An iterated sample construction with path relinking method: Application to switch allocation in electrical distribution networks
Introduction
Most of the faults of an electrical power system take place in the distribution network [1], [2]. The installation of redundant lines and switches is a common method to improve the reliability of a distribution network. In this way, in case of failures, service providers can modify the network topology and reduce the areas without energy. The installation of switches in every line is impracticable due to high costs. For this reason, companies must carefully choose the lines to install switches. This combinatorial optimization problem is called the switch allocation problem. To assess the reliability of an allocation proposal for a set of switches, we have to determine the expected non-supplied energy for a given distribution of failures. Since the actual non-supplied energy depends on how much of the service area can be restored by reconfiguring the network, the service restoration with electrical constraints occurs as a subproblem of the switch allocation problem.
In this paper, we propose a sample construction and a sample local search for the switch allocation problem, and, based on these algorithms, a new iterated sample construction with path relinking (ISCPR) to solve the switch allocation problem. Another contribution is that our treatment of the service restoration problem makes no assumption on the topology of the network and includes electrical restrictions.
In Section 2 we give a formal description of the problem. In Section 3 we describe the construction and local search algorithms based on sampling. In Section 4 we introduce the ISCPR algorithm which uses the sample construction to modify the current solution and the path relinking to perform a guided local search. Section 5 first compares the performance of sample based construction and local search methods to other such methods, and then compares several heuristics for the switch allocation problem. When compared to a heuristic based on Greedy Randomized Adaptive Search Procedure (GRASP) [3], ISCPR shows the best performance. Another comparison with a branch-and-bound procedure attests the quality of the solutions yielded by our approach.
Section snippets
Description of the problems
Fig. 1a shows an example of an electric power distribution network in normal operation. The basic circuit of an operational distribution network has no cycles. It is composed of substations (square nodes), consumers (round nodes), and feeder lines (solid lines). Additionally, redundant lines (dotted lines) can restore the energy in areas affected by failures. Switches control the power flow. In normal operation, switches of redundant lines are open, and switches in the basic circuit are closed.
Construction and local search
This section describes four construction algorithms (random, sample, greedy and semi-greedy) and three local search strategies (sample search, first and best improvement) for the switch allocation problem.
Iterated sample construction with path relinking (ISCPR)
ISCPR is a variant of iterated local search (ILS) [27]. At each iteration, ISCPR perturbs the last solution with a partial random destruction followed by a sample construction, and uses path relinking as a guided local search. Path relinking [28] explores the neighbourhood between two solutions. It repeatedly relocates one switch of the initial solution, to a position defined by the guiding solution. It can be seen as a local search where the neighbourhood is limited to the differences between
Computational experiments
All tests have been executed on a PC with an Intel Core i7 processor (2.8 GHz, 12 GB RAM). The algorithms have been implemented in C++, and compiled with GNU C++ with optimization level 2 (-O2).
Concluding remarks
Our results show that sample construction is efficient and can create high quality solutions for the switch allocation problem. A restriction of the neighbourhood by random samples also can speed up the local search, leading to good solutions in short times. The use of path relinking as guided local search can improve the solutions efficiently.
These components together form an efficient heuristic, ISCPR, that is capable of reducing the number of reliability estimations, and is able to perform
Acknowledgements
This work has been supported by the project “Metodologia Multiobjetivo para Análise e Melhoria da Confiabilidade de Sistemas de Distribuição de Energia Elérica” (Auxílio Integrado CNPq, CTEnerg processo 554900/2006-8). We also thank Prof. Dr. Alysson M. Costa (ICMC-USP), Prof. Dr. Vinícius J. Garcia (UNIPAMPA), and two anonymous reviewers for valuable comments.
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