Solving a Cryptarithmetic Problem Using a Social Learning Heuristic

The premiss that a group of cooperating agents - a collective brain - can solve a problem more efficiently than the same group of agents working independently is widespread, despite the little quantitative groundwork to support it. Here we use extensive agent-based simulations to investigate the performance of a system of N agents in solving a cryptarithmetic problem. Cooperation is taken into account through imitative learning which allows information to pass from one agent to another. At each trial the agents can either perform individual trial-and-test operations to explore the solution space or copy cues from a model agent, i.e., the agent that exhibits the lowest cost solution at the trial. We find a trade-off between the number of trial-and-test operations and the number of imitation attempts: too much imitation results in a performance which is poorer than that exhibited by noncooperative agents. For the optimal balance between trial-and-test operations and imitation attempts we find a thirtyfold speedup of the mean time to find the correct solution with respect to the time taken by the noncooperative group. Most significantly, we find that increasing the number of agents N beyond a certain value can greatly harm the performance of the cooperative system which can then perform much worse than in the noncooperative case. Low diversity and the following of a bad leader are the culprits for the poor performance in this case.