[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84625-en":3,"doc-seo-84625-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84625,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Mechanism and Stability Analysis of Metabolic Closed-Loop Metaheuristics","Mechanism and stability analysis for the Metabolic Multi-Agent Optimizer (MMAO) is developed at the framework level, focusing on how a private-public metabolic resource loop—private energy, communal budget, role drift, and lifecycle turnover—can be given a principled state-model interpretation beyond metaphor. A generic MMAO state model is introduced, abstracting move operators while retaining resource bookkeeping. Under mild bounded-gain and bounded-spending assumptions, boundedness and nonnegativity are established for key internal variables. The loop’s endogenous regimes are characterized as contraction, reinvestment, and search redistribution, with claims kept conservative and theory-focused rather than benchmark-comparative.","Mechanism and Stability Analysis of Metabolic Closed-Loop Metaheuristics  \nJinliang Xu∗ and Liping Ma  \narXiv :2607 .0 155 1v2 [ cs .NE] 4 Jul 2026  \nAbstract—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 frameworklevel interpretation beyond narrative metaphor. We introduce a generic MMAO state model that abstracts away domainspecific 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 mechanismvalidation 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 strongest resulting claim is therefore theoretical identity rather than full theory: MMAO admits a bounded, regenerative, resource-regulated interpretation even though many implementation-level performance questions remain outside the reach of the present analysis.  \nIndex Terms—Metaheuristic theory, parameter control, resource allocation, adaptive population dynamics, closed-loop optimization, MMAO.  \nI. INTRODUCTION  \nMETAHEURISTIC optimization is full of adaptive de  \nvices: dynamic populations, restart rules, archives, selfadaptive parameters, operator-selection schemes, and resourceallocation schedules. These mechanisms often work, but they are frequently introduced as separate modules, each justified locally and analyzed only partially. As a result, a framework can become operationally effective while remaining theoretically fragmented. It may be hard to say which observed behaviors follow from a coherent control principle and which are simply consequences of implementation choices.  \nThe Metabolic Multi-Agent Optimizer (MMAO) was proposed against that background. Its defining claim is not that  \nJinliang Xu is an independent researcher in Beijing, China; e-mail: jlxu[fly@gmail.com](fly@gmail.com).  \nLiping Ma is with the Department of Disease Control and Prevention, The Seventh Medical Center of Chinese PLA General Hospital, Beijing, China; e-mail: [lipingmaqzx@163.com](lipingmaqzx@163.com).  \nit introduces one more move operator or one more biological metaphor. Rather, it claims that heterogeneous search behavior can be organized by a private-public metabolic economy. Agents earn or lose private energy according to recent utility, donate part of successful gains to a communal pool, drift continuously between exploratory and exploitative roles, and are removed or regenerated when their search activity ceases to justify its cost. In this view, adaptation should emerge from aresource loop rather than from a stack of disconnected control heuristics.  \nEarlier MMAO studies established progressively stronger empirical evidence for that idea, spanning framework formulation, contraction, broader benchmarking, and domain derivation [1]–[5] . However, these studies still leave a deeper question unresolved: what, in generic terms, does the metabolic loop itself guarantee or at least s","cbCainfpF5HFNATC","https://ap.wps.com/l/cbCainfpF5HFNATC","pdf",782324,1,12,"English","en",105,"# Introduction\n## Core motivation and framework-level question\n## Research questions and analysis goals","[{\"question\":\"What is the main focus of the MMAO analysis in this document?\",\"answer\":\"The document analyzes the Metabolic Multi-Agent Optimizer at the framework level, studying how the metabolic resource loop can be structurally interpreted rather than treating it as just an implementation detail or metaphor.\"},{\"question\":\"What assumptions are used to prove boundedness and nonnegativity properties?\",\"answer\":\"Under mild bounded-gain and bounded-spending assumptions, the paper establishes boundedness and nonnegativity for private energy, communal budget, role state, and active population size.\"},{\"question\":\"What endogenous behavioral regimes are characterized for the resource loop?\",\"answer\":\"The analysis characterizes three regimes: contraction under sustained resource deficit, reinvestment under surplus communal accumulation, and search redistribution driven by heterogeneous marginal returns across agents or 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