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node-depth encoding and Multiobjective Evolutionary Algorithm Applied to Large-Scale Distribution System Reconfiguration

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IEEE TRANSACTIONS ON POWER SYSTEMS 2010年第3期25卷 1254-1265页

作者： Santos, A. C. Delbem, A. C. B. London, J. B. A., Jr. Bretas, N. G. Fed Inst Educ Sci & Technol Tocantins IFTO BR-77021090 Palmas Brazil Univ Sao Paulo Inst Math & Comp Sci Sao Carlos SP Brazil Univ Sao Paulo Sao Carlos Engn Sch Sao Carlos SP Brazil

The power loss reduction in distribution systems (DSs) is a nonlinear and multiobjective problem. Service restoration in DSs is even computationally hard since it additionally requires a solution in real-time. Both DS problems are computationally complex. For large-scale networks, the usual problem formulation has thousands of constraint equations. The node-depth encoding (NDE) enables a modeling of DSs problems that eliminates several constraint equations from the usual formulation, making the problem solution simpler. On the other hand, a multiobjective evolutionary algorithm (EA) based on subpopulation tables adequately models several objectives and constraints, enabling a better exploration of the search space. The combination of the multiobjective EA with NDE (MEAN) results in the proposed approach for solving DSs problems for large-scale networks. Simulation results have shown the MEAN is able to find adequate restoration plans for a real DS with 3860 buses and 632 switches in a running time of 0.68 s. Moreover, the MEAN has shown a sublinear running time in function of the system size. Tests with networks ranging from 632 to 5166 switches indicate that the MEAN can find network configurations corresponding to a power loss reduction of 27.64% for very large networks requiring relatively low running time.

关键词： Data structure evolutionary algorithms graph representation large-scale network node-depth encoding system reconfiguration

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A node-depth encoding-Based Tabu Search Algorithm for Power Distribution System Restoration

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JOURNAL OF CONTROL AUTOMATION AND ELECTRICAL SYSTEMS 2016年第3期27卷 317-327页

作者： Mathias-Neto, Waldemar Pereira Sanches Mantovani, Jose Roberto UNESP Univ Estadual Paulista LaPSEE Power Syst Planning Lab Dept Elect Engn Campus Ilha Solteira Sao Paulo Brazil

This paper presents a new algorithm to solve the distribution power system restoration problem based on a joint application of tabu search (TS) algorithm and the node-depth encoding (NDE). The integration of NDE, its operators, and the TS algorithm results in a methodology that combines the best of each technique. The main purpose of the proposed meta-heuristic approach is to minimize the costs involved in the restoration process while electrical and operational constraints are met. Simulation results for three scenarios of a modified IEEE 37-node test case are presented. The results show the computational performance and the robustness of the proposed algorithm.

关键词： Tabu search algorithm node-depth encoding Power distribution system Restoration

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MNDE: node-depth encoding can do better in evolutionary multitask algorithms

MNDE: Node-depth encoding can do better in evolutionary mult...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Cong Dao Tran Tuan Anh Do Huynh Thi Thanh Binh Duc Anh Do Ban, Ha-Bang Su Nguyen FPT Software AI Ctr Hanoi Vietnam Hanoi Univ Sci & Technol Hanoi Vietnam La Trobe Univ Melbourne Vic Australia

ISBN: (纸本)9798400701207

Evolutionary multitask algorithms that adopt multitask optimization paradigms have been proposed to tackle multiple problems simultaneously and improve the performance of traditional evolutionary algorithms. One of the most crucial challenges in evolutionary multitasking applied to network design is the lack of an efficient unified representation to encode solutions. This paper presents the first representation based on node-depth encoding for evolutionary multitask algorithms to tackle network design problems. Remarkably, we propose an encoding method to represent solutions modeled by trees of arbitrary graphs in the form of a unified representation and design a corresponding decoding method to reconstruct solutions from a unified search space for each task. To verify the efficiency of our proposed methods, extensive experiments are conducted on well-known network design problems and demonstrate that our approach performs significantly better than previous approaches regarding solution quality.

关键词： evolutionary multitask algorithm representation node-depth encoding network design

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Multiobjective evolutionary algorithm with a discrete differential mutation operator developed for service restoration in distribution systems

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2014年 62卷 700-711页

作者： Sanches, Danilo Sipoli London, Joao Bosco A., Jr. Delbem, Alexandre Claudio B. Prado, Ricardo S. Guimaraes, Frederico G. Neto, Oriane M. de Lima, Telma W. Fed Technol Univ Parana Cornelia Procopio Brazil Univ Sao Paulo Sao Carlos Sch Engn Sao Carlos SP Brazil Univ Sao Paulo Inst Math & Comp Sci Sao Carlos SP Brazil Fed Inst Minas Gerais Ouro Preto Brazil Univ Fed Minas Gerais Dept Elect Engn Belo Horizonte MG Brazil Univ Fed Goias Inst Informat Goiania Go Brazil

Network reconfiguration for service restoration in distribution systems is a combinatorial complex optimization problem that usually involves multiple non-linear constraints and objective functions. For large scale distribution systems no exact algorithm has found adequate restoration plans in real-time. On the other hand, the combination of Multi-Objective Evolutionary Algorithms (MOEAs) with the node-depth encoding (NDE) has been able to efficiently generate adequate restoration plans for relatively large distribution systems (with thousands of buses and switches). The approach called MEAN results from the combination of NDE with a technique of MOEA based on subpopulation tables. In order to improve the capacity of MEAN to explore both the search and objective spaces, this paper proposes a new approach that results from the combination of MEAN with characteristics from the mutation operator of the Differential Evolution (DE) algorithm. Simulation results have shown that the proposed approach, called MEAN-DE, is able to find adequate restoration plans for distribution systems from 3860 to 30,880 switches. Comparisons have been performed using the Hypervolume metric and the Wilcoxon rank-sum test. In addition, a MOEA using subproblem Decomposition and NDE (MOEA/D-NDE) was investigated. MEAN-DE has shown the best average results in relation to MEAN and MOEA/D-NDE. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Large-Scale Distribution Systems Service restoration node-depth encoding Multi-Objective Evolutionary Algorithms Differential Evolution

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Multi-Objective Evolutionary Algorithm for single and multiple fault service restoration in large-scale distribution systems

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ELECTRIC POWER SYSTEMS RESEARCH 2014年第May期110卷 144-153页

作者： Sanches, Danilo Sipoli London Junior, Joao Bosco A. Delbem, Alexandre Claudio B. Fed Technol Univ Parana BR-86300000 Cornell Procopio PR Brazil Univ Sao Paulo Sao Carlos Sch Engn BR-13566590 Sao Carlos SP Brazil Univ Sao Paulo Inst Math & Comp Sci BR-13566590 Sao Carlos SP Brazil

Network reconfiguration for service restoration (SR) in distribution systems is a complex optimization problem. For large-scale distribution systems, it is computationally hard to find adequate SR plans in real time since the problem is combinatorial and non-linear, involving several constraints and objectives. Two Multi-Objective Evolutionary Algorithms that use node-depth encoding (NDE) have proved able to efficiently generate adequate SR plans for large distribution systems: (i) one of them is the hybridization of the Non-Dominated Sorting Genetic Algorithm-II(NSGA-II) with NDE, named NSGA-N;(ii) the other is a Multi-Objective Evolutionary Algorithm based on subpopulation tables that uses NDE, named MEAN. Further challenges are faced now, i.e. the design of SR plans for larger systems as good as those for relatively smaller ones and for multiple faults as good as those for one fault (single fault). In order to tackle both challenges, this paper proposes a method that results from the combination of NSGA-N, MEAN and a new heuristic. Such a heuristic focuses on the application of NDE operators to alarming network zones according to technical constraints. The method generates similar quality SR plans in distribution systems of significantly different sizes (from 3860 to 30,880 buses). Moreover, the number of switching operations required to implement the SR plans generated by the proposed method increases in a moderate way with the number of faults. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Large-scale distribution system Service restoration Multiple faults node-depth encoding Multi-Objective Evolutionary Algorithms

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Differential evolution using ancestor tree for service restoration in power distribution systems

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APPLIED SOFT COMPUTING 2014年 23卷 498-508页

作者： Prado, Ricardo S. Pedrosa Silva, Rodrigo C. Neto, Oriane M. Guimaraes, Frederico G. Sanches, Danilo Sipoli London, Joao Bosco A., Jr. Delbem, Alexandre C. B. IFMG Area Automat & Control Ouro Preto Brazil Univ Fed Minas Gerais Dept Elect Engn Belo Horizonte MG Brazil McGill Univ Dept Elect & Comp Engn Montreal PQ Canada Fed Technol Univ Paran UTFPR Cornelio Procopio Brazil Univ Sao Paulo Sao Carlos Sch Engn Sao Carlos SP Brazil Univ Sao Paulo Inst Math & Comp Sci Sao Carlos SP Brazil

Problems in power distribution system reconfiguration (PDSR), such as service restoration, power loss reduction, and expansion planning, are usually formulated as complex multi-objective and multiconstrained optimization problems. Several evolutionary algorithms (EAs) have been developed to deal with PDSR problems, but the majority of EAs still demand high running time when applied to large-scale distribution systems (thousands of buses and switches). This paper presents a new approach for service restoration in large scale distribution systems that employs a discrete differential evolution with ancestor tree (DE-Tree). We combine the node-depth encoding (NDE) to represent computationally the electrical topology of the system and the ancestor tree presented here to implement differential evolution for service restoration problems. The ancestor tree is used to build a list of elementary movements that maps one solution in the search space into another, thus capturing the "difference" between forests encoded with the NDE, which is essential in the search engine of differential evolution. The use of an ancestor tree is not only central to implement differential mutation in our algorithm but also can track the sequence of switching operations in the restoration of the system after the optimization process is finished. The proposed approach makes differential evolution suitable for treating combinatorial optimization problems related to PDSR. Results presented on distribution system reconfiguration problems suggest the benefits and fast convergence of the proposed approach. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Differential evolution node-depth encoding Large-scale distribution system Service restoration

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Combining exhaustive search and multi-objective evolutionary algorithm for service restoration in large-scale distribution systems

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ELECTRIC POWER SYSTEMS RESEARCH 2016年 134卷 1-8页

作者： Camillo, Marcos H. M. Fanucchi, Rodrigo Z. Romero, Marcel E. V. de Lima, Telma Woerle Soares, Anderson da Silva Botazzo Delbem, Alexandre Claudio Marques, Leandro Tolomeu Maciel, Carlos Dias Augusto London Junior, Joao Bosco Paranaense Co Energy Londrina Brazil Univ Fed Goias Inst Comp Sci Goiania Go Brazil Univ Sao Paulo Inst Math Sci & Computat BR-05508 Sao Paulo Brazil Univ Sao Paulo Sao Carlos Sch Engn BR-05508 Sao Paulo Brazil

Service restoration problem in distribution systems emerges after the faulted areas have been identified and isolated. A solution is obtained by determining the minimal number of switching operations that results in a configuration with a minimal number of healthy out-of-service areas without violating the operational and radiality constraints. Recently a practical and efficient methodology was developed and demonstrated through tests performed on the real and large-scale distribution system of Londrina city (Brazil). This methodology, named MEAN-MH, combines a Multi-objective Evolutionary Algorithm with node-depth encoding, Multiple criteria tables and an alarming Heuristic. As any methodology based on meta-heuristics, the MEAN-MH does not guarantee to find the optimal solution of the service restoration problem, even when the optimal solution requires operations only in normally open switches incident to the healthy out-of-service areas (named as Tier 1 normally open switches). This paper proposes an extension of MEAN-MH that incorporates an Exhaustive Search (ES) procedure as a previous stage before MEAN-MH. The proposed ES guarantees the generation and analysis of all possible radial configurations that restore the service to all healthy out-of-service areas requiring operations only in Tier 1 normally open switches. Therefore, when the optimal solution of the service restoration problem requires operations only in Tier I NO switches, the proposed methodology, named MEAN-MH+ES, guarantees the optimum. However, when the optimal solution requires operations also in other switches, the MEAN-MH+ES searches by a feasible solution minimizing both the number of switching operations and the number of healthy out-of-service areas. To demonstrate the effectiveness of the proposal, both MEAN-MH and MEAN-MH+ES are applied to two real and large-scale distribution systems of Brazil. Moreover, the results obtained by MEAN-MH+ES are compared with those found in another publishe

关键词： Energy distribution systems Service restoration problem Combinatorial optimization Meta-heuristic node-depth encoding

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Analysis of Solution Quality of Multiobjective Evolutionary Algorithms for Service Restoration in Distribution Systems

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JOURNAL OF CONTROL AUTOMATION AND ELECTRICAL SYSTEMS 2017年第6期28卷 796-805页

作者： Sanches, Danilo Sipoli Castoldi, Marcelo Favoretto Augusto London, Joao Bosco, Jr. Botazzo Delbem, Alexandre Claudio Univ Tecnol Fed Parana Av Alberto Carazzai Cornelio Procopio PR Brazil Univ Sao Paulo Sao Carlos Sch Engn Sao Carlos SP Brazil Univ Sao Paulo Inst Math & Comp Sci Sao Carlos SP Brazil

This paper presents a comparative study of six multiobjective evolutionary algorithms (MOEAs) with the node-depth encoding (NDE) which have been used to solve the service restoration in distribution systems. The study has been divided into three steps: (1) the MOEAs have been evaluated taking into account the switching operations necessary to find adequate restoration plans considering multiple nonlinear constraints and objective functions;(2) the MOEAs have been employed to solve four different datasets with 3860, 7720, 15,440 and 30,880 buses, respectively;(3) comparisons have been performed using the hypervolume indicator and the results obtained with each approach are statistically compared using Kruskal-Wallis nonparametric tests and multiple comparisons. In addition, this paper provides a comprehensive evaluation of six combinations of MOEAs based on NDE and our objective is to identify the features of each approach that consistently produce best results applied to network reconfiguration for service restoration in distribution systems. Simulations results have shown that MOEA based on NDE with crowding distance and strength pareto found good configurations with low switching operations and explored the search space better than others approaches used in this paper, approximating better the pareto-optimal front.

关键词： Large-scale distribution systems Service restoration node-depth encoding Multiobjective evolutionary algorithms Differential evolution

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Multiobjective Discrete Differential Evolution for Service Restoration in Energy Distribution Systems

Multiobjective Discrete Differential Evolution for Service R...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Sanches, Danilo S. London, Joao Bosco A., Jr. Delbem, Alexandre C. B. Univ Tecnol Fed Parana Cornelio Procopio PR Brazil Univ Sao Paulo Sao Carlos Sch Engn Sao Carlos SP Brazil Univ Sao Paulo Inst Math & Comp Sci Sao Carlos SP Brazil

ISBN: (纸本)9781450343237

This paper presents a new multiobjective discrete differential evolution for service restoration in distribution systems. The proposed approach was compared with other five multiobjective evolutionary algorithms (MOEAs), which use node-depth encoding (NDE). The proposed approach have been evaluated taking into account the switching operations necessary to find adequate restoration plans considering multiple non-linear constraints and objective functions. The MOEAs used in this paper have been employed to solve four different datasets with 3,860, 7,720, 15,440 and 30,880 buses, respectively. Simulations results have shown that proposed approach reached good solutions with low switching operations and reduced running time when compared with others MOEAs.

关键词： Large-Scale Distribution Systems Service Restoration node-depth encoding Multi-Objective Evolutionary Algorithms Differential Evolution

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node-depth based Genetic Algorithm to solve Inter-Domain path computation problem

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KNOWLEDGE-BASED SYSTEMS 2024年 284卷

作者： Anh, Do Tuan Binh, Huynh Thi Thanh Kien, Do Luong Long, Nguyen Hoang Dao, Tran Cong Ban, Ha-Bang Hanoi Univ Sci & Technol Sch Informat & Commun Technol Hanoi Vietnam FPT Software AI Ctr Hanoi Vietnam

Inter-Domain Path Computation problem under node-defined Domain Uniqueness Constraint (IDPC-NDU) is an NP-Hard problem that applies to packet routing in multi-domain networks, particularly Hierarchical Path Computation Element (h-PCE) architecture. Its objective is to determine the shortest route between two specified nodes that visit each domain no more than once. In recent years, many proposals have been made to tackle this problem and improve existing algorithms. However, most of these strategies retain a potential weakness that lies in the complex encoding and decoding methods, which consume a lot of computer resources and computation time, especially for large-scale problems. For this reason, this paper introduces an effective node-depth based Genetic Algorithm (NDEGA) for IDPC-NDU. We propose a novel solution encoding for the problem by using tree representation that helps to satisfy the domain constraint and makes the corresponding solution construction more practical. Instead of conventional encoding techniques, NDEGA is equipped with an improved node-depth encoding, which is famous for its low time complexity and efficiency for tree problems. Besides, a corresponding decoding method, as well as node-depth search operators, are also well-developed for the problem. To examine the efficiency of NDEGA, we carefully conduct extensive experiments and compare our approach to many competitive baselines on a wide range of synthetic datasets. The empirical results demonstrate that our proposed algorithm significantly outperforms all compared algorithms regarding solution quality, convergence trend, and computation time and obtains the state-of-the-art performance for IDPC-NDU. Notably, our NDEGA achieves 65.17-85.66% solution quality improvement on average compared to the previous approaches while running faster, approximately 50 - 70 times.

关键词： node-depth encoding Genetic algorithm Evolutionary algorithm Inter-domain path computation Multi-domain network

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