Variant Multi Objective Tsp Model

travelling salesman, tour, distance, cost, head quarter INTRODUCTION:

Authors

  • K.Vijaya Kumar Department of Mathematics, Sri Venkateswara University, Tirupati, Andhra Pradesh, India-517502
  • P.Madhu Mohan Reddy Dept of Mathematics, Siddharth Institute of Engg &Technology, Puttur, Andhra Pradesh, India -517583
  • C. Suresh Babu Dept of Mathematics, Siddharth Institute of Engg &Technology, Puttur, Andhra Pradesh, India -517583
  • M.Sundara Murthy Department of Mathematics, Sri Venkateswara University, Tirupati, Andhra Pradesh, India-517502
June 16, 2016

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Let there be a set of 'n' cities. Pair of distances between the cities are known and distance between th i cities to th j city is given. The cost of travel between pair of cities is given. The cost ofC(i, j) and Distance D(i, j) need not be related. These two matrices C(i, j) and D(i, j) can be simply write as C and D respectively. The travelling salesman starts his business from head quarter city 1 and he wants to travel 0 n cities less than n .The travelling salesman in his tour visits 0 n cities with minimum distances then the same route need not be with minimum costs and same way a route with minimum costs need not be with a minimum distance. The cost and distance are different unrelated factors but the salesman wants to minimize in both cases as much as possible. The objective is he wants to visit 0 n cities nearly with minimum cost and minimum distance. Both the factors distance and cost being independent, absolutely in both cases minimum is not possible. The salesman may be interested in one factor when compared with the other factor or vice versa. We want to suggest tours where both factors are considered and considerable minimum tours are planned, with different constraints under considerations.