MMAO: A Metabolic Multi-Agent Optimizer with Endogenous Resource Allocation for Continuous and Discrete Optimization

The challenge of solving complex, high-dimensional, and multimodal optimization problems has long plagued researchers and practitioners. Classical algorithms like genetic algorithms, simulated annealing, and particle swarm optimization laid foundational work but often rely heavily on manually tuned parameters and fixed search strategies. These methods struggle to adapt efficiently in dynamic, uncertain, or large-scale environments, leading to suboptimal solutions and high computational costs.

Recent advances have introduced adaptive variants such as CMA-ES and L-SHADE, which dynamically tune parameters but still depend on externally prescribed schedules and fixed population structures. Meanwhile, bio-inspired algorithms mimicking plant roots or other biological systems have shown promise in enhancing exploration and adaptability. However, these often remain static or heuristic, lacking a unified mechanism for resource regulation.

Addressing these limitations, this paper proposes MMAO, a biologically inspired, self-regulating optimization framework based on the metaphor of plant root metabolism. Each agent in MMAO is an autonomous entity with internal energy, a role state, and local memory, while the entire population shares a communal resource pool. The core innovation lies in modeling the search process as a metabolic loop, where fitness improvements are converted into normalized rewards that dynamically regulate sensing, movement, and behavioral shifts. This endogenous resource cycle enables the algorithm to adapt search scales, behaviors, and population dynamics without manual intervention.

In continuous spaces, MMAO employs energy-regulated symmetric zero-order probing and role interpolation to balance exploration and exploitation smoothly. In discrete spaces, it maps the same control logic onto structural sensing, local route improvements, guided perturbations, and energy-weighted edge reuse. This unified approach allows the same mechanism to operate seamlessly across different problem domains, reducing parameter dependence and enhancing robustness.

Experimental validation on the CEC2017 benchmark suite and TSPLIB instances demonstrates that MMAO outperforms traditional algorithms like CMA-ES and L-SHADE in terms of solution quality, stability, and convergence speed. Notably, the resource self-regulation mechanism significantly contributes to performance gains, especially in complex, multimodal landscapes. Theoretical analysis confirms the boundedness of energies and resources, ensuring system stability and agent turnover.

This work marks a significant step toward autonomous, adaptive optimization algorithms that emulate biological resource management. Its cross-domain applicability and mechanism-driven design open new avenues for scalable, intelligent solutions in industrial, transportation, and network optimization. Future directions include enhancing computational efficiency, extending to dynamic and multi-objective problems, and integrating learning components for further autonomy and performance.