• Dr U Balakrishna
• N Vasantha Kumar
• Dr E Keshava Reddy

This paper deals with the constrained asymmetric three dimensional generalized travelling salesman problem (CTGTSP) that concerns the generalization of classical travelling salesman problem. The GTSP is known to be an NP-hard problem and has many interesting applications. In CTGTSP, the cities can be categorized into different grade cities. The objective of this problem is to design optimal route that starts and ends at the same city and visits a subset of cities at a minimum cost such that the salesman has to visit from any grade city to another grade city with at least one city of each grade city and also consecutive visiting times(facilities) should be different. To find optimal solution, an exact pattern recognition technique based Lexi Search algorithm(LSA) is developed.A numerical example is demonstrated in order to understand the search mechanism of the Lexi Search Algorithm. Further, to test the performance of Lexi Search Algorithm, computational experiments have been carried out on some benchmark as well as randomly generated test instances for CTGTSP, and results are reported. The overall computational results demonstrate that the proposed Lexi Search Algorithm is efficient in providing optimal within the considerable CPU times.

Constraint Asymmetric three dimensional Generalized Travelling Salesman Problem (CTGTSP), Lexi Search Algorithm(LSA), Pattern Recognition Technique.

"CONSTRAINED ASYMMETRIC THREE DIMENSIONAL GENERALIZED TRAVELLING SALESMAN PROBLEM::PATTERN RECOGNITION LEXI SEARCH APPROACH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 3, page no.172-179, March-2019, Available :http://www.jetir.org/papers/JETIR1903G28.pdf

"CONSTRAINED ASYMMETRIC THREE DIMENSIONAL GENERALIZED TRAVELLING SALESMAN PROBLEM::PATTERN RECOGNITION LEXI SEARCH APPROACH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 3, page no. pp172-179, March-2019, Available at : http://www.jetir.org/papers/JETIR1903G28.pdf