  An artificial Ant Colony System (ACS) algorithm to solve general-purpose
combinatorial Optimization Problems (COP) that extends previous AC models [21]
by the inclusion of a negative pheromone, is here described. Several Travelling
Salesman Problem (TSP) were used as benchmark. We show that by using two
different sets of pheromones, a second-order co-evolved compromise between
positive and negative feedbacks achieves better results than single positive
feedback systems. The algorithm was tested against known NP-complete
combinatorial Optimization Problems, running on symmetrical TSP's. We show that
the new algorithm compares favourably against these benchmarks, accordingly to
recent biological findings by Robinson [26,27], and Gruter [28] where "No
entry" signals and negative feedback allows a colony to quickly reallocate the
majority of its foragers to superior food patches. This is the first time an
extended ACS algorithm is implemented with these successful characteristics.
