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GDBA Revisited: Unleashing the Power of Guided Local Search for Distributed Constraint Optimization

Yanchen Deng, Xinrun Wang, Bo An

TL;DR

This work analyzes the Generalized Distributed Breakout Algorithm (GDBA) for distributed constraint optimization, identifies three pathologies that hamper performance on general-valued problems, and introduces Distributed Guided Local Search (DGLS). DGLS integrates an adaptive violation condition, an evaporation mechanism to bound penalty growth, and a synchronization scheme for coordinated penalty updates, and it is shown to induce a bounded, potential-game dynamic. The approach achieves state-of-the-art performance across diverse DCOP benchmarks, notably excelling on structured, cost-structured, and general-valued problems, and provides thorough theoretical guarantees. The results suggest DGLS offers a robust, scalable alternative to existing local-search DCOP methods with practical impact for large multi-agent systems.

Abstract

Local search is an important class of incomplete algorithms for solving Distributed Constraint Optimization Problems (DCOPs) but it often converges to poor local optima. While Generalized Distributed Breakout Algorithm (GDBA) provides a comprehensive rule set to escape premature convergence, its empirical benefits remain marginal on general-valued problems. In this work, we systematically examine GDBA and identify three factors that potentially lead to its inferior performance, i.e., over-aggressive constraint violation conditions, unbounded penalty accumulation, and uncoordinated penalty updates. To address these issues, we propose Distributed Guided Local Search (DGLS), a novel GLS framework for DCOPs that incorporates an adaptive violation condition to selectively penalize constraints with high cost, a penalty evaporation mechanism to control the magnitude of penalization, and a synchronization scheme for coordinated penalty updates. We theoretically show that the penalty values are bounded, and agents play a potential game in DGLS. Extensive empirical results on various benchmarks demonstrate the great superiority of DGLS over state-of-the-art baselines. Compared to Damped Max-sum with high damping factors, our DGLS achieves competitive performance on general-valued problems, and outperforms by significant margins on structured problems in terms of anytime results.

GDBA Revisited: Unleashing the Power of Guided Local Search for Distributed Constraint Optimization

TL;DR

This work analyzes the Generalized Distributed Breakout Algorithm (GDBA) for distributed constraint optimization, identifies three pathologies that hamper performance on general-valued problems, and introduces Distributed Guided Local Search (DGLS). DGLS integrates an adaptive violation condition, an evaporation mechanism to bound penalty growth, and a synchronization scheme for coordinated penalty updates, and it is shown to induce a bounded, potential-game dynamic. The approach achieves state-of-the-art performance across diverse DCOP benchmarks, notably excelling on structured, cost-structured, and general-valued problems, and provides thorough theoretical guarantees. The results suggest DGLS offers a robust, scalable alternative to existing local-search DCOP methods with practical impact for large multi-agent systems.

Abstract

Local search is an important class of incomplete algorithms for solving Distributed Constraint Optimization Problems (DCOPs) but it often converges to poor local optima. While Generalized Distributed Breakout Algorithm (GDBA) provides a comprehensive rule set to escape premature convergence, its empirical benefits remain marginal on general-valued problems. In this work, we systematically examine GDBA and identify three factors that potentially lead to its inferior performance, i.e., over-aggressive constraint violation conditions, unbounded penalty accumulation, and uncoordinated penalty updates. To address these issues, we propose Distributed Guided Local Search (DGLS), a novel GLS framework for DCOPs that incorporates an adaptive violation condition to selectively penalize constraints with high cost, a penalty evaporation mechanism to control the magnitude of penalization, and a synchronization scheme for coordinated penalty updates. We theoretically show that the penalty values are bounded, and agents play a potential game in DGLS. Extensive empirical results on various benchmarks demonstrate the great superiority of DGLS over state-of-the-art baselines. Compared to Damped Max-sum with high damping factors, our DGLS achieves competitive performance on general-valued problems, and outperforms by significant margins on structured problems in terms of anytime results.

Paper Structure

This paper contains 17 sections, 7 theorems, 17 equations, 5 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Distributed Constraint Optimization Problems
  4. Guided Local Search
  5. Generalized Distributed Breakout Algorithm
  6. Distributed Guided Local Search
  7. Motivation
  8. DGLS Framework
  9. Adaptive violation condition
  10. Evaporation mechanism
  11. Coordinated penalty update
  12. Theoretical Results
  13. Empirical Evaluations
  14. Benchmarks and baselines
  15. Performance comparison
  16. ...and 2 more sections

Key Result

Theorem 1

With evaporation rate $0<\gamma<1$, the penalty values in any cost modifier are bounded by $1/(1-\gamma)$.

Figures (5)

  • Figure 1: Analysis of penalty dynamics of GDBA
  • Figure 2: Performance on random DCOPs
  • Figure 3: Performance on topology-structured problems
  • Figure 4: Performance on cost-structured problems
  • Figure 5: Ablation study on sparse random DCOPs

Theorems & Definitions (12)

  • Theorem 1
  • proof
  • Corollary 1
  • Lemma 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • ...and 2 more