Preliminary studies on the fixed destination mmtsp solved by discrete firefly algorithm

The fixed destination MmTSP (multi-depot multiple travelling salesman problem) is an np hard problem, which can't be solved in polynomial t ime. Against the traditional TSP problem here there are more travelling salesmen which seek out t he cities. Every city is visited by once by any of the salesmen and after the round route the salesman go back to its home location. But unlike at the TSP the salesman does not start from the same locat ion. The firefly algorithm is a member of the swarm optimizations family. Originally it was devel oped to solve continuous state space problems but with discretization it is capable to solve combinat orial problems also. In this article we will show a potential discretization variant. In the firefly al gorithm every firefly represent a solution. In our algorithm the salesmen using a multi chromosome model, where there are a separate list for every salesman for the cities to visit. Keywords: supplier selection, optimization, firefly algorith m, MS Excel solver 1. The problem The problem of the MmTSP has an important role in logistics. The problem is the generalization of the TSP problem (1), in the MTSP there are more salesmen instead of one which are visiting the cities starting from the sam e location. The agents starting from the same location is the MmTSP problem. MmTSP means multi depot multiple salesman problem, which represents more complexity compared to the original problem. We can differentiate fixed destination and non-fixed desti nation cases. In case of fixed destination problem the salesman have to return to the same loc ation where he started. In case of non- fixed destination problem this constraint is not pr esent; the salesmen can arrive at any locations (2). The fixed destination case suits to a huge amount of logistic problems like the large scale technical inspection and maintenance sy stems, like the elevator maintenance networks (3) or water quality monitoring systems or natural gas transfer station networks. 2. Literature The pure MSTP problem is widely discussed in the literature, the range of the solution methods and the application is extensive (4)(5)(6). But the literature of the special cases are small sometimes even not exists. The authors found a solution of this problem which uses Ant Colony Algorithm (7). In our former articles we show the optimization problems of large scale technical inspection and maintenance sy stems, where we solved the general fixed destination multiple depot multiple salesman problem with multiple tours with the very special constraints of these type of systems, there are no known another solution so far (8)(9). In this early stage of the research we exam ine and judge the usability of the firefly