A graph-based ant system with walking stepped pattern

A graph-based ant system with walking stepped pattern was proposed for solving subset problems. The set in subset problem was denoted an equivalent ordering denotation set, and based on that the structure map was defined. The denotation of set was mapped stepped route. Then the subset problem was transformed ordering problem. The ants' next step route choosing area was controlled by route choosing probability, then the walk stepped pattern control of ants' was realized. The algorithm was described, and its complexity was analyzed. Finally, the effectiveness of the algorithm were illustrated with multidimensional knapsack problem.