A novel hybrid algorithm for generalized traveling salesman problems in different environments

Khan, Indadul; Maiti, Manas Kumar

doi:10.1007/s40595-017-0099-z

Cited by 14 publications

(9 citation statements)

References 31 publications

(59 reference statements)

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“…Among them stochastic estimation [37], fuzzy estimation [4,15,26] and rough estimation [40] draws more attention. Fuzzy or rough estimation of travel costs is more applicable in a real-life application, like, GTSP [20,21]. Actually, these estimations are based on the expert's opinion and hence less past data are required for the same.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, these types of estimations are less erroneous. Though there are some research works on the TSPs incorporating fuzzy costs [5,4,26,27], not much attention has been paid on the GTSPs with imprecise cost matrices [20,21]. Though there are two publications on the GTSPs with imprecise cost matrices [20,21], the approaches proposed in these studies can not deal with the cost matrices with different types of fuzzy/rough estimation.…”

Section: Introductionmentioning

confidence: 99%

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RETRACTED: A Heuristic With Multiple Search Strategies for the Gtsps in Different Environments

DUTTA,

KHAN,

BASULI

et al. 2023

Preprint

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A meta-heuristic approach with multiple perturbation rules is proposed to solve the generalized travelling salesman problems in different environments. The proposed approach consists of two phases. The first phase is devoted for the sequencing of the groups and in the second phase one node is selected from each group to minimize the tour cost. In the first stage a group sequence is generated randomly. After that a K-bit shuffling approach is used to regenerate the new group sequences. In the second phase, for every group sequence several selection rules are used for selecting the nodes/cities from different groups of a particular group sequence. At a regular interval, K-Opt operation is used to update the paths and the corresponding group sequences are updated according to the group elements. The proposed algorithm is capable of solving the problem in crisp as well as different imprecise environments, like, fuzzy environment, rough environment, etc. Proper decision making approaches are outlined for decision making in fuzzy and rough environments. Simulation approaches in fuzzy and rough environments are also presented to deal with the problem for different types of fuzzy and rough estimations. In the crisp environment, the algorithm has been tested using different sizes benchmark test instances from GTSPLIB having sizes upto 318 nodes with 64 groups. There are no benchmark data sets available for the GTSPs in imprecise environments. Test problems in imprecise environments are generated from different benchmark crisp test problems of the GTSPLIB and are used to test the algorithm in the corresponding imprecise environments. It is observed from the numerical illustration and graphical representation that the proposed approach obtains 100% accurate results in all the runs of the algorithm for different seeds of the random number generator for all the considered benchmark test problems under consideration. Another observation is visualized from the table that the algorithm has found multiple optimal paths for some test instances. It can be concluded from the observations that the proposed algorithm is capable of solving the GTSPs in crisp as well as in imprecise environments for a significantly large size problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

RETRACTED: A Heuristic With Multiple Search Strategies for the Gtsps in Different Environments

DUTTA,

KHAN,

BASULI

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…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%

“…Here K-Opt operation is applied on a complete tour of a CSP for its possible improvement. For detailed of K-Opt operation, one can refer [11].…”

Section: Optimization In Imprecise Environmentmentioning

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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Multi-objective covering salesman problem: a decomposition approach using grey wolf optimization

Khan¹,

Basuli

Maiti³

2022

Knowl Inf Syst

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A novel hybrid algorithm for generalized traveling salesman problems in different environments

Cited by 14 publications

References 31 publications

RETRACTED: A Heuristic With Multiple Search Strategies for the Gtsps in Different Environments

RETRACTED: A Heuristic With Multiple Search Strategies for the Gtsps in Different Environments

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

Multi-objective covering salesman problem: a decomposition approach using grey wolf optimization

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