Mechanism and Stability Analysis of Metabolic Closed-Loop Metaheuristics
For researchers in metaheuristics, this work offers a theoretical foundation for understanding the internal regulation properties of MMAO, but it is incremental as it does not claim global convergence or universal superiority.
This paper analyzes the Metabolic Multi-Agent Optimizer (MMAO) at a framework level, introducing a generic state model to study its metabolic resource loop. It establishes boundedness and nonnegativity properties under mild assumptions and characterizes three endogenous behavioral regimes, providing empirical validation on representative realizations.
This paper studies the Metabolic Multi-Agent Optimizer (MMAO) at the framework level rather than at the implementation or benchmark level. The central question is whether the metabolic resource loop of private energy, communal budget, role drift, and lifecycle turnover has a framework-level interpretation beyond narrative metaphor. We introduce a generic MMAO state model that abstracts away domain-specific move operators while retaining the resource bookkeeping that defines the framework. Under mild bounded-gain and bounded-spending assumptions, we establish boundedness and nonnegativity properties for private energy, communal budget, role state, and active population size. We then characterize three endogenous behavioral regimes of the loop: contraction under sustained resource deficit, reinvestment under surplus communal accumulation, and search redistribution under heterogeneous marginal returns across agents or subgroups. The analysis is intentionally conservative. It does not claim global convergence of the full adaptive system, universal superiority over specialist optimizers, or a complete stationary characterization of the resulting process. Instead, it identifies which internal regulation properties are generic consequences of the loop and which remain implementation specific. A compact mechanism-validation package on representative continuous and discrete MMAO realizations provides supporting empirical evidence for this reading, but is not intended to replace a full benchmark study. The resulting contribution is therefore a bounded, regenerative, resource-regulated interpretation of MMAO, rather than a complete proof of all adaptive behaviors of the full algorithm family.