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Distributed Stackelberg Strategies in State-based Potential Games for Autonomous Decentralized Learning Manufacturing Systems

Steve Yuwono, Dorothea Schwung, Andreas Schwung

TL;DR

The paper tackles distributed multi-objective optimization in autonomous, modular manufacturing by introducing DS2-SbPG, which embeds Stackelberg leader–follower dynamics within State-Based Potential Games to manage competing objectives without tuning global weights. It formalizes two variants—DS2-SbPG with a single leader–follower pair and Stack DS2-SbPG with stacked leaders and followers—together with a learning algorithm that uses performance maps and Stackelberg-gradient updates, plus a convergence proof showing SbPG validity. Experimental validation on the Bulk Good Laboratory Plant demonstrates that DS2-SbPG and Stack DS2-SbPG reduce power consumption by approximately 10% and improve a global potential metric, confirming practical benefits in decentralized, real-world manufacturing settings. The approach offers a scalable, fully distributed framework for handling diverse internal objectives and large objective sets, with potential extensions to constrained optimization and applications beyond manufacturing, such as MARL and evolutionary algorithms.

Abstract

This article describes a novel game structure for autonomously optimizing decentralized manufacturing systems with multi-objective optimization challenges, namely Distributed Stackelberg Strategies in State-Based Potential Games (DS2-SbPG). DS2-SbPG integrates potential games and Stackelberg games, which improves the cooperative trade-off capabilities of potential games and the multi-objective optimization handling by Stackelberg games. Notably, all training procedures remain conducted in a fully distributed manner. DS2-SbPG offers a promising solution to finding optimal trade-offs between objectives by eliminating the complexities of setting up combined objective optimization functions for individual players in self-learning domains, particularly in real-world industrial settings with diverse and numerous objectives between the sub-systems. We further prove that DS2-SbPG constitutes a dynamic potential game that results in corresponding converge guarantees. Experimental validation conducted on a laboratory-scale testbed highlights the efficacy of DS2-SbPG and its two variants, such as DS2-SbPG for single-leader-follower and Stack DS2-SbPG for multi-leader-follower. The results show significant reductions in power consumption and improvements in overall performance, which signals the potential of DS2-SbPG in real-world applications.

Distributed Stackelberg Strategies in State-based Potential Games for Autonomous Decentralized Learning Manufacturing Systems

TL;DR

The paper tackles distributed multi-objective optimization in autonomous, modular manufacturing by introducing DS2-SbPG, which embeds Stackelberg leader–follower dynamics within State-Based Potential Games to manage competing objectives without tuning global weights. It formalizes two variants—DS2-SbPG with a single leader–follower pair and Stack DS2-SbPG with stacked leaders and followers—together with a learning algorithm that uses performance maps and Stackelberg-gradient updates, plus a convergence proof showing SbPG validity. Experimental validation on the Bulk Good Laboratory Plant demonstrates that DS2-SbPG and Stack DS2-SbPG reduce power consumption by approximately 10% and improve a global potential metric, confirming practical benefits in decentralized, real-world manufacturing settings. The approach offers a scalable, fully distributed framework for handling diverse internal objectives and large objective sets, with potential extensions to constrained optimization and applications beyond manufacturing, such as MARL and evolutionary algorithms.

Abstract

This article describes a novel game structure for autonomously optimizing decentralized manufacturing systems with multi-objective optimization challenges, namely Distributed Stackelberg Strategies in State-Based Potential Games (DS2-SbPG). DS2-SbPG integrates potential games and Stackelberg games, which improves the cooperative trade-off capabilities of potential games and the multi-objective optimization handling by Stackelberg games. Notably, all training procedures remain conducted in a fully distributed manner. DS2-SbPG offers a promising solution to finding optimal trade-offs between objectives by eliminating the complexities of setting up combined objective optimization functions for individual players in self-learning domains, particularly in real-world industrial settings with diverse and numerous objectives between the sub-systems. We further prove that DS2-SbPG constitutes a dynamic potential game that results in corresponding converge guarantees. Experimental validation conducted on a laboratory-scale testbed highlights the efficacy of DS2-SbPG and its two variants, such as DS2-SbPG for single-leader-follower and Stack DS2-SbPG for multi-leader-follower. The results show significant reductions in power consumption and improvements in overall performance, which signals the potential of DS2-SbPG in real-world applications.
Paper Structure (27 sections, 3 theorems, 32 equations, 10 figures, 2 algorithms)

This paper contains 27 sections, 3 theorems, 32 equations, 10 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Multi-Objective Optimizations
  4. Decentralized Learning Manufacturing Systems
  5. Dynamic GT with Engineering Applications
  6. Problem Descriptions
  7. Preliminary Game Structures
  8. State-based Potential Games
  9. Stackelberg Games
  10. Distributed Stackelberg Strategies in State-Based Potential Games
  11. DS2-SbPG for Single-Leader-Follower Objective
  12. Stack DS2-SbPG for Multi-Leader-Follower Objective
  13. Learning Algorithm
  14. Policy Representation using Performance Maps
  15. Stackelberg Game-based Gradient Update Law
  16. ...and 12 more sections

Key Result

Lemma 1

Zazo2016 A game $\Gamma(\mathcal{N}, A, S, P, \{U_i\}, \phi)$ is considered a SbPG if the players' utilities satisfy the following conditions: $\forall i,j \in \mathcal{N}$, $\forall s_m \in S^{A_i}$, and $\forall s_n \in S^{A_j}$.

Figures (10)

  • Figure 1: An illustration of modular production units configured with multiple objectives within each module.
  • Figure 2: A schematic diagram of a production chain with serial-parallel connected subsystems, each with multiple objectives within its module.
  • Figure 3: An overview between SbPG and two variants of DS2-SbPG in multi-objective optimizations for distributed manufacturing systems.
  • Figure 4: DS2-SbPG on a modular manufacturing unit.
  • Figure 5: An illustration of the relation between the objective hierarchy $H_i$ and the stack Stackelberg games $g_i$.
  • ...and 5 more figures

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Remark 1
  • Definition 3
  • Definition 4
  • Remark 2
  • Lemma 1
  • Theorem 1
  • Theorem 2