Max-Min Ant System with Linear Memory Complexity

We improved memory complexity of Max-Min Ant System algorithm, which is one of the best performing Ant Colony Optimization algorithms. Standard implementation uses n(2) matrix of artificial pheromone to solve the Traveling Salesman Problem, where n is the number of cities. We show, that only small fraction of values in the pheromone matrix is changed from a global value and so the matrix can be replaced by an array of hash tables in order to reduce the memory complexity. This improvement is very useful in case of parallelization on multi-core architectures, where frequent transfers of random parts of matrices cause radical slowdown. Also it enables the algorithm to be competitive with others when solving large instances.