Adaptive price update in distributed Lagrangian relaxation protocol

Katsutoshi Hirayama, Toshihiro Matsui, Makoto Yokoo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

Distributed Lagrangian Relaxation Protocol (DisLRP) has been proposed to solve a distributed combinatorial maximization problem called the Generalized Mutual Assignment Problem (GMAP). In DisLRP, when updating Lagrange multipliers (prices) of goods, the agents basically control their step length, which determines the degree of update, by a static rule. A merit of this updating rule is that since it is static, it is easy to implement even without a central control. Furthermore, if we choose this static rule appropriately, we have observed empirically that DisLRP converges to a state providing a good upper bound. However, it must be difficult to devise such a good static rule for updating step length since it naturally depends on problem instances to be solved. On the other hand, in a centralized context, the Lagrangian relaxation approach has conventionally computed step length by exploiting the least upper bound obtained during the search and a lower bound obtained through preprocessing. In this paper, we achieve this approach in a distributed environment where no central control exists and name the resultant protocol Adaptive DisLRP (ADisLRP). The key ideas of this new protocol are to 1) compute global information with a spanning tree, 2) update step length simultaneously with a synchronization protocol, and 3) estimate lower bounds during the search. We also show the robustness of ADisLRP through experiments where we compared ADisLRP with the previous protocols on the critically hard benchmark instances.

Original languageEnglish
Title of host publication8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages886-893
Number of pages8
ISBN (Print)9781615673346
Publication statusPublished - Jan 1 2009
Event8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009 - Budapest, Hungary
Duration: May 10 2009May 15 2009

Publication series

NameProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume2
ISSN (Print)1548-8403
ISSN (Electronic)1558-2914

Other

Other8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009
CountryHungary
CityBudapest
Period5/10/095/15/09

Fingerprint

Lagrange multipliers
Synchronization
Experiments

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering

Cite this

Hirayama, K., Matsui, T., & Yokoo, M. (2009). Adaptive price update in distributed Lagrangian relaxation protocol. In 8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009 (pp. 886-893). (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 2). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

Adaptive price update in distributed Lagrangian relaxation protocol. / Hirayama, Katsutoshi; Matsui, Toshihiro; Yokoo, Makoto.

8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), 2009. p. 886-893 (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 2).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hirayama, K, Matsui, T & Yokoo, M 2009, Adaptive price update in distributed Lagrangian relaxation protocol. in 8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009. Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS, vol. 2, International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), pp. 886-893, 8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009, Budapest, Hungary, 5/10/09.
Hirayama K, Matsui T, Yokoo M. Adaptive price update in distributed Lagrangian relaxation protocol. In 8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS). 2009. p. 886-893. (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS).
Hirayama, Katsutoshi ; Matsui, Toshihiro ; Yokoo, Makoto. / Adaptive price update in distributed Lagrangian relaxation protocol. 8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), 2009. pp. 886-893 (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS).
@inproceedings{1d4b63b9a01842a3a918c55b07998189,
title = "Adaptive price update in distributed Lagrangian relaxation protocol",
abstract = "Distributed Lagrangian Relaxation Protocol (DisLRP) has been proposed to solve a distributed combinatorial maximization problem called the Generalized Mutual Assignment Problem (GMAP). In DisLRP, when updating Lagrange multipliers (prices) of goods, the agents basically control their step length, which determines the degree of update, by a static rule. A merit of this updating rule is that since it is static, it is easy to implement even without a central control. Furthermore, if we choose this static rule appropriately, we have observed empirically that DisLRP converges to a state providing a good upper bound. However, it must be difficult to devise such a good static rule for updating step length since it naturally depends on problem instances to be solved. On the other hand, in a centralized context, the Lagrangian relaxation approach has conventionally computed step length by exploiting the least upper bound obtained during the search and a lower bound obtained through preprocessing. In this paper, we achieve this approach in a distributed environment where no central control exists and name the resultant protocol Adaptive DisLRP (ADisLRP). The key ideas of this new protocol are to 1) compute global information with a spanning tree, 2) update step length simultaneously with a synchronization protocol, and 3) estimate lower bounds during the search. We also show the robustness of ADisLRP through experiments where we compared ADisLRP with the previous protocols on the critically hard benchmark instances.",
author = "Katsutoshi Hirayama and Toshihiro Matsui and Makoto Yokoo",
year = "2009",
month = "1",
day = "1",
language = "English",
isbn = "9781615673346",
series = "Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS",
publisher = "International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)",
pages = "886--893",
booktitle = "8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009",

}

TY - GEN

T1 - Adaptive price update in distributed Lagrangian relaxation protocol

AU - Hirayama, Katsutoshi

AU - Matsui, Toshihiro

AU - Yokoo, Makoto

PY - 2009/1/1

Y1 - 2009/1/1

N2 - Distributed Lagrangian Relaxation Protocol (DisLRP) has been proposed to solve a distributed combinatorial maximization problem called the Generalized Mutual Assignment Problem (GMAP). In DisLRP, when updating Lagrange multipliers (prices) of goods, the agents basically control their step length, which determines the degree of update, by a static rule. A merit of this updating rule is that since it is static, it is easy to implement even without a central control. Furthermore, if we choose this static rule appropriately, we have observed empirically that DisLRP converges to a state providing a good upper bound. However, it must be difficult to devise such a good static rule for updating step length since it naturally depends on problem instances to be solved. On the other hand, in a centralized context, the Lagrangian relaxation approach has conventionally computed step length by exploiting the least upper bound obtained during the search and a lower bound obtained through preprocessing. In this paper, we achieve this approach in a distributed environment where no central control exists and name the resultant protocol Adaptive DisLRP (ADisLRP). The key ideas of this new protocol are to 1) compute global information with a spanning tree, 2) update step length simultaneously with a synchronization protocol, and 3) estimate lower bounds during the search. We also show the robustness of ADisLRP through experiments where we compared ADisLRP with the previous protocols on the critically hard benchmark instances.

AB - Distributed Lagrangian Relaxation Protocol (DisLRP) has been proposed to solve a distributed combinatorial maximization problem called the Generalized Mutual Assignment Problem (GMAP). In DisLRP, when updating Lagrange multipliers (prices) of goods, the agents basically control their step length, which determines the degree of update, by a static rule. A merit of this updating rule is that since it is static, it is easy to implement even without a central control. Furthermore, if we choose this static rule appropriately, we have observed empirically that DisLRP converges to a state providing a good upper bound. However, it must be difficult to devise such a good static rule for updating step length since it naturally depends on problem instances to be solved. On the other hand, in a centralized context, the Lagrangian relaxation approach has conventionally computed step length by exploiting the least upper bound obtained during the search and a lower bound obtained through preprocessing. In this paper, we achieve this approach in a distributed environment where no central control exists and name the resultant protocol Adaptive DisLRP (ADisLRP). The key ideas of this new protocol are to 1) compute global information with a spanning tree, 2) update step length simultaneously with a synchronization protocol, and 3) estimate lower bounds during the search. We also show the robustness of ADisLRP through experiments where we compared ADisLRP with the previous protocols on the critically hard benchmark instances.

UR - http://www.scopus.com/inward/record.url?scp=84899820358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899820358&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781615673346

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 886

EP - 893

BT - 8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009

PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)

ER -