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In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the non-regular part of such model are ordered followed by ordering the nodes of the regular part. With this ordering the graph matrices will be separated into two blocks. The eigensolution of the non-regular part can be performed by an iterative method, and those of the regular part can easily be calculated using decomposition approaches studied in our previous articles. Some numerical examples are included to illustrate the efficiency of the new method.

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In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the non-regular part of such model are ordered followed by ordering the nodes of the regular part. With this ordering the graph matrices will be separated into two blocks. The eigensolution of the non-regular part can be performed by an iterative method, and those of the regular part can easily be calculated using decomposition approaches studied in our previous articles. Some numerical examples are included to illustrate the efficiency of the new method.

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This paper presents a Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) for the optimal operation of a complex multipurpose and multi-reservoir system. Firstly, MOEA/D decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems and optimizes them simultaneously. It uses information of its several neighboring sub-problems for optimizing each sub-problem. This simple procedure makes MOEA/D have lower computational complexity compared with non-dominated sorting genetic algorithm II (NSGA-II). The algorithm (MOEA/D) is compared with the Genetic Algorithm (NSGA-II) using a set of common test problems and the real-world Zohre reservoir system in southern Iran. The objectives of the case study include water supply of minimum flow and agriculture demands over a long-term simulation period. Experimental results have demonstrated that MOEA/D can improve system performance to reduce the effect of drought compared with NSGA-II superiority. Therefore, MOEA/D is highly competitive and recommended to solve multi-objective optimization problems for water resources planning and management.

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In this paper the performance of four well-known metaheuristics consisting of Artificial Bee Colony (ABC), Biogeographic Based Optimization (BBO), Harmony Search (HS) and Teaching Learning Based Optimization (TLBO) are investigated on optimal domain decomposition for parallel computing. A clique graph is used for transforming the connectivity of a finite element model (FEM) into that of the corresponding graph, and k-median approach is employed. The performance of these methods is investigated through four FE models with different topology and number of meshes. A comparison of the numerical results using different algorithms indicates, in most cases the BBO is capable of performing better or identical using less time with equal computational effort.