Partitioning of supply/demand graphs with capacity limitations: an ant colony approach

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In recent years there has been a growing interest for the problem of the minimal partitioning of graphs with supply and demand, due to its close connection to electrical distribution systems, especially in the context of smartgrids. In this paper we present a new version of the problem which is more suitable for practical applications in modeling such systems. More precisely, the constraint of having a unique supply node in a subgraph (partition) is substituted with a limit on the number of subgraphs and the capacity for each of them. The problem is initially solved by a two stage greedy method. With the goal of further improving the quality of found solutions, a corresponding GRASP and an ant colony optimization algorithm are developed. Due to the novelty of the problem, we include a description of a method for generating test instances with known optimal solutions. In our computational experiments we evaluate the performance of the proposed algorithms on both trees and general graphs. The tests show that the proposed ant colony approach manages to frequently find optimal solutions. It has an average relative error of less than 2 % when compared to known optimal solutions. Moreover, it outperform the GRASP.

Original languageEnglish
JournalJournal of Combinatorial Optimization
DOIs
Publication statusAccepted/In press - 18 Aug 2015

Fingerprint

Ant Colony
Partitioning
Ant colony optimization
Optimal Solution
Graph in graph theory
Subgraph
Smart Grid
Distribution System
Relative Error
System Modeling
Computational Experiments
Optimization Algorithm
Experiments
Partition
Demand
Evaluate
Vertex of a graph

Keywords

  • Ant colony optimization
  • Combinatorial optimization
  • Demand vertex
  • Graph partitioning
  • GRASP
  • Microgrid
  • Supply vertex

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Control and Optimization

Cite this

@article{547ee55584204220b8faec68d1e4901d,
title = "Partitioning of supply/demand graphs with capacity limitations: an ant colony approach",
abstract = "In recent years there has been a growing interest for the problem of the minimal partitioning of graphs with supply and demand, due to its close connection to electrical distribution systems, especially in the context of smartgrids. In this paper we present a new version of the problem which is more suitable for practical applications in modeling such systems. More precisely, the constraint of having a unique supply node in a subgraph (partition) is substituted with a limit on the number of subgraphs and the capacity for each of them. The problem is initially solved by a two stage greedy method. With the goal of further improving the quality of found solutions, a corresponding GRASP and an ant colony optimization algorithm are developed. Due to the novelty of the problem, we include a description of a method for generating test instances with known optimal solutions. In our computational experiments we evaluate the performance of the proposed algorithms on both trees and general graphs. The tests show that the proposed ant colony approach manages to frequently find optimal solutions. It has an average relative error of less than 2 {\%} when compared to known optimal solutions. Moreover, it outperform the GRASP.",
keywords = "Ant colony optimization, Combinatorial optimization, Demand vertex, Graph partitioning, GRASP, Microgrid, Supply vertex",
author = "Raka Jovanovic and Abdelkader Bousselham and Stefan Vo{\ss}",
year = "2015",
month = "8",
day = "18",
doi = "10.1007/s10878-015-9945-z",
language = "English",
journal = "Journal of Combinatorial Optimization",
issn = "1382-6905",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Partitioning of supply/demand graphs with capacity limitations

T2 - an ant colony approach

AU - Jovanovic, Raka

AU - Bousselham, Abdelkader

AU - Voß, Stefan

PY - 2015/8/18

Y1 - 2015/8/18

N2 - In recent years there has been a growing interest for the problem of the minimal partitioning of graphs with supply and demand, due to its close connection to electrical distribution systems, especially in the context of smartgrids. In this paper we present a new version of the problem which is more suitable for practical applications in modeling such systems. More precisely, the constraint of having a unique supply node in a subgraph (partition) is substituted with a limit on the number of subgraphs and the capacity for each of them. The problem is initially solved by a two stage greedy method. With the goal of further improving the quality of found solutions, a corresponding GRASP and an ant colony optimization algorithm are developed. Due to the novelty of the problem, we include a description of a method for generating test instances with known optimal solutions. In our computational experiments we evaluate the performance of the proposed algorithms on both trees and general graphs. The tests show that the proposed ant colony approach manages to frequently find optimal solutions. It has an average relative error of less than 2 % when compared to known optimal solutions. Moreover, it outperform the GRASP.

AB - In recent years there has been a growing interest for the problem of the minimal partitioning of graphs with supply and demand, due to its close connection to electrical distribution systems, especially in the context of smartgrids. In this paper we present a new version of the problem which is more suitable for practical applications in modeling such systems. More precisely, the constraint of having a unique supply node in a subgraph (partition) is substituted with a limit on the number of subgraphs and the capacity for each of them. The problem is initially solved by a two stage greedy method. With the goal of further improving the quality of found solutions, a corresponding GRASP and an ant colony optimization algorithm are developed. Due to the novelty of the problem, we include a description of a method for generating test instances with known optimal solutions. In our computational experiments we evaluate the performance of the proposed algorithms on both trees and general graphs. The tests show that the proposed ant colony approach manages to frequently find optimal solutions. It has an average relative error of less than 2 % when compared to known optimal solutions. Moreover, it outperform the GRASP.

KW - Ant colony optimization

KW - Combinatorial optimization

KW - Demand vertex

KW - Graph partitioning

KW - GRASP

KW - Microgrid

KW - Supply vertex

UR - http://www.scopus.com/inward/record.url?scp=84939456058&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939456058&partnerID=8YFLogxK

U2 - 10.1007/s10878-015-9945-z

DO - 10.1007/s10878-015-9945-z

M3 - Article

AN - SCOPUS:84939456058

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

ER -