Elsevier

ISA Transactions

Volume 121, February 2022, Pages 206-216
ISA Transactions

Research article
An efficient and global interactive optimization methodology for path planning with multiple routing constraints

https://doi.org/10.1016/j.isatra.2021.03.041Get rights and content

Highlights

  • The constraints are transformed into mathematical analytic expressions.

  • An adaptive strategy for the vertex priority in coding is proposed.

  • A methodology based on swarm intelligence algorithms is proposed.

  • The convergence condition of the methodology is proved theoretically.

  • Results confirm the effectiveness and superiority of the proposed methodology.

Abstract

Path planning problem is attracting wide attention in autonomous system and process industry system. The existed research mainly focuses on finding the shortest path from the source vertex to the termination vertex under loose constraints of vertex and edge. However, in realistic, the constraints such as specified vertexes, specified paths, forbidden paths and forbidden vertexes have to be considered, which makes the existing algorithms inefficient even infeasible. Aiming at solving the problems of complex path planning with multiple routing constraints, this paper organizes transforms the constraints into appropriate mathematical analytic expressions. Then, in order to overcome the defects of existing coding and optimization algorithms, an adaptive strategy for the vertex priority is proposed in coding, and an efficient and global optimization methodology based on swarm intelligence algorithms is put forward, which can make full use of the high efficiency of the local optimization algorithm and the high search ability of the global optimization algorithm. Moreover, the optimal convergence condition of the methodology is proved theoretically. Finally, two experiments are inducted, and the results demonstrated its efficiency and superiority.

Introduction

As a type of classical graph theory problem, the existing researches on the Path Planning (PP) mainly fours on the shortest path (SP) between single pair of vertexes, the shortest path from a single vertex to all other vertexes, the K shortest paths, the real-time shortest path, and the vertex-constrained shortest path which must pass through the specified vertex vertexes set. At present, the more research attention has been attached to find the shortest path from a given source vertex to a destination vertex in a given graph while satisfying the constraints and minimizing the total cost. The PP analysis is fundamental to many optimization problems, such as resource allocation, route design and analysis, etc. Many optimization problems in the field of product manufacturing, national defense construction, aerospace, transport and logistics can be converted into finding the shortest path problem. The PP analysis not only stands for finding the shortest length of the spatial distance, but also can be extended to other metrics, such as time, money and resources. As a result, it has been widely applied in the transportation system [1], [2], [3], [4], [5], [6], [7], operation routing in the communication network [8], [9], and the system for path-planning and the other related issues [10], [11], [12], [13], [14].

For solving the PP problems, the optimal result can be searched through applying the traversal method when the data size is modest. However, when the data size is dramatically expanded, the number of selectable paths will be exponentially increased, which leads to an unaccepted computational cost and makes the exhaustive search algorithm become infeasible to apply. Therefore, in order to find the optimal result in a more efficient way, the exploration of proposing better new optimization methods has always been the hot issues in the PP research. Dijkstra firstly proposed the classical Dijkstra algorithm for the PP problem [15]. Thereafter, many new PP algorithms, such as the Floyd algorithm [16], the A* algorithm [17], the particle swarm [18], [19], the genetic algorithm [20], the ant colony algorithm [21], the artificial bee colony algorithm [22] and the other intelligent optimization algorithms, were put forward. However, there is no perfect algorithm, and each of these proposed algorithms has its own drawbacks. For instance, the Dijkstra algorithm, a type of blind search algorithms, is very easy to implement but the search efficiency is low. By compiling simple code, the Floyd algorithm can calculate the shortest distance between any two vertexes, however, the time complexity is high, which is not suitable for processing a large amount of data. The A* algorithm is one of the common heuristic search algorithms, which presents a faster retrieval speed but is prone to be trapped in local optimum. Although some intelligent optimization algorithms, such as ant colony, particle swarm optimization and genetic algorithm, have achieved a certain level of success in solving the PP problem, they could still fall into the local optimum. In recent years, some new PP algorithms have been proposed, such as pulse coupled network algorithm [23], Lagrange relaxation and enumeration algorithm [24], algebraic algorithm [25], [26], dynamic programming algorithm [27] and new K shortest path algorithm [28], [29], [30], which can effectively improve the accuracy and efficiency of the existing path planning methods.

Further, in order to solve the problems more conveniently, these methods tend to apply simplification in dealing with real-world practices, which may lead to inaccurate optimization result in telecommunication system, emergency services, transport system, terrain analysis, urban planning and network access control. In order to overcome these aforementioned shortcomings, by considering specified vertexes, specified paths, forbidden vertexes, forbidden paths and the limit condition of used vertex number, paper aims to:

(1) Put forward the effective shortest path problem model under the multi-type constraint;

(2) Propose the multi-constrained priority-based shortest path coding algorithm;

(3) Raise the interactive intelligent optimization algorithm methodology of multi-stage learning;

(4) Prove the global convergence of the algorithm.

The reminder of this paper is arranged as follow: a mathematical model of the multi-type constrained PP programming problem is formulated in Section 2; an improved path coding is designed in Section 3; Then, an interactive optimization methodology with multi-stage learning is proposed with its convergence prof in Section 4; two case studies are conducted and the results are analyzed in Section 5; Finally, the conclusion is summarized in Section 6.

Section snippets

Problem formulation

In order to formulate a proper mathematical model for the PP problem, firstly, an indicative illustration of the path planning problem is demonstrated in Fig. 1. For the PP problem shown in Fig. 1, the definition is presented as follows:

Definition 1

G=V,E,C, where V=v1,v2,,vn, E=e1,e2,,em and C=cij|i,jV represents a set of vertices, edges, and non-negative weights in the graph G respectively; the source vertex is SV, the termination vertex is DV, the set of specified vertexes is Vp, the set of

Coding

Firstly, the key issue to solve the PP problem is effectively encoding the paths. Considering that the invalid and circular paths may occur by direct coding which is based on the concept of random, an improved coding algorithm based on priority is proposed in this section by considering the variety of constraints of vertexes and edges, which can enhance the robustness and improve the efficiency.

Interactive optimization methodology of swarm intelligence

This section mainly focuses on finding out the shortest path. Owing to the increasing scale and constraints of networks, a single intelligent optimization algorithm is either extremely time-consuming or easily falling into the local optimum. Therefore, Martinez-de-Pison et al. combined Bayesian optimization (BO) with a constrained version of GA- PARSIMONY method to obtain parsimony models to reduce sizeable computation [43], [44]. Considering that if the optimization algorithm can avoid

Experiments and results analysis

In this paper, two networks are used to test the applicability of the proposed algorithm under various constraints and the ability to obtain the optimal solution. The optimal solution of the path is defined as the shortest path under various constraints, including the specified vertexes, specified paths, forbidden vertexes, forbidden paths and the number of vertexes in the path. At the end of the experiment, the number of vertexes in the network is gradually increased to analyze the

Conclusion

By considering the constraints of specified vertexes, specified paths, forbidden vertexes, and forbidden paths, an efficient coding method based on dynamic property was designed, an interactive optimization methodology with high efficiency and performance was proposed, and the convergence was proven in this paper. The methodology can dynamically adopt variety of intelligent algorithms, and can make full use of the high efficiency of the local optimization algorithm and the high search ability

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work was supported by the National Key R&D Program of China (No. 2018YFB1201500), the National Science Foundation of China (No. 61873201, No. U2034209, and No. U1934222), the Natural Science Foundation of Shaanxi Province of China (2021JC-42), the Natural Science Foundation of Shaanxi Provincial Department of Education (19JS051), and the Key Laboratory of Complex System Intelligent Control and Decision, Beijing Institute of Technology .

Guo Xie received the Ph.D degree from Nihon University, Tokyo, Japan, in 2013. He was the holder of the Japanese Government Scholarship from the Japanese Ministry of Education, Culture, Sports, Science and Technology. He is with School of Automation and Information Engineering, Xi’an University of Technology, Shaanxi, China. His current research interests include safety and reliability of railway systems, intelligent information processing, and fault diagnosis.

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    Guo Xie received the Ph.D degree from Nihon University, Tokyo, Japan, in 2013. He was the holder of the Japanese Government Scholarship from the Japanese Ministry of Education, Culture, Sports, Science and Technology. He is with School of Automation and Information Engineering, Xi’an University of Technology, Shaanxi, China. His current research interests include safety and reliability of railway systems, intelligent information processing, and fault diagnosis.

    Xulong Du is studying for a master’s degree in control theory and control engineering at Xi’an University of Technology. His main research interests include industrial equipment life prediction, reliability analysis and intelligent optimization.

    Siyu Li is studying for a master’s degree in control theory and control engineering at Xi’an University of Technology. Her main research interests include fault diagnosis and intelligent information processing.

    Jing Yang received the B.S. degree in automation from Central South University (CSU), China, in 2008 and the M.S. degree from the Information Engineering Faculty, Science Central and South University (CSU), China, in 2011. She is currently working toward the Ph.D. degree in School of Automation and Information Engineering, Xi’an University of Technology (XUT), China. Her research interests include machine learning, pattern recognition and data based fault diagnosis.

    Xinhong Hei is an ACM member, senior member of the China computer society, and member of the IEEJ.majored in computer application technology in 2003, March 2008 from Nihon University. His current research interests include safety and reliability of railway systems, intelligent information processing, and software.

    Tao Wen received his B.Eng degree from the School of Computer Science, Hangzhou Dianzi University, Hangzhou, China, and Master degree from the Department of Electrical and Electronic Engineering, University of Bristol, Bristol, UK, in 2011 and 2013, respectively. From 2013 to 2017, he was a Ph.D. candidate at the Birmingham Centre for Railway Research and Education at the University of Birmingham, Birmingham, UK, and received his Ph.D. degree in 2018. His research interests include CBTC system optimization, railway signaling simulation, railway condition monitoring, wireless signal processing and digital filter research.

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