Research articleAn efficient and global interactive optimization methodology for path planning with multiple routing constraints
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 , where , and represents a set of vertices, edges, and non-negative weights in the graph respectively; the source vertex is , the termination vertex is , the set of specified vertexes is , 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.
References (65)
- et al.
An adaptive amoeba algorithm for shortest path tree computation in dynamic graphs
Inform Sci
(2017) - et al.
Techniques in multimodal shortest path in public transport systems
Transp Res Procedia
(2014) - et al.
Benchmarking a recurrent neural network based efficient shortest path problem (SPP) solver concept under difficult dynamic parameter settings conditions
Neurocomputing
(2016) - et al.
Fast centralized integer resource allocation algorithm and its distributed extension over digraphs
Neurocomputing
(2017) - et al.
Solving shortest path problem using particle swarm optimization
Appl Soft Comput
(2008) - et al.
An ant colony optimization algorithm for the bi-objective shortest path problem
Appl Soft Comput
(2010) - et al.
Finding the k, reliable shortest paths under travel time uncertainty
Transp Res B
(2016) - et al.
K: A heuristic search algorithm for finding the k shortest paths
Artificial Intelligence
(2011) - et al.
An enhanced K-SP algorithm with pruning strategies to solve the constrained shortest path problem
Appl Math Comput
(2015) - et al.
A parametric approach to solving bicriterion shortest path problems
European J Oper Res
(1991)
Bicriterion shortest path problem with a general nonadditive cost
Transp Res B
The shortest path problem with forbidden paths
European J Oper Res
Hybrid methodology based on Bayesian optimization and GA-PARSIMONY to search for parsimony models by combining hyperparameter optimization and feature selection
Neurocomputing
Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems
Comput Aided Des
A novel numerical optimization algorithm inspired from weed colonization
Ecol Inform
Grey wolf optimizer
Adv Eng Softw
The ant lion optimizer
Adv Eng Softw
Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm
Knowl-Based Syst
SCA: A sine cosine algorithm for solving optimization problems
Knowl-Based Syst
The whale optimization algorithm
Adv Eng Softw
Cockroach swarm optimization algorithm for travel planning
Entropy
The electric vehicle shortest-walk problem with battery exchanges
Netw Spat Econ
A collaborative method for route discovery using taxi drivers’ experience and preferences
IEEE Trans Intell Transp Syst
A MapReduce-based approach for shortest path problem in large-scale networks
Eng Appl Artif Intell
Finding the shortest path in stochastic vehicle routing: A cardinality minimization approach
IEEE Trans Intell Transp Syst
Stochastic online shortest path routing: The value of feedback
IEEE Trans Automat Control
Shortest path bridging: Efficient control of larger ethernet networks
IEEE Commun Mag
Adaptive robot path planning using a spiking neuron algorithm with axonal delays
IEEE Trans Cogn Dev Syst
Robot path routing for shortest moving distance in wireless robotic sensor networks
IEICE Trans Commun
Social-class pigeon-inspired optimization and time stamp segmentation for multi-UAV cooperative path planning
Neurocomputing
A note on two problems in connexion with graphs
Numer Math
Algorithm 97: Shortest path
Commun ACM
Cited by (4)
Research progress of laser triangulation on-machine measurement technology for complex surface: A review
2023, Measurement: Journal of the International Measurement ConfederationCrowd evacuation navigation for evasive maneuver of brownian based dynamic obstacles using reciprocal velocity obstacles
2022, Bulletin of Electrical Engineering and InformaticsInert and mobile agents navigation interaction using reciprocal velocity obstacles for collisions avoidance
2022, Indonesian Journal of Electrical Engineering and Computer Science
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.
- 1
Member, IEEE.