New models for shortest path problem with fuzzy arc lengths

Ji, Xiaoyu; Iwamura, Kakuzo; Shao, Zongshu

doi:10.1016/j.apm.2005.09.001

Cited by 68 publications

(34 citation statements)

References 21 publications

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“…These concepts are described in Ji et al (2007). Let z be a fuzzy variable and its membership function (MF) is ()  x and r is a real value, then the following equations are true:…”

Section: Fuzzy Simulationmentioning

confidence: 99%

“…Hence, the main task is to minimize the expected length of pathways. The following model is considered for this purpose (Ji et al, 2007). First the next definition should be provided.…”

Section: Figure 1 Illustration Of a Netmentioning

confidence: 99%

“…It has been exposed that { ( , ) }  st x x s t A is considered as a path in a Net if and only if (Ji et al, 2007):…”

Section: Figure 1 Illustration Of a Netmentioning

confidence: 99%

“…Furthermore, the vertices of an acyclic directed network ( , )  Net v A is reordered so that s<t for every ( , )  s t A . Each path can be represented by (Ji et al, 2007):…”

Section: Fuzzy Shortest Path Problem (Fspp)mentioning

confidence: 99%

“…Klein (1991) proposed a method that helps decision makers to set a threshold for membership degree and attain promising paths. Ji et al (2007) proposed different models to tackle SPP in fuzzy situations.…”

Section: Introductionmentioning

confidence: 99%

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A Modified Genetic Algorithm for Finding Fuzzy Shortest Paths in Uncertain Networks

Heidari

Delavar

2016

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT: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 insta nces 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.

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“…These concepts are described in Ji et al (2007). Let z be a fuzzy variable and its membership function (MF) is ()  x and r is a real value, then the following equations are true:…”

Section: Fuzzy Simulationmentioning

confidence: 99%

“…Hence, the main task is to minimize the expected length of pathways. The following model is considered for this purpose (Ji et al, 2007). First the next definition should be provided.…”

Section: Figure 1 Illustration Of a Netmentioning

confidence: 99%

“…It has been exposed that { ( , ) }  st x x s t A is considered as a path in a Net if and only if (Ji et al, 2007):…”

Section: Figure 1 Illustration Of a Netmentioning

confidence: 99%

“…Furthermore, the vertices of an acyclic directed network ( , )  Net v A is reordered so that s<t for every ( , )  s t A . Each path can be represented by (Ji et al, 2007):…”

Section: Fuzzy Shortest Path Problem (Fspp)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Modified Genetic Algorithm for Finding Fuzzy Shortest Paths in Uncertain Networks

Heidari

Delavar

2016

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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Finding time‐robust fuel‐efficient paths for a call‐taxi in a stochastic city road network

Godwin

Sajeev

George

2016

J of Advced Transportation

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Summary Intra‐city commuting is being revolutionized by call‐taxi services in many developing countries such as India. A customer requests a taxi via phone, and it arrives at the right time and at the right location for the pick‐up. This mode of intra‐city travel has become one of the most reliable and convenient modes of transportation for customers traveling for business and non‐business purposes. The increased number of vehicles on city roads and raising fuel costs has prompted a new type of transportation logistics problem of finding a fuel‐efficient and quickest path for a call‐taxi through a city road network, where the travel times are stochastic. The stochastic travel time of the road network is induced by obstacles such as the traffic signals and intersections. The delay and additional fuel consumption at each of these obstacles are calculated that are later imputed to the total travel time and fuel consumption of a path. A Monte‐Carlo simulation‐based approach is proposed to identify unique fuel‐efficient paths between two locations in a city road network where each obstacle has a delay distribution. A multi‐criteria score is then assigned to each unique path based on the probability that the path is fuel efficient, the average travel time of the path and the coefficient of variation of the travel times of the path. Copyright © 2016 John Wiley & Sons, Ltd.

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