MMAO-Dyn: A Metabolic Multi-Agent Optimizer for Dynamic Optimization

Traditional meta-heuristics often rely on fixed population sizes, manually chosen search scales, and externally attached parameter-control modules. This paper presents the \textit{Metabolic Multi-Agent Optimizer} (MMAO), a cross-domain optimization framework in which adaptation is derived endogenously from a private-public metabolic resource loop. Each agent carries internal energy, a continuous role state, motion or structural memory, and local search history, while the population shares a communal resource pool. Fitness improvements are converted into normalized metabolic gains through a robust progress scale and a recent success statistic; the same closed loop then regulates sensing intensity, search amplitude, role drift, branching, pruning, respawning, and elite reinvestment. In the continuous setting, MMAO uses energy-regulated symmetric zero-order probing and role-interpolated motion. In the discrete setting, the same control law is instantiated through structural sensing, local route improvement, guided perturbation, and energy-weighted edge reuse. The paper combines an implementation-faithful formulation with a reproducible experimental study on a CEC2017 subset (10D/30D, 20 seeds) and five TSPLIB instances (100 discrete runs in total). The current evidence supports MMAO primarily as a parameter-light, self-calibrating optimization framework whose main validated originality lies in metabolically endogenous resource allocation across heterogeneous search behaviors, rather than as a universally superior optimizer.

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.

This paper presents the Metabolic Multi-Agent Optimizer (MMAO) as an adaptive metaheuristic built around endogenous resource circulation. The central premise is that search intensity, exploration--exploitation balance, and lifecycle turnover should be induced by a shared metabolic controller rather than by separately attached schedules. We formulate MMAO through bounded private energy, a communal budget, normalized reward, continuous role adaptation, and resource-financed branching and pruning. The method is then instantiated in both continuous and discrete domains and evaluated on a matched small-scale suite including Sphere, Rastrigin, a synthetic Euclidean TSP, and two TSPLIB instances. The results show a consistent pattern: the same metabolic loop remains workable across domains, the discrete realization remains relatively stable under a compact design, and continuous refinement quality is the main cost of keeping the method lean. Taken together, these findings position MMAO as a coherent framework for adaptive heuristic design rather than a loose collection of operators.