A Genetic Algorithms Approach for Inverse Shortest Path Length Problems

2014 ◽  
Vol 4 (4) ◽  
pp. 36-54 ◽  
Author(s):  
António Leitão ◽  
Adriano Vinhas ◽  
Penousal Machado ◽  
Francisco Câmara Pereira
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Path Length ◽  
Shortest Paths ◽  
Research Subject ◽  
Relevant Research ◽  
Real Cost ◽  
Shortest Path Problems ◽  
The Past ◽  
Specific Outcome

Inverse Combinatorial Optimization has become a relevant research subject over the past decades. In graph theory, the Inverse Shortest Path Length problem becomes relevant when people don't have access to the real cost of the arcs and want to infer their value so that the system has a specific outcome, such as one or more shortest paths between nodes. Several approaches have been proposed to tackle this problem, relying on different methods, and several applications have been suggested. This study explores an innovative evolutionary approach relying on a genetic algorithm. Two scenarios and corresponding representations are presented and experiments are conducted to test how they react to different graph characteristics and parameters. Their behaviour and differences are thoroughly discussed. The outcome supports that evolutionary algorithms may be a viable venue to tackle Inverse Shortest Path problems.

scholarly journals A MODIFIED GENETIC ALGORITHM FOR FINDING FUZZY SHORTEST PATHS IN UNCERTAIN NETWORKS

2016 ◽  
Vol XLI-B2 ◽  
pp. 299-304 ◽  
Author(s):  
A. A. Heidari ◽  
M. R. Delavar
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Shortest Paths ◽  
The Body ◽  
Shortest Path Problems ◽  
Conventional Procedure ◽  
Path Lengths ◽  
The Cost ◽  
Uncertain Networks ◽  
Exploration Exploitation

In realistic network analysis, there are several uncertainties in the measurements and computation of the arcs and vertices. These uncertainties should also be considered in realizing the shortest path problem (SPP) due to the inherent fuzziness in the body of expert's knowledge. In this paper, we investigated the SPP under uncertainty to evaluate our modified genetic strategy. We improved the performance of genetic algorithm (GA) to investigate a class of shortest path problems on networks with vague arc weights. The solutions of the uncertain SPP with considering fuzzy path lengths are examined and compared in detail. As a robust metaheuristic, GA algorithm is modified and evaluated to tackle the fuzzy SPP (FSPP) with uncertain arcs. For this purpose, first, a dynamic operation is implemented to enrich the exploration/exploitation patterns of the conventional procedure and mitigate the premature convergence of GA technique. Then, the modified GA (MGA) strategy is used to resolve the FSPP. The attained results of the proposed strategy are compared to those of GA with regard to the cost, quality of paths and CPU times. Numerical instances are provided to demonstrate the success of the proposed MGA-FSPP strategy in comparison with GA. The simulations affirm that not only the proposed technique can outperform GA, but also the qualities of the paths are effectively improved. The results clarify that the competence of the proposed GA is preferred in view of quality quantities. The results also demonstrate that the proposed method can efficiently be utilized to handle FSPP in uncertain networks.

scholarly journals A MODIFIED GENETIC ALGORITHM FOR FINDING FUZZY SHORTEST PATHS IN UNCERTAIN NETWORKS

2016 ◽  
Vol XLI-B2 ◽  
pp. 299-304 ◽  
Author(s):  
A. A. Heidari ◽  
M. R. Delavar
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Shortest Paths ◽  
The Body ◽  
Shortest Path Problems ◽  
Conventional Procedure ◽  
Path Lengths ◽  
The Cost ◽  
Uncertain Networks ◽  
Exploration Exploitation

In realistic network analysis, there are several uncertainties in the measurements and computation of the arcs and vertices. These uncertainties should also be considered in realizing the shortest path problem (SPP) due to the inherent fuzziness in the body of expert's knowledge. In this paper, we investigated the SPP under uncertainty to evaluate our modified genetic strategy. We improved the performance of genetic algorithm (GA) to investigate a class of shortest path problems on networks with vague arc weights. The solutions of the uncertain SPP with considering fuzzy path lengths are examined and compared in detail. As a robust metaheuristic, GA algorithm is modified and evaluated to tackle the fuzzy SPP (FSPP) with uncertain arcs. For this purpose, first, a dynamic operation is implemented to enrich the exploration/exploitation patterns of the conventional procedure and mitigate the premature convergence of GA technique. Then, the modified GA (MGA) strategy is used to resolve the FSPP. The attained results of the proposed strategy are compared to those of GA with regard to the cost, quality of paths and CPU times. Numerical instances are provided to demonstrate the success of the proposed MGA-FSPP strategy in comparison with GA. The simulations affirm that not only the proposed technique can outperform GA, but also the qualities of the paths are effectively improved. The results clarify that the competence of the proposed GA is preferred in view of quality quantities. The results also demonstrate that the proposed method can efficiently be utilized to handle FSPP in uncertain networks.

scholarly journals Accelerating exact constrained shortest paths on GPUs

2020 ◽  
Vol 14 (4) ◽  
pp. 547-559
Author(s):  
Shengliang Lu ◽  
Bingsheng He ◽  
Yuchen Li ◽  
Hao Fu
Keyword(s):  
Exact Solutions ◽  
Shortest Path ◽  
Performance Optimization ◽  
Autonomous Vehicles ◽  
Shortest Paths ◽  
Approximate Solutions ◽  
Shortest Path Problems ◽  
Labeling Algorithm ◽  
Constrained Shortest Paths ◽  
Computational Resources

The recently emerging applications such as software-defined networks and autonomous vehicles require efficient and exact solutions for constrained shortest paths (CSP), which finds the shortest path in a graph while satisfying some user-defined constraints. Compared with the common shortest path problems without constraints, CSP queries have a significantly larger number of subproblems. The most widely used labeling algorithm becomes prohibitively slow and impractical. Other existing approaches tend to find approximate solutions and build costly indices on graphs for fast query processing, which are not suitable for emerging applications with the requirement of exact solutions. A natural question is whether and how we can efficiently find the exact solution for CSP. In this paper, we propose Vine , a framework that parallelizes the labeling algorithm to efficiently find the exact CSP solution using GPUs. The major challenge addressed in Vine is how to deal with a large number of subproblems that are mostly unpromising but require a significant amount of memory and computational resources. Our solution is twofold. First, we develop a two-level pruning approach to eliminate the subproblems by making good use of the GPU's hierarchical memory. Second, we propose an adaptive parallelism control model based on the observations that the degree of parallelism (DOP) is the key to performance optimization with the given amount of computational resources. Extensive experiments show that Vine achieves 18× speedup on average over the widely adopted CPU-based solution running on 40 CPU threads. Vine also has over 5× speedup compared with a GPU approach that statically controls the DOP. Compared to the state-of-the-art approximate solution with preprocessed indices, Vine provides exact results with competitive or even better performance.

An oriented spanning tree based genetic algorithm for multi-criteria shortest path problems

2012 ◽  
Vol 12 (1) ◽  
pp. 506-515 ◽  
Author(s):  
Linzhong Liu ◽  
Haibo Mu ◽  
Xinfeng Yang ◽  
Ruichun He ◽  
Yinzhen Li
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Spanning Tree ◽  
Shortest Path Problems

scholarly journals A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths

2013 ◽  
Vol 57 (1-2) ◽  
pp. 84-99 ◽  
Author(s):  
Reza Hassanzadeh ◽  
Iraj Mahdavi ◽  
Nezam Mahdavi-Amiri ◽  
Ali Tajdin
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Shortest Path Problems ◽  
Arc Lengths

ON SOLVING SHORTEST PATHS WITH A LEAST-SQUARES PRIMAL-DUAL ALGORITHM

2008 ◽  
Vol 25 (02) ◽  
pp. 135-150
Author(s):  
I.-LIN WANG
Keyword(s):  
Linear Programming ◽  
Least Squares ◽  
Shortest Path ◽  
Shortest Paths ◽  
Arc Length ◽  
Dual Algorithm ◽  
Shortest Path Problems ◽  
Dijkstra's Algorithm ◽  
Primal Dual ◽  
Linear Programming Problems

Recently a new least-squares primal-dual (LSPD) algorithm, that is impervious to degeneracy, has effectively been applied to solving linear programming problems by Barnes et al., 2002. In this paper, we show an application of LSPD to shortest path problems with nonnegative arc length is equivalent to the Dijkstra's algorithm. We also compare the LSPD algorithm with the conventional primal-dual algorithm in solving shortest path problems and show their difference due to degeneracy in solving the 1-1 shortest path problems.

scholarly journals Finding Shortest Path for Road Network Using Dijkstra’s Algorithm

2019 ◽  
Vol 1 (2) ◽  
pp. 41-45
Author(s):  
Md. Almash Alam ◽  
Md. Omar Faruq
Keyword(s):  
Shortest Path ◽  
Road Network ◽  
Shortest Paths ◽  
Road Networks ◽  
Transportation Systems ◽  
Shortest Path Problem ◽  
Dijkstra’S Algorithm ◽  
Traffic Condition ◽  
Shortest Path Problems ◽  
Dijkstra's Algorithm

Roads play a Major role to the people live in various states, cities, town and villages, from each and every day they travel to work, to schools, to business meetings, and to transport their goods. Even in this modern era whole world used roads, remain one of the most useful mediums used most frequently for transportation and travel. The manipulation of shortest paths between various locations appears to be a major problem in the road networks. The large range of applications and product was introduced to solve or overcome the difficulties by developing different shortest path algorithms. Even now the problem still exists to find the shortest path for road networks. Shortest Path problems are inevitable in road network applications such as city emergency handling and drive guiding system. Basic concepts of network analysis in connection with traffic issues are explored. The traffic condition among a city changes from time to time and there are usually huge amounts of requests occur, it needs to find the solution quickly. The above problems can be rectified through shortest paths by using the Dijkstra’s Algorithm. The main objective is the low cost of the implementation. The shortest path problem is to find a path between two vertices (nodes) on a given graph, such that the sum of the weights on its constituent edges is minimized. This problem has been intensively investigated over years, due to its extensive applications in graph theory, artificial intelligence, computer network and the design of transportation systems. The classic Dijkstra’s algorithm was designed to solve the single source shortest path problem for a static graph. It works starting from the source node and calculating the shortest path on the whole network. Noting that an upper bound of the distance between two nodes can be evaluated in advance on the given transportation network.

SHORTEST PATHS AMONG OBSTACLES IN THE PLANE

1996 ◽  
Vol 06 (03) ◽  
pp. 309-332 ◽  
Author(s):  
JOSEPH S.B. MITCHELL
Keyword(s):  
Voronoi Diagram ◽  
Shortest Path ◽  
Path Length ◽  
Shortest Paths ◽  
Multiple Source ◽  
Worst Case ◽  
Visibility Graphs ◽  
Shortest Path Map ◽  
Continuous Dijkstra ◽  
Time Bounds

We give a subquadratic (O(n3/2+∊) time and O(n) space) algorithm for computing Euclidean shortest paths in the plane in the presence of polygonal obstacles; previous time bounds were at least quadratic in n, in the worst case. The method avoids use of visibility graphs, relying instead on the continuous Dijkstra paradigm. The output is a shortest path map (of size O(n)) with respect to a given source point, which allows shortest path length queries to be answered in time O( log n). The algorithm extends to the case of multiple source points, yielding a method to compute a Voronoi diagram with respect to the shortest path metric.

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