A modified particle swarm optimization algorithm for solving traveling salesman problem with imprecise cost matrix

Khan, Indadul; Pal, Sova; Maiti, Manas Kumar

doi:10.1109/rait.2018.8389060

Cited by 8 publications

(5 citation statements)

References 37 publications

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“…To test the proposed algorithm in a fuzzy environment these fuzzy CSPs are used. In a crisp CSP, if travel cost between node i and node j is d ij then following Khan et al [12,13], the corresponding fuzzy cost is generated as dij =(d ij1 ,d ij2 ,d ij3 ), where…”

Section: Table-5 and Table-6 Present The Results Due To The Different...mentioning

confidence: 99%

“…Moreover, none have studied the CSPs in imprecise environments. There are some studies on the TSPs and GTSPs with fuzzy cost matrices and rough cost matrices [11,12,13], using the credibility measure on fuzzy events and the trust measure on rough events, where TFNs are used as the fuzzy parameters and the Lebesgue measure is used for the estimation of rough parameters. Their approach can not deal with such problems involving fuzzy cost matrices with non-linear membership functions.…”

Section: Background Of the Csp And Challengesmentioning

confidence: 99%

“…This type of estimation is less error prone as it is done using experts' opinion. Though there are algorithms to solve basic TSPs and its variants in the imprecise environments [11,12,13], none has introduced any algorithm to solve the CSPs in any imprecise environment.…”

Section: Introductionmentioning

confidence: 99%

“…• Though algorithms are available to solve TSPs in the imprecise environments [12,13], the approach cannot deal with the problems involving fuzzy data with non-linear membership functions (e.g., Parabolic Fuzzy Number(PFN)) or TSPs involving Rough data where the estimation can not be done using Lebesgue measure.…”

Section: Introductionmentioning

confidence: 99%

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A modified ACO with K-Opt for restricted covering salesman problems in different environments

Dutta¹,

Khan²,

Basuli

et al. 2022

Soft Comput

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In this study, the ant colony optimization (ACO) algorithm is modified with the K-opt operation to solve the covering salesman problem(CSP) under one restriction in crisp and imprecise (fuzzy, rough) environments. A CSP involves two phases-the division of cities into groups with the selection of the visiting cities and searching of the Hamiltonian circuit through the visiting cities. But, none of the studies in the literature is made following the direct approach. Also, none of the studies in the literature gives attention to reduce the total travel distance of the unvisited cities from the visited city of a group. Moreover, there is no algorithm in the literature which provides the solution of a CSP with the specified coverage range r. Also, none has introduced any algorithm to solve CSPs in imprecise environments. Though algorithms are available to solve the Traveling Salesman Problems in the imprecise environments, the approach cannot deal with the problems involving fuzzy data with non-linear membership functions or the problems involving rough data where the rough estimation can not be done using Lebesgue measure. The well establish algorithm for any routing problem is the ACO, but not much attention has been paid to solve the CSP using ACOs. To overcome these limitations on the studies of the ACO on the CSPs, here, an algorithm is proposed for the division of groups of the set of cities depending upon the maximum number of cities in a group and the total number of groups. Then ACO is used to find the shortest/minimum-cost path of the problem by selecting only one visiting the city from each group without violating the restriction of the specified coverage range r of the location of the unvisited cities. K-opt operation is applied periodically at the end of ACO operation to improve the quality of the best found solution so far by the ACO algorithm and to arrest any premature convergence. For the restricted problems paths are searched in such a manner that the total distance/travel cost of different unvisited cities of a group from the visited city of the group should not exceed a predefined upper limit. To solve the problem in an imprecise environment some approach is followed so that the tour is searched without transferring the imprecise optimisation problem into an equivalent crisp optimisation problem. Also, the simulation approaches in fuzzy and rough environments are proposed to deal with the CSPs with any type of estimation of the imprecise data set. Algorithm is tested with the standard benchmark crisp problems available in the literature. To test the algorithm in the imprecise environments, the imprecise instances are derived randomly from the standard crisp instances using a specified rule. Test results imply that the proposed algorithm is efficient enough in solving the CSPs in the crisp as well as in the imprecise environments.

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Section: Table-5 and Table-6 Present The Results Due To The Different...mentioning

confidence: 99%

Section: Background Of the Csp And Challengesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A modified ACO with K-Opt for restricted covering salesman problems in different environments

Dutta¹,

Khan²,

Basuli

et al. 2022

Soft Comput

Self Cite

View full text Add to dashboard Cite

show abstract

“…Nonetheless, the search process lacks feedback information and learning due to having less values of parameters to optimize. In [36] strengthened PSO to solve the imprecise cost matrix TSP. The PSO modifications consist of the adoption of the swap series, the swap process, and the guidelines for various speed updates.…”

Section: Literature Reviewmentioning

confidence: 99%

Improved discrete plant propagation algorithm for solving the traveling salesman problem

Almazini

Mortada

Almazini

et al. 2022

IJ-AI

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The primary goal of traveling salesman problem (TSP) is for a salesman to visit many cities and return to the starting city via a sequence of potential shortest paths. Subsequently, conventional algorithms are inadequate for large-scale problems; thus, metaheuristic algorithms have been proposed. A recent metaheuristic algorithm that has been implemented to solve TSP is the plant propagation algorithm (PPA), which belongs to the rose family. In this research, this existing PPA is modified to solve TSP. Although PPA is claimed to be successful, it suffers from the slow convergence problem, which significantly impedes its applicability for getting good solution. Therefore, the proposed partial-partitioned greedy algorithm (PPGA) offers crossover and three mutation operations (flip, swap, and slide), which allow local and global search and seem to be wise methods to help PPA in solving the TSP. The PPGA performance is evaluated on 10 separate datasets available in the literature and compared with the original PPA. In terms of distance, the computational results demonstrate that the PPGA outperforms the original PPA in nine datasets which assures that it is 90% better than PPA. PPGA produces good solutions when compared with other algorithms in the literature, where the average execution time reduces by 10.73%.

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Solving Travelling Salesman Problem Using a Modified Grey Wolf Optimizer

Boualem

Meftah

Debbat

2021

Lecture Notes in Networks and Systems

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A modified particle swarm optimization algorithm for solving traveling salesman problem with imprecise cost matrix

Cited by 8 publications

References 37 publications

A modified ACO with K-Opt for restricted covering salesman problems in different environments

A modified ACO with K-Opt for restricted covering salesman problems in different environments

Improved discrete plant propagation algorithm for solving the traveling salesman problem

Solving Travelling Salesman Problem Using a Modified Grey Wolf Optimizer

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