route

Determination of the optimum route is often encountered in daily life. The purpose of the optimum route itself is to find the best trajectory of the two pairs of vertices contained in a map or graph. The search algorithm applied is A*. This algorithm has the evaluation function to assist the search. The function is called heuristic. Two methods which have been introduced as a step to obtain the value of heuristic function are by using Euclidean and Manhattan distance. Both of these methods create the optimum distance in shortest path problem, but these functions gain the different results. This research performs the development of the heuristic function using Euclidean, Manhattan, Euclidean Square and the author method (Andysah).

scholarly journals Computing technical capacities in the European entry-exit gas market is NP-hard

2020 ◽  
Vol 295 (1) ◽  
pp. 337-362
Author(s):  
Lars Schewe ◽  
Martin Schmidt ◽  
Johannes Thürauf
Keyword(s):  
Optimization Problem ◽  
Mathematical Optimization ◽  
Entry And Exit ◽  
Flow Models ◽  
Graph Classes ◽  
System Operator ◽  
Mathematical Optimization Problem ◽  
Market Organization ◽  
Gas Market

Abstract As a result of its liberalization, the European gas market is organized as an entry-exit system in order to decouple the trading and transport of natural gas. Roughly summarized, the gas market organization consists of four subsequent stages. First, the transmission system operator (TSO) is obliged to allocate so-called maximal technical capacities for the nodes of the network. Second, the TSO and the gas traders sign mid- to long-term capacity-right contracts, where the capacity is bounded above by the allocated technical capacities. These contracts are called bookings. Third, on a day-ahead basis, gas traders can nominate the amount of gas that they inject or withdraw from the network at entry and exit nodes, where the nominated amount is bounded above by the respective booking. Fourth and finally, the TSO has to operate the network such that the nominated amounts of gas can be transported. By signing the booking contract, the TSO guarantees that all possibly resulting nominations can indeed be transported. Consequently, maximal technical capacities have to satisfy that all nominations that comply with these technical capacities can be transported through the network. This leads to a highly challenging mathematical optimization problem. We consider the specific instantiations of this problem in which we assume capacitated linear as well as potential-based flow models. In this contribution, we formally introduce the problem of () and prove that it is -complete on trees and -hard in general. To this end, we first reduce the problem to for the case of capacitated linear flows in trees. Afterward, we extend this result to with potential-based flows and show that this problem is also -complete on trees by reducing it to the case of capacitated linear flow. Since the hardness results are obtained for the easiest case, i.e., on tree-shaped networks with capacitated linear as well as potential-based flows, this implies the hardness of for more general graph classes.

scholarly journals Un Método de Optimización Proximal para Problemas de Localización Cuasi-convexa

2019 ◽  
pp. 25-32
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Optimal Location ◽  
Proximal Point Method ◽  
Localization Problem ◽  
Proximal Point ◽  
Localization Theory ◽  
Mathematical Optimization Problem

Un Método de Optimización Proximal para Problemas de Localización Cuasi-convexa Miguel A. Cano Lengua, Erik A. Papa Quiroz Facultad de Ciencias Naturales y Matemática -FCNM/ Universidad Nacional del Callao Callao- Perú DOI: https://doi.org/10.33017/RevECIPeru2011.0018/ RESUMEN El problema de localización es de gran interés para poder establecer de manera óptima diferentes demandas de ubicación en el sector estatal o privado. El modelo de este problema se reduce generalmente a un problema de optimización matemática. En el presente trabajo presentamos un método de optimización proximal para resolver problemas de localización donde la función objetivo es cuasi-convexa y no diferenciable. Probamos que las iteraciones dadas por el método están bien definidas y bajo algunas hipótesis sobre la función objetivo probamos la convergencia del método. Descriptores: Método del punto proximal, teoría de localización, convergencia global, función cuasi-convexa. ABSTRACT The localization problem is of great interest to establish the optimal location of the different demands in the state or private sector. The model of this problem is generally reduced to solve a mathematical optimization problem. In the present work we present a proximal optimization method to solve localization problems where the objective function is non differentiable and quasiconvex. We prove that the iterations of the method are well defined and under some assumption on the objective function we prove the convergence of the method. Keywords: Proximal point method, localization theory, global convergence, quasiconvex function.

Minimum Vibration Cam Profiles

1968 ◽  
Vol 10 (3) ◽  
pp. 219-227 ◽  
Author(s):  
H. Kwakernaak ◽  
J. Smit
Keyword(s):  
Linear Programming ◽  
Optimization Problem ◽  
Numerical Solutions ◽  
Mathematical Optimization ◽  
Problem Formulation ◽  
Programming Formulation ◽  
Quadratic Problem ◽  
Linear Programming Formulation ◽  
Mathematical Optimization Problem ◽  
Minimal Residual

The problem of finding cam profiles with limited follower velocity, acceleration and jerk and minimal residual vibrations over a prescribed range of cam speeds is formulated as a mathematical optimization problem. Two versions of the problem are considered: a quadratic problem formulation and a linear programming formulation. Numerical solutions have been found through the use of a digital computer and the methods are compared. Examples of profiles are presented which compare favourably with the well-known cycloidal profile.

Optimal Sythesis of Planar Six-Link Chains Using Least-Squares Gradient Search

1972 ◽  
Vol 1 (1) ◽  
pp. 31-36 ◽  
Author(s):  
F.Y. Chen ◽  
V.M. Dalsania
Keyword(s):  
Least Squares ◽  
Optimization Problem ◽  
Mathematical Optimization ◽  
Dimensional Synthesis ◽  
Gradient Search ◽  
Computer Solution ◽  
Numerical Examples ◽  
Function Generators ◽  
Mathematical Optimization Problem

The approximate dimensional synthesis of three basic forms of the planar six-link chain as function generators is formulated as a mathematical optimization problem. Least-squares gradient search scheme is used for the computer solution. Numerical examples are given.

scholarly journals A reduction heuristic for the all-colors shortest path problem

2020 ◽  
Author(s):  
Francesco Carrabs ◽  
Raffaele Cerulli ◽  
Andrea Raiconi
Keyword(s):  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Optimization Problem ◽  
Weighted Graph ◽  
Shortest Path Problem ◽  
Traveling Salesman ◽  
Np Hard ◽  
Computational Results ◽  
Solution Path ◽  
Generalized Traveling Salesman Problem

The All-Colors Shortest Path is a recently introduced NP-Hard optimization problem, in which a color is assigned to each vertex of an edge weighted graph, and the aim is to find the shortest path spanning all colors. The solution path can be not simple, that is it is possible to visit multiple times the same vertices if it is a convenient choice. The starting vertex can be constrained (ACSP) or not (ACSP-UE). We propose a reduction heuristic based on the transformation of any ACSP-UE instance into an Equality Generalized Traveling Salesman Problem one. Computational results show the algorithm to outperform the best previously known one.

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