Hybrid SAS-MAS Paradigm Overview

• Hybrid SAS-MAS paradigm is a unified framework that integrates symbiotic autonomous systems with multi-agent coordination for adaptive and cooperative decision-making.
• It employs advanced modeling, semantic interoperability, and dynamic communication mechanisms to enhance distributed reasoning and error cancellation.
• Applications span manufacturing, optimization, and agentic web technologies, leveraging both discrete and continuous controls for robust scalability.

A hybrid SAS-MAS paradigm unifies principles from Symbiotic Autonomous Systems (SAS)—focusing on symbiotic intelligence, collective cognition, and human-machine synergy—with those of Multi-Agent Systems (MAS)—emphasizing distributed, autonomous coordination between interacting agents. This integration aims to yield robust, scalable intelligent systems capable of adaptive, cooperative behavior and resource-efficient problem solving across a wide range of domains, including manufacturing, dynamic optimization, distributed AI, and agentic web technologies. Hybrid SAS-MAS systems often embed explicit mechanisms for semantic interoperability, structured reasoning, dynamic communication, and hierarchical or service-oriented orchestration, thereby enabling not only autonomous action at the agent level but also emergent properties at the system scale.

1. Philosophical and Mathematical Foundations of Hybrid SAS-MAS Systems

The theoretical framework underlying SAS extends the multi-agent paradigm beyond simple distributed autonomy by formalizing inter-agent symbiosis. Each agent’s decision making is both autonomous and enriched by explicit knowledge fusion, collective learning, and human participation (Wang et al., 2021). The mathematical formalism describes an individual SAS as an eight-tuple:

$S = (C, B, R_c, R_b, R_f, \alpha, R_i, R_0)$

where $C$ represents components (e.g. agent subsystems), $B$ their behaviors, $R_c$ and $R_b$ component/behavioral relations, $R_f$ the mapping between components and behaviors, $\alpha$ environmental context, $R_i$ input (potentially human or sensor data), and $R_0$ output relations. By analogy, a hybrid SAS-MAS aggregates agents each modeled as SAS instances and fuses their knowledge via relations:

$$R_{hybrid} = \bigcup_{i=1}^{N} R(S_i) \cup \bigcup_{i \neq j} AR_{ij}(C_i, C_j)$$

where $AR_{ij}$ represents symbiotic gains from inter-agent linkage, enabling emergent error cancellation and increased system reliability:

$\Theta(SS) \gg \sum_{k=1}^{n} \Theta(ES(k))$

Thus, hybrid paradigms mathematically formalize the augmentation of intelligence by cooperative fusion and supervised recalibration, often incorporating human feedback as a central mechanism for system adaptation.

2. Formal Modeling and Dynamic Interaction Mechanisms

Hybrid SAS-MAS systems require advanced agent modeling to support asynchronous, reconfigurable, and semantically-rich interactions (Alrahman et al., 2019). Each agent is defined as a tuple $$\langle V_i, f_i, g_{si}, g_{ri}, T_{si}, T_{ri}, \theta_i \rangle$$, with local and shared variables, guard predicates, and transition relations, facilitating flexible composition:

• Local behavior: Agents update internal variables.
• Global interaction: Communication via channels—broadcast, multicast, or dynamically assigned.
• Guard predicates ($g_{si}, g_{ri}$) select target agents based on shared state, supporting runtime reconfiguration of communication topology. This is complemented by a logical extension, \ltal, enabling explicit specification and reasoning about agent intentions:

$$\phi ::= v \mid \neg v \mid \phi \vee \phi \mid \phi \wedge \phi \mid \phi U \phi \mid \phi R \phi \mid O \phi \mid O \phi$$

where $O$ is an observation descriptor over channels, sender, and message metadata.

Complexity analyses reveal PSPACE/EXPSPACE-completeness for satisfiability and model-checking, though practical agent verification remains tractable for typical parameter sizes.

3. Hybrid Control and Optimization in Distributed Systems

Application to distributed manufacturing and continuous optimization exemplifies hybrid SAS-MAS engineering (Krzywicki et al., 2015, Barenji et al., 2016). In massively-concurrent EMAS, each candidate solution is realized as an autonomous agent operating asynchronously, using energy-based local strategies:

• Fight: Energy transfer based on fitness comparison,

$$E_i^{new} = E_i \pm \Delta, \quad E_j^{new} = E_j \mp \Delta$$

• Reproduction: Condition $E > E_{rep}$ triggers genetic variation. Functional programming environments (Erlang, Scala/Akka) are leveraged for lightweight process management and message exchange, enabling millions of concurrent agents with low overhead.

In manufacturing, dual simulation platforms combine Hardware Simulation Agents (CPN-based) for physical processes and RFID-enabled multi-agent MES for control decisions, with hybrid agents (XML-mediated) bridging layers. Lead time and throughput metrics are defined as:

$$T_{lead} = T_{order} + T_{queue} + T_{setup} + T_{process} + T_{move} + T_{inspection} + T_{putaway}$$

$\text{Throughput} = \frac{N_{products}}{T_{total}}$

This design supports agility, modularity, real-time synchronization, and robust adaptation to disturbances.

4. Self-Adaptive Swarm Systems and Ensemble Learning

The SASS framework (Yang, 2021) advances hybrid paradigms by combining agent-level “needs hierarchies” with distributed negotiation, recursive task decomposition, and game-theoretic planning:

• Behavior trees with Selector and Sequence nodes encode multi-level needs (Safety, Basic, Capability, Teaming, Self-upgrade).
• Game-theoretic Utility Tree (GUT): State-space Bayesian network for strategy planning.
• Relative Needs Entropy (RNE): Trust metric for inter-agent agreement,

$RNE(P\|Q) = \sum_n P(n) \log \frac{P(n)}{Q(n)}$

In ensemble AMAS for non-linear classification (Fourez et al., 2022), local agents with linear models interact via explicit rules (expansion, retraction, push, absorption, exclusion), collectively resolving non-linear tasks with higher accuracy (e.g. raising logistic regression from 0.65 to 0.74).

5. Service-Oriented, Heterogeneous, and Hierarchical Architectures

Recent advances focus on modular, service-oriented and heterogeneous frameworks:

• Agent-as-a-Service (AaaS-AN) (Zhu et al., 13 May 2025): Agents and agent-groups form vertices in a dynamic graph, interact via hard/soft/extensible routes, and are orchestrated by Service Schedulers and Execution Graphs allowing distributed coordination and context tracking. Validation on mathematical reasoning and code generation demonstrates accuracy gains over competing frameworks; release of long-horizon workflow datasets catalyzes further research.
• HASHIRU (Pai et al., 1 Jun 2025): A hierarchical “CEO” manages agent instantiation, balancing performance and resource cost via explicit economic models,

$$\min_{\{E_i\}} \sum_{i=1}^{N} (\alpha \cdot \text{Cost}_i - \beta \cdot G_i)$$

Autonomous tool generation and adaptive, resource-aware agent selection yield demonstrated performance improvements (GSM8K: 96%, SVAMP: 92%, JEEBench: 80%).

• Heterogeneous MAS (X-MAS) (Ye et al., 22 May 2025): Assigning diverse LLMs to agent roles achieves monotonic performance improvements, with domain-function optimization yielding up to 8.4% (MATH) and 47% (AIME) gains.

6. Hybrid Decision-Making, Maneuvering, and Policy Autonomy

Hybrid SAS-MAS paradigms increasingly integrate discrete semantics, dynamic coordination, and continuous control:

• Semantic maps and claim policies (area reservation) decouple coordination from model-predictive control, eliminating multi-agent collision constraints and enabling scalable, deadlock-free navigation (Vos et al., 16 Oct 2024).
• Dynamic maneuvering (AWorld) (Xie et al., 13 Aug 2025): An Execution Agent’s reasoning is continually corrected via a supervising Guard Agent, inspired by linearized vessel control equations, yielding robust performance (pass@1 67.89%, reduced variance) even with noisy, tool-augmented contexts.
• Allen (Zhou et al., 15 Aug 2025): Step-level policy autonomy—agents select operational logic at execution-unit granularity. Four-tier state architecture (Task, Stage, Agent, Step) balances topological optimization, autonomous progress, and human oversight, with open-source code available for independent validation.

7. Semantic Web, Agentic AI, and Socio-Technical Integration

A unified narrative of the Web of Agents (WoA) (Petrova et al., 14 Jul 2025) reveals longitudinal convergence: from early semantic web (ontologies, FIPA ACL) to MAS (platform-driven intelligence) and finally agentic AI (LLM-embedded reasoning). This evolution is systematized along semantic, communication, intelligence, and discovery axes. MCP and A2A protocols address prior limitations, enabling lightweight, decentralized inter-agent coordination. The hybrid SAS-MAS paradigm thus encompasses semantic interoperability, distributed coordination, and emergent intelligence in model-centric agents. Persistent challenges in identity, economic friction, security, and governance remain focal areas for future research.

Conclusion

Hybrid SAS-MAS paradigms represent an overview of advanced theoretical models, pragmatic engineering, and emergent semantic, reasoning, and collaborative technologies. They deliver resource-adaptive, robust, and semantically-integrated multi-agent intelligence applicable to manufacturing, optimization, machine learning, agentic web platforms, and autonomous systems. Current research emphasizes modular orchestration, dynamic policy autonomy, hierarchical control, heterogeneous agent deployment, and socio-technical integration as drivers for future developments in scalable, trustworthy collective AI.