The traveling salesman problem

The traveling salesman problem (TSP) is an NP-hard problem, and it has been an interesting problem for several decades now in the area of discrete or combinatorial optimization domain. This paper deals with the symmetric traveling salesman problem often denoted as (sTSP), which is a variant of the generalised TSP. An efficient hybrid algorithm is constructed combining two global optimization metaheuristics and some local search techniques. The hybridized algorithms include symbiotic organisms search, simulated annealing and iterated local search heuristic. To verify the performance of the hybrid method, thirty (30) well-known TSP benchmarks were considered from the TSPLIB. More so, experimental evaluation of the proposed algorithm that confirms its efficiency over existing optimal solutions of the sTSP instances is presented. The numerical results show that the algorithm is able to find new optimal solution for sTSP instances of up to 264 graph nodes. The results also show that the new method provides a good quality solution in very short time for large problem instance. Noticeably, it was observed that increasing the computations time bound gradually improve the quality of solutions found.

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