Evolutionary resilience in open multiagent optimization: From preset trust to emergent defense

Abstract

Can defensive behavior in multiagent optimization emerge through evolutionary competition rather than being pre-installed? We study this question in open, adversarial environments where agents can enter, leave, or be compromised, and where the global optimum drifts continuously as the agent pool changes, thereby creating an endogenous fitness landscape. We formulate a self-organizing three-layer dynamics: a fast optimization layer converging toward the moving target, a slow evolutionary layer in which defensive and undefended strategies replicate based on locally observable optimization performance, and a perturbation layer capturing random turnover and Byzantine attacks. Under a time-scale separation, we establish conditions under which the defensive strategy becomes evolutionarily resilient, identifying a critical attack intensity characterized in terms of the replacement rate, the exploration rate, the algebraic connectivity of the communication graph, and the condition number of the objective functions. Extensive simulations on diverse topologies confirm the spontaneous emergence of a resilient backbone without centralized provisioning, reveal a sharp phase transition in the strategy distribution, and demonstrate the hybridization of gradient-based optimization with fitness-driven replication. Our framework establishes design principles for self-organizing resilience in dynamic multiagent optimization, with implications for evolutionary dynamic optimization, swarm robotics, and federated learning.