Mathematical Problems in Engineering

Volume 2019, Article ID 8709042, 8 pages

https://doi.org/10.1155/2019/8709042

## Solution to Shortest Path Problem Using a Connective Probe Machine

Correspondence should be addressed to Yuan Kong; nc.ude.tsuds@nauygnok and Yong Fang; nc.ude.tsuds@gnoygnaf

Received 23 June 2019; Revised 16 September 2019; Accepted 22 October 2019; Published 7 November 2019

Academic Editor: Haopeng Zhang

Copyright © 2019 Jiuyun Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With the continuous urban scale expansion, traffic networks have become extremely complex. Finding an optimal route in the shortest time has become a difficult and important issue in traffic engineering study. In this study, a novel computing model, namely, probe machine, is used to solve this problem. Similar to previous studies, urban transport networks can be abstracted into maps, in which points representing places of origin, destinations, and other buildings constitute the data library and edges representing the road make up the probe library. The true solution can be obtained after one probe operation on the computing platform. And by comparing the solving process with Dijkstra’s and Floyd’s algorithms, the computing efficiency of the probe machine is clearly superior, although all three methods can solve the shortest path problem and obtain the same solution.

#### 1. Introduction

Traffic engineering is the basic theory of the research and development of traffic engineering discipline. Its main purpose is to seek the transportation system planning, construction and management scheme with the largest travel efficiency, the least traffic accidents, the fastest traffic speed, the least transportation cost, and the lowest energy consumption. The rapid development of urban traffic and increase in the number of vehicles has made travelling more convenient for people in recent years. However, urban traffic is not smooth due to the numerous traffic network nodes and complex sections; some cities suffer from traffic congestion [1, 2]. Finding a suitable path for drivers is not only one of the solutions to promote the development of urban transportation [3–5], but also one of the main purposes in traffic engineering research. Therefore, we must address this issue by determining the shortest path. In traffic engineering, “shortest path” does not necessarily mean the shortest distance, but also the shortest time or the lowest cost.

The shortest path problem is a classical problem in graph theory, which has been applied in many fields [6]. Finding the path with the shortest distance is the most basic application of the shortest path problem, which is also a very practical problem. The basic objective of the shortest path problem is to find the path, with the lowest weight, between two points where every edge in the graph has its own weight value. Many algorithms to solve the shortest path problem have been proposed in previous studies, such as Dijkstra’s algorithm [7], Bellman–Ford algorithm [8], and Floyd’s algorithm [9]. The most classical algorithm for solving such a problem is Dijkstra’s algorithm. It can solve the shortest path problem from a given point to any point; however, it fails to solve the shortest path problem with a negative weight. Therefore, Floyd’s algorithm and other algorithms were proposed to solve the above problem.

In 2016, Xu proposed a new computing model, i.e., the probe machine [10]. Probe machine is a completely parallel computing model that can simultaneously process multiple pairs of data. Parallel computing can speed up operations, expand the scale of processing problems, and facilitate the ability of algorithms to handle problems [11, 12]. Compared with turing machines, probe machines can solve NP-complete problems after a probe operation, such as the Hamiltonian cycle problem [10], vertex problem [10], travelling salesman problem [13], working operation problem [14], and so on. The probes of a probe machine can be divided into connective probes and transitive probes. A connective probe can connect data fibers from different data, while a transitive probe can transmit information between data fibers from different data. The probe machine is a form of bionic computing. It achieves complete parallelism by imitating the process of information transmission of neurons and reduces computation complexity. Bionic computing refers to the use of biological models to deal with practical problems, and it can often yield unexpected results in some fields [15, 16]. In recent studies, more computational models are used to solve all kinds of NP problems, such as SAT problem [17–21], vehicle routing problem [22–24], graph coloring problem [10, 25, 26], partner selection problem [27], and the other problems [28–33].

In this study, we first introduce a probe machine. Then, a shortest path problem, which is a problem of finding the path with the minimum distance, is solved by using Dijkstra’s algorithm, Floyd’s algorithm, and probe machine; the process using the three methods is then compared.

#### 2. Probe Machine

The probe machine was first proposed by Professor Xu in 2016. It consists of nine parts including data library (), probe library (), data controller (), probe controller (), probe operation (), computing platform (), detector (), true solution storage (), and residue collector ().

The data placement mode of the data library is nonlinear. The data library is divided into *n* data pools . Data pool includes one type of data , and data comprises a body and data fibers, as shown in Figure 1.