In this paper, we propose a new cooperative search algorithm based on pheromone communication for solving the Vehicle Routing Problems. In this algorithm, multi-agents can partition the problem cooperatively and search partial solutions independently using pheromone communication, which mimics the communication method of real ants. Through some computer experiments the cooperative search of multi-agents is confirmed.

For two finite disjoint sets P and Q of strings over an alphabet Σ, an alphabet indexing for P, Q by an indexing alphabet Γ with |Γ||Σ| is a mapping :ΣΓ satisfying (P)(Q), where :Σ*Γ* is the homomorphism derived from . We defined this notion through experiments of knowledge acquisition from amino acid sequences of proteins by learning algorithms. This paper analyzes the complexity of finding an alphabet indexing. We first show that the problem is NP-complete. Then we give a local search algorithm for this problem and show a result on PLS-completeness.