Travelling salesman problem ant system algorithm pheromone updating
Exploring the whole Nkf) takes O(nk) operations and, thus, 2-opt and rarely 3-opt are used in practice. The procedure is repeated as long as the current solution can be improved. This paper considers self-configuring GA, selfconfiguring ACO and their application in one of the most known combinatorial optimization problem named Travelling Salesman problem (TSP).
IWD’s soil is increased by removing some soil of the path ij.
TSP solution is presented by cyclic graph f The k-opt neighborhood Nk(f) includes all the tours which can be obtained by removing k edges from the original tour f and adding k different edges such that the resulting tour is feasible.
Results of numerical experiments on benchmark problems show that suggested approach demonstrates competitive effectiveness. One of the classical methods for solving the traveling salesman problem is a local search , in particular so called k-opt algorithm (Lin-Kernighan heuristic ).
This approach was then successfully used in solving real world optimization problems with algorithmically given functions and mixed variables .
In: IEEE Congress on Evolutionary Computation (CEC'2011), New Orleans, LA, 2011. Considered way of GA self-configuration was introduced in  where its usefulness was demonstrated on benchmark problems and in applied problems of neural networks weights adjustment.