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Latency-Aware 2-Opt Monotonic Local Search for Distributed Constraint Optimization

Ben Rachmut, Roie Zivan, William Yeoh

TL;DR

This work addresses distributed constraint optimization under message latency by extending DCOPs to CA-DCOPs and introducing LAMDLS-2, a monotonic, latency-resilient 2-opt local search that uses DOCS-based pairing to coordinate bilateral value replacements. The method guarantees monotonic improvement and convergence to a $2$-opt solution, with theoretical guarantees and an empirical demonstration that it converges faster than MGM-2 across diverse latency patterns while maintaining comparable solution quality. The results show reduced communication overhead and less idle time, highlighting practical robustness in realistic networks. The paper also outlines a region-optimal extension (LAMDLS-ROpt) and future work toward general $k$-opt algorithms.

Abstract

Researchers recently extended Distributed Constraint Optimization Problems (DCOPs) to Communication-Aware DCOPs so that they are applicable in scenarios in which messages can be arbitrarily delayed. Distributed asynchronous local search and inference algorithms designed for CA-DCOPs are less vulnerable to message latency than their counterparts for regular DCOPs. However, unlike local search algorithms for (regular) DCOPs that converge to k-opt solutions (with k > 1), that is, they converge to solutions that cannot be improved by a group of k agents), local search CA-DCOP algorithms are limited to 1-opt solutions only. In this paper, we introduce Latency-Aware Monotonic Distributed Local Search-2 (LAMDLS-2), where agents form pairs and coordinate bilateral assignment replacements. LAMDLS-2 is monotonic, converges to a 2-opt solution, and is also robust to message latency, making it suitable for CA-DCOPs. Our results indicate that LAMDLS-2 converges faster than MGM-2, a benchmark algorithm, to a similar 2-opt solution, in various message latency scenarios.

Latency-Aware 2-Opt Monotonic Local Search for Distributed Constraint Optimization

TL;DR

This work addresses distributed constraint optimization under message latency by extending DCOPs to CA-DCOPs and introducing LAMDLS-2, a monotonic, latency-resilient 2-opt local search that uses DOCS-based pairing to coordinate bilateral value replacements. The method guarantees monotonic improvement and convergence to a -opt solution, with theoretical guarantees and an empirical demonstration that it converges faster than MGM-2 across diverse latency patterns while maintaining comparable solution quality. The results show reduced communication overhead and less idle time, highlighting practical robustness in realistic networks. The paper also outlines a region-optimal extension (LAMDLS-ROpt) and future work toward general -opt algorithms.

Abstract

Researchers recently extended Distributed Constraint Optimization Problems (DCOPs) to Communication-Aware DCOPs so that they are applicable in scenarios in which messages can be arbitrarily delayed. Distributed asynchronous local search and inference algorithms designed for CA-DCOPs are less vulnerable to message latency than their counterparts for regular DCOPs. However, unlike local search algorithms for (regular) DCOPs that converge to k-opt solutions (with k > 1), that is, they converge to solutions that cannot be improved by a group of k agents), local search CA-DCOP algorithms are limited to 1-opt solutions only. In this paper, we introduce Latency-Aware Monotonic Distributed Local Search-2 (LAMDLS-2), where agents form pairs and coordinate bilateral assignment replacements. LAMDLS-2 is monotonic, converges to a 2-opt solution, and is also robust to message latency, making it suitable for CA-DCOPs. Our results indicate that LAMDLS-2 converges faster than MGM-2, a benchmark algorithm, to a similar 2-opt solution, in various message latency scenarios.

Paper Structure

This paper contains 16 sections, 6 theorems, 5 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Distributed Constraint Optimization Problems (DCOPs)
  4. k-opt and Region-opt Algorithms
  5. Communication-Aware DCOPs (CA-DCOPs)
  6. Latency-Aware Monotonic Distributed Local Search (LAMDLS)
  7. LAMDLS-2
  8. Ordering Phase
  9. Pair Selection Phase
  10. Demonstration of LAMDLS-2
  11. Theoretical Properties
  12. Extension to a Region-Optimal Algorithm
  13. Experimental Evaluation
  14. Experimental Design
  15. Experimental Evaluation
  16. ...and 1 more sections

Key Result

Lemma 1

In a DCOP (with symmetric constraints), when an agent $A_i$ is the only agent replaces its assignment, while none of its neighbors ($NC(i)$) replace their assignments, and this replacement results in a local gain, it also results in an improvement of the global cost.

Figures (5)

  • Figure 1: Two different numerical graph color partitions.
  • Figure 2: Solution quality as a function of NCLOs. Message delays are sampled from a uniform distribution.
  • Figure 3: Solution quality as a function of NCLOs. Message delays sampled from a Poisson distribution linked to message volume.
  • Figure 4: Solution quality as a function of different matrices in environments with different message delays.
  • Figure 5: Average costs at convergence with error bars.

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Proposition 4
  • Proposition 5
  • Proposition 6