Study on a novel genetic algorithm for the combinatorial optimization problem

A genetic algorithm simulating Darwinian evolution is proposed to yield near-optimal solutions to the multiple traveling salesmen problem (MTSP). A new transformation of the N-city M-salesmen MTSP to the standard traveling salesman problem (TSP) is introduced. The transformed problem is represented by a city-position map with (N +M-1) -cities and a single fictitious Salesman. Nothing that Darwinian evolution is itself an optimization process; we propose a heuristic algorithm that incorporates the tents of natural selection. The time complexity of this algorithm is equivalent to the fastest sorting scheme. Computer simulations indicate rapid convergence is maintained even with increasing problem complexity. This methodology can be adapted to tackle a host of other combinatorial problems.