基于种群划分与变异策略的粒子群优化算法

粒子群算法因其形式比较简洁，参数设置灵活，操作简便易行，并且能够快速收敛，从而引起广泛关注。但是传统的粒子群算法也有缺陷：收敛速度慢以及容易陷入局部最优等。针对这些问题，本文借鉴小生境的方法，在进化初始阶段，对种群进行划分，将初始种群分为子种群，对不同的子种群进行不同的变异策略；在进化过程中，针对不同的子种群，设置不同的惯性权重因子ω，用来增强全局搜索能力与局部搜索能力。实验结果表明，本文提出的算法较传统的粒子群算法具有较快的收敛性以及找寻的全局最优解更接近真实解集，收敛精度比较高。     

A cell-based smoothed radial point interpolation method with virtual nodes for three-dimensional mid-frequency acoustic problems

It is well known that the finite element method (FEM) encounters dispersion errors in coping with mid-frequency acoustic problems due to its “overly stiff” nature. By introducing the generalized gradient smoothing technique and the idea of condensed shape functions with virtual nodes, a cell-based smoothed radial point interpolation method is proposed to solve the Helmholtz equation for the purpose of reducing dispersion errors. With the properly selected virtual nodes, the proposed method can provide a close-to-exact stiffness of continuum, leading to a conspicuous decrease in dispersion errors and a significant improvement in accuracy. Numerical examples are examined using the present method by comparing with both the traditional FEM using four-node tetrahedral elements (FEM-T4) and the FEM model using eight-node hexahedral elements with modified integration rules (MIR-H8). The present cell-based smoothed radial point interpolation method has been demonstrated to possess a number of superiorities, including the automatically generated tetrahedral background mesh, high computational efficiency, and insensitivity to mesh distortion, which make the method a good potential for practical analysis of acoustic problems.     

Binary whale optimization algorithm: a new metaheuristic approach for profit-based unit commitment problems in competitive electricity markets

This article presents a metaheuristic approach, the binary whale optimization algorithm (BWOA), to solve complex, constrained, non-convex, binary-nature profit-based unit commitment (PBUC) optimization problems of a price-taking generation company (GenCo) in the electricity market. To simulate the binary-nature PBUC problem, the continuous, real-value whale position/location is mapped into binary search space through various transfer functions. This article introduces three variants of BWOA using tangential hyperbolic, inverse tangent (arctan) and sigmoidal transfer functions. The effectiveness of the BWOA approaches is examined in test systems with different market mechanisms, i.e. an energy-only market, and energy and reserve market participation with different reserve payment methods. The simulation results are presented, discussed and compared with other existing approaches. The convergence characteristics, solution quality and consistency of the results across different BWOA variants are discussed. The superiority and statistical significance of the proposed approaches with respect to existing approaches is also presented.     

最优化算法与纯元素谱剥离相结合的能量色散X射线荧光谱解谱方法

在进行能量色散X射线荧光光谱(EDXRF)解谱时,如果给定样品的元素构成,采用纯元素谱图剥离的方式会更加合理,但由于每个元素的谱线都不止一条,如果仅仅针对主线对齐做剥离,会导致结果的严重失真,同时剥离次序对解谱结果有较大影响。介绍了一种最优化算法与纯元素谱剥离相结合的EDXRF解谱方法,该方法以多个纯元素谱的强度大小和峰位漂移道数作为变量构建残差方程,并用最优化计算的方法去调整,直至残差达到极小。实验采用强度顺序剥离、能量顺序剥离和最优化算法拟合3种方法分别对谱线重叠较为严重的La-Ce-Pr-Nd混合液样品的L系谱线进行了解析,结果表明最优化计算方法拟合的谱图与原始谱的残差 (1415.0)比另两种方法(166094.0和3192.7)大幅度缩小,拟合谱与原始谱更为吻合,并且方法在实现时对初值不敏感,解谱精度也不依赖于剥离次序。     

Couple-based particle swarm optimization for short-term hydrothermal scheduling

A novel couple-based particle swarm optimization (CPSO) is presented in this paper, and applied to solve the short-term hydrothermal scheduling (STHS) problem. In CPSO, three improvements are proposed compared to the canonical particle swarm optimization, aimed at overcoming the premature convergence problem. Dynamic particle couples, a unique sub-group structure in maintaining population diversity, is adopted as the population topology, in which every two particles compose a particle couple randomly in each iteration. Based on this topology, an intersectional learning strategy using the partner learning information of last iteration is employed in every particle couple, which can automatically reveal useful history information and reduce the overly rapid evolution speed. Meanwhile, the coefficients of each particle in a particle couple are set as distinct so that the particle movement patterns can be described and controlled more precisely. In order to demonstrate the effectiveness of our proposed CPSO, the algorithm is firstly tested with four multimodal benchmark functions, and then applied to solve an engineering multimodal problem known as STHS, in which two typical test systems with four different cases are tested, and the results are compared with those of other evolutionary methods published in the literature.     

A novel differential evolution mapping technique for generic combinatorial optimization problems

Differential evolution is primarily designed and used to solve continuous optimization problems. Therefore, it has not been widely considered as applicable for real-world problems that are characterized by permutation-based combinatorial domains. Many algorithms for solving discrete problems using differential evolution have been proposed, some of which have achieved promising results. However, to enhance their performance, they require improvements in many aspects, such as their convergence speeds, computational times and capabilities to solve large discrete problems. In this paper, we present a new mapping method that may be used with differential evolution to solve combinatorial optimization problems. This paper focuses specifically on the mapping component and its effect on the performance of differential evolution. Our method maps continuous variables to discrete ones, while at the same time, it directs the discrete solutions produced towards optimality, by using the best solution in each generation as a guide. To judge its performance, its solutions for instances of well-known discrete problems, namely: 0/1 knapsack, traveling salesman and traveling thief problems, are compared with those obtained by 8 other state-of-the-art mapping techniques. To do this, all mapping techniques are used with the same differential evolution settings. The results demonstrated that our technique significantly outperforms the other mapping methods in terms of the average error from the best-known solution for the traveling salesman problems, and achieves promising results for both the 0/1 knapsack and the traveling thief problems.     

New approach to identify the initial condition in degenerate hyperbolic equation

This paper deals with the determination of an initial condition in degenerate hyperbolic equation from final observations. With the aim of reducing the execution time, this inverse problem is solved using an approach based on double regularization: a Tikhonov’s regularization and regularization in equation by viscose-elasticity. So, we obtain a sequence of weak solutions of degenerate linear viscose-elastic problems. Firstly, we prove the existence and uniqueness of each term of this sequence. Secondly, we prove the convergence of this sequence to the weak solution of the initial problem. Also we present some numerical experiments to show the performance of this approach.     

Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

The process of electrodeposition can be described in terms of a reaction-diffusion partial differential equation (PDE) system that models the dynamics of the morphology profile and the chemical composition. Here we fit such a model to the different patterns present in a range of electrodeposited and electrochemically modified alloys using PDE constrained optimization. Experiments with simulated data show how the parameter space of the model can be divided into zones corresponding to the different physical patterns by examining the structure of an appropriate cost function. We then use real data to demonstrate how numerical optimization of the cost function can allow the model to fit the rich variety of patterns arising in experiments. The computational technique developed provides a potential tool for tuning experimental parameters to produce desired patterns.     

A constrained portfolio selection model at considering risk-adjusted measure by using hybrid meta-heuristic algorithms

Portfolio selection is a key issue in the business world and financial fields. This article presents a new decision making method of portfolio optimization (PO) issues in different risk measures by using new evolutionary computing method and cardinality constrains which is mentioned as hybrid meta-heuristic algorithms. Based on mean–variance (MV) Method by Markowitz we collected three risk levels; mean absolute deviation (MAD), semi variance (SV) and variance with skewness (VWS). The developed algorithms are Electromagnetism-like algorithm (EM), particle swarm optimization (PSO), genetic algorithm (GA), genetic network programming (GNP) and simulated annealing (SA). Also a diversification mechanism strategy is implemented and hybridized with the developed algorithms to increase the diversity and overcome local optimality. The sustainability of this proposed model is verified by 50 factories on the Iranian stock exchange. Finally, experimental results of proposed algorithms with cardinality constraint are compared with each other by four effective metrics in which the algorithms performance for achieving the optimal solution discussed. In addition, we have done the analysis of variance technique to confirm the validity and accurately analyze of the results which the success of this method was proved.     

Maximization of quadruple phase boundary for alkaline membrane fuel cell using non-stoichiometric α-MnO2 as cathode catalyst

Oxygen can only be reduced at the quadruple phase boundary (catalyst, carbon support, ionomer and oxygen) of the cathode catalyst layer with non-conducting electrocatalyst. To maximize the quadruple phase boundary sites is crucial to increase the peak power density of each membrane electrode assembly. The quadruple phase boundary is depending on the ratio of catalyst, carbon support and ionomer. The loading of catalyst layer is also crucial to the fuel cell performance. In this study, non-stoichiometric α-MnO₂ manganese dioxide nanorod material has been synthesized and the ratios of carbon, ionomer and catalyst loadings were optimized in alkaline membrane fuel cell. In total, ten membrane electrode assemblies have been manufactured and tested. Taguchi design method has been applied in order to understand the effect of each parameter. The conclusion finds out the ionomer has more influence on the alkaline membrane fuel cell peak power performance than carbon and loading.