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. B Raka Jovanovic

Chance-Constrained Optimal Distribution Network Partitioning to Enhance Power Grid Resilience

“…This optimal distribution network partitioning (ODNP) task seeks to identify potential self-adequate sub-networks that can survive the loss of the main grid as islands. Both exact [9]- [11] and heuristic [12]- [15] methods have been proposed in literature to address the ODNP problem. Selfadequacy in the objective function has been surrogated by either expected load-generation imbalance within microgrids [13]- [15], or expected power flow on boundary lines [9]- [12].…”

“…Both exact [9]- [11] and heuristic [12]- [15] methods have been proposed in literature to address the ODNP problem. Selfadequacy in the objective function has been surrogated by either expected load-generation imbalance within microgrids [13]- [15], or expected power flow on boundary lines [9]- [12]. Some works additionally suggest dynamic identification of boundary lines in response to faults [16], [17].…”

Fixed set search applied to the traveling salesman problem

“…Although it generally has a worse performance than combining one of the more complex methods with a local search it is extensively used. The advantage of more complex metaheuristics often occurs only for very large problem instances, some examples in case of ACO can be seen in [19,17]. Because of this, it is reasonable to attempt to increase the size of problems that GRASP can solve, but in a way that there is a minimal increase in complexity of the original method.…”

A heuristic approach for dividing graphs into bi-connected components with a size constraint

“…In case of such problems the general approach is to grow several subgraphs in parallel with the constraint that no vertex can be added to more than one of them. The effectiveness of this type of method is well presented on the problem of partitioning supply/demand graphs into connected subgraphs (Jovanovic et al, 2015b(Jovanovic et al, ,a, 2016. It is important to note that the concept of growing a solution gives a high level of flexibility of the method, in the sense of potential applications.…”

“…(Bazgan et al, 2010). Partitioning problems defined on supply/demand graphs have proven to be essential in modeling systems of interconnected microgrids (Arefifar et al, 2012(Arefifar et al, , 2013Jovanovic et al, 2015b;Popa, 2013;Jovanovic and Voss, 2015;Morishita and Nishizeki, 2013;Ito et al, 2012). Clustering in For many of them it would be reasonable to substitute the constraint of connectivity with bi-connectivity, producing the benefit of higher reliability of the system.…”