Heurisic approaches for no-depot k-traveling salesmen problem with a minmax objective

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Title: Heurisic approaches for no-depot k-traveling salesmen problem with a minmax objective
Author: Na, Byungsoo
Abstract: This thesis deals with the no -depot minmax Multiple Traveling Salesmen Problem (MTSP ) , which can be formulated as follows . Given a set of n cities and k salesmen ,find k disjoint tours (one for each salesmen ) such that each city belongs to exactly one tour and the length of the longest of k tours is minimized . The no -depot assumption means that the salesmen do not start from and return to one fixed depot . The no -depot model can be applied in designing patrolling routes , as well as in business situations , especially where salesmen work from home or the company has no central office . This model can be also applied to the job scheduling problem with n jobs and k identical machines . Despite its potential applicability to a number of important situations , the research literature on the no -depot minmax k -TSP has been limited , with no reports on computational experiments . The previously published results included the proof of NP -hardness of the problem of interest , which motivates using heuristics for its solution . This thesis proposes several construction heuristic algorithms , including greedy algorithms , cluster first and route second algorithms , and route first and cluster second algorithms . As a local search method for a single tour , 2 -opt search and Lin -Kernighan were used , and for a local search method between multiple tours , relocation and exchange (edge heuristics ) were used . Furthermore , to prevent the drawback of trapping in the local minima , the simulated annealing method is used . Extensive computational experiments were carried out using TSPLIB instances . Among construction algorithms , route first and cluster second algorithms including removing two edges method performed best . In terms of running time , clustering first and routing second algorithms took shorter time on large -scale instances . The simulated annealing could produce better solutions than the descent method , but did not always perform well in terms of average solution . To evaluate the performance of the proposed heuristic methods , their solutions were compared with the optimal solutions obtained using a mixed -integer programming formulation of the problem . For small -scale problems , heuristic solutions were equal to the optimal solution output by CPLEX .
URI: http : / /hdl .handle .net /1969 .1 /5825
Date: 2007-09-17

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Heurisic approaches for no-depot k-traveling salesmen problem with a minmax objective. Available electronically from http : / /hdl .handle .net /1969 .1 /5825 .

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