Network communications have been widely studied in the last decades in different research fields: artificial intelligence, computer science, biology, medicine and psychology among others. Some important efforts have been carried out to analyse communication features such as overhead, connectivity or communication protocols in these areas from their own perspectives. When this problem is restricted to intelligent agents or multi‐agent systems, networks are built by a set of interconnected agents that can be software or hardware. In multi‐agent systems, communication optimization is used to improve the overall performance of the system by reducing the information sharing (i.e. number of messages or message size) between the agents. This paper analyses a scale‐free network topology of agents to solve a multi‐sorting problem. The agents use their local information as well as a bio‐inspired identity discrimination process to select only those messages that are relevant for each agent to solve jigsaw puzzles. We provide a comprehensive study on the influence of some essential parameters (memory information size and reconnection probability) in an agent network, and how they can be set to obtain a better performance in the system. The experiments show that this strategy contributes to reduce the number of iterations needed to solve the problem.