Hybrid krill herd algorithm with differential evolution for global numerical optimization

In order to overcome the poor exploitation of the krill herd (KH) algorithm, a hybrid differential evolution KH (DEKH) method has been developed for function optimization. The improvement involves adding a new hybrid differential evolution (HDE) operator into the krill, updating process for the purpose of dealing with optimization problems more efficiently. The introduced HDE operator inspires the intensification and lets the krill perform local search within the defined region. DEKH is validated by 26 functions. From the results, the proposed methods are able to find more accurate solution than the KH and other methods. In addition, the robustness of the DEKH algorithm and the influence of the initial population size on convergence and performance are investigated by a series of experiments.     

An improved krill herd algorithm with global exploration capability for solving numerical function optimization problems and its application to data clustering

Krill herd algorithm is a stochastic nature-inspired algorithm for solving optimization problems. The performance of krill herd algorithm is degraded by poor exploitation capability. In this study, we propose an improved krill herd algorithm (IKH) by making the krill the global search capability. The enhancement comprises of adding global search operator for exploration around the defined search region and thus the krill individuals move towards the global best solution. The elitism strategy is also applied to maintain the best krill during the krill update steps. The proposed method is tested on a set of twenty six well-known benchmark functions and is compared with thirteen popular optimization algorithms, including original KH algorithm. The experimental results show that the proposed method produced very accurate results than KH and other compared algorithms and is more robust. In addition, the proposed method has high convergence rate. The high performance of the proposed algorithm is then employed for data clustering problems and is tested using six real datasets available from UCI machine learning laboratory. The experimental results thus show that the proposed algorithm is well suited for solving even data clustering problems.     

基于改进磷虾群算法的SVDD参数优化

支持向量数据描述（SVDD）是构造单类数据描述的分类算法,惩罚参数[C]和核参数[σ]作为影响SVDD分类效果的关键,其合理选取一直是个难点。针对这一问题,提出了一种基于改进磷虾群算法的SVDD参数优化算法（IKH-SVDD）。依据仿真实验,分析参数[C]和[σ]对描述边界的影响;引入磷虾群算法并分析其优劣,通过在随机扩散行为中定义扰动因子,增强算法的全局搜索能力;将一种新的精英选择和保留策略引入迭代过程,提高算法的收敛精度;将改进的磷虾群算法引入SVDD参数优化过程,构建了IKH-SVDD参数优化模型。基于UCI标准数据库进行实验并与其他几种参数优化算法进行比较,结果表明了IKH-SVDD算法具有更高的分类准确性。     

基于改进磷虾群算法的服务组合优化

面向服务的架构（SOA）下,针对服务组合优化过程中易陷入局部最优、时间开销大的问题,提出一种加入自适应交叉算子和随机扰动算子的改进磷虾群算法PRKH。首先基于服务质量（QoS）建立了服务组合优化模型,并给出不同结构下QoS的计算公式和归一化处理方法。然后在磷虾群（KH）算法的基础上加入自适应的交叉概率和基于实际偏移量的随机扰动,从而在磷虾群的全局搜索能力和局部搜索能力之间达到良好平衡。最后通过仿真,把所提算法与KH算法、粒子群优化（PSO）算法、人工蜂群（ABC）算法和花朵授粉算法（FPA）进行对比,实验结果表明,PRKH算法能够更快找到QoS更优的复合服务。     

基于磷虾群算法的并网电动汽车功率优化分配

为提高并网电动汽车(EV)集群的功率优化分配效率,提出基于磷虾群算法的EV集群并网两阶段功率高效分配策略。考虑用户的需求差异,将并网EV细化为不可调度集及可调度集,分别建立充放电控制模型,提出可调度集EV的优先权评估指标。采用动态自适应权重策略及余弦递减步长演进策略改进磷虾群(KH)算法,将可调度集EV的优先权映射为迭代算法的演变步长,通过两阶段交互迭代实现并网EV集群的功率高效分配。仿真实验验证了模型的可行性以及所提策略的高效性。     

An improved differential evolution algorithm with triangular mutation for global numerical optimization

This paper presents an Improved Differential Evolution (IDE) algorithm for solving global numerical optimization problems over continuous space. The proposed algorithm introduces a new triangular mutation rule based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vector between the best and the worst individuals among the three randomly selected vectors. The mutation rule is combined with the basic mutation strategy through a non-linear decreasing probability rule. Furthermore, a restart mechanism is also proposed to avoid premature convergence. IDE is tested on a well-known set of unconstrained problems and shows its superiority to state-of-the-art differential evolution variants.     

Hybrid Taguchi-genetic algorithm for global numerical optimization

In this paper, a hybrid Taguchi-genetic algorithm (HTGA) is proposed to solve global numerical optimization problems with continuous variables. The HTGA combines the traditional genetic algorithm (TGA), which has a powerful global exploration capability, with the Taguchi method, which can exploit the optimum offspring. The Taguchi method is inserted between crossover and mutation operations of a TGA. Then, the systematic reasoning ability of the Taguchi method is incorporated in the crossover operations to select the better genes to achieve crossover, and consequently, enhance the genetic algorithm. Therefore, the HTGA can be more robust, statistically sound, and quickly convergent. The proposed HTGA is effectively applied to solve 15 benchmark problems of global optimization with 30 or 100 dimensions and very large numbers of local minima. The computational experiments show that the proposed HTGA not only can find optimal or close-to-optimal solutions but also can obtain both better and more robust results than the existing algorithm reported recently in the literature.     

基于对立搜索和混沌变异的磷虾觅食优化算法

针对磷虾觅食算法存在容易陷入局部极值、收敛速度慢的问题, 提出一种新的改进算法. 首先, 给出启发式二次对立点的定义并证明其性能优势, 进而构造一种启发式二次对立搜索算子, 以加快算法的收敛速度, 提高全局探索能力; 然后, 采用分段线性混沌映射(PWLCM) 混沌函数构造一种变尺度混沌变异算子, 以增强算法跳出局部极值的能力. 仿真实验表明, 所提出算法能有效避免陷入局部极值, 在收敛速度和寻优精度上得到大幅改善.

     

An adaptive single-point algorithm for global numerical optimization

This paper describes a novel algorithm for numerical optimization, called Simple Adaptive Climbing (SAC). SAC is a simple efficient single-point approach that does not require a careful fine-tunning of its two parameters. SAC algorithm shares many similarities with local optimization heuristics, such as random walk, gradient descent, and hill-climbing. SAC has a restarting mechanism, and a powerful adaptive mutation process that resembles the one used in Differential Evolution. The algorithms SAC is capable of performing global unconstrained optimization efficiently in high dimensional test functions. This paper shows results on 15 well-known unconstrained problems. Test results confirm that SAC is competitive against state-of-the-art approaches such as micro-Particle Swarm Optimization, CMA-ES or Simple Adaptive Differential Evolution.     

Dynamic partition search algorithm for global numerical optimization

This paper presents a novel evolutionary algorithm entitled Dynamic Partition Search Algorithm (DPSA) for global optimization problems with continuous variables. The DPSA is a population-based stochastic search algorithm in nature, which mainly consists of initialization process and evolution process. In the initialization process, the DPSA randomly generates an initial population of members from a specific search space and finds a leader. In the evolution process, the DPSA applies two groups to balance exploration ability and exploitation ability, in which one group is in charge of exploring new region via a dynamic partition strategy, and the other group relies on Cauchy distributions to exploit the region around the best member. Later, numerical experiments are conducted for 24 classical benchmark functions with 100, 1000 or even 10000 dimensions. And the performance of the proposed DPSA is compared with a state-of-the-art cooperative coevolving particle swarm optimization (CCPSO2), and two existing differential evolution (DE) algorithms. The experimental results show that DPSA has a better performance than the algorithms used for comparison, especially for high dimensional optimization problems. In addition, the numerical computational results also demonstrate that the DPSA has good scalability, and it is an effective evolutionary algorithm for solving large-scale global optimization problems.     

用于多维函数优化的实数编码量子蚁群算法*

基于量子计算理论及蚂蚁群体寻优策略,提出了一种用于连续优化问题的新方法——实数编码量子蚁群算法（RQACOA）。针对量子比特编码和二进制编码在连续优化问题上的不足,引入一种新的实数编码表示方法,设计了智能量子蚂蚁,一条染色体携带指定范围内的多个个体信息。智能量子蚂蚁利用量子态纠缠和相干机理,通过叠加、变异及自学习来完成前期进化过程,然后以蚂蚁群体智能寻优方式进一步求解。实验结果表明,该算法具有强的全局寻优能力及快速搜索能力。     

An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization

Differential evolution (DE) is one of the most powerful stochastic real parameter optimizers of current interest. In this paper, we propose a new mutation strategy, a fitness-induced parent selection scheme for the binomial crossover of DE, and a simple but effective scheme of adapting two of its most important control parameters with an objective of achieving improved performance. The new mutation operator, which we call DE/current-to-gr_best/1, is a variant of the classical DE/current-to-best/1 scheme. It uses the best of a group (whose size is q% of the population size) of randomly selected solutions from current generation to perturb the parent (target) vector, unlike DE/current-to-best/1 that always picks the best vector of the entire population to perturb the target vector. In our modified framework of recombination, a biased parent selection scheme has been incorporated by letting each mutant undergo the usual binomial crossover with one of the p top-ranked individuals from the current population and not with the target vector with the same index as used in all variants of DE. A DE variant obtained by integrating the proposed mutation, crossover, and parameter adaptation strategies with the classical DE framework (developed in 1995) is compared with two classical and four state-of-the-art adaptive DE variants over 25 standard numerical benchmarks taken from the IEEE Congress on Evolutionary Computation 2005 competition and special session on real parameter optimization. Our comparative study indicates that the proposed schemes improve the performance of DE by a large magnitude such that it becomes capable of enjoying statistical superiority over the state-of-the-art DE variants for a wide variety of test problems. Finally, we experimentally demonstrate that, if one or more of our proposed strategies are integrated with existing powerful DE variants such as jDE and JADE, their performances can also be enhanced.     

A multiagent genetic algorithm for global numerical optimization.

In this paper, multiagent systems and genetic algorithms are integrated to form a new algorithm, multiagent genetic algorithm (MAGA), for solving the global numerical optimization problem. An agent in MAGA represents a candidate solution to the optimization problem in hand. All agents live in a latticelike environment, with each agent fixed on a lattice-point. In order to increase energies, they compete or cooperate with their neighbors, and they can also use knowledge. Making use of these agent-agent interactions, MAGA realizes the purpose of minimizing the objective function value. Theoretical analyzes show that MAGA converges to the global optimum. In the first part of the experiments, ten benchmark functions are used to test the performance of MAGA, and the scalability of MAGA along the problem dimension is studied with great care. The results show that MAGA achieves a good performance when the dimensions are increased from 20-10,000. Moreover, even when the dimensions are increased to as high as 10,000, MAGA still can find high quality solutions at a low computational cost. Therefore, MAGA has good scalability and is a competent algorithm for solving high dimensional optimization problems. To the best of our knowledge, no researchers have ever optimized the functions with 10,000 dimensions by means of evolution. In the second part of the experiments, MAGA is applied to a practical case, the approximation of linear systems, with a satisfactory result.     

Hybrid clustering analysis using improved krill herd algorithm

In this paper, a novel text clustering method, improved krill herd algorithm with a hybrid function, called MMKHA, is proposed as an efficient clustering way to obtain promising and precise results in this domain. Krill herd is a new swarm-based optimization algorithm that imitates the behavior of a group of live krill. The potential of this algorithm is high because it performs better than other optimization methods; it balances the process of exploration and exploitation by complementing the strength of local nearby searching and global wide-range searching. Text clustering is the process of grouping significant amounts of text documents into coherent clusters in which documents in the same cluster are relevant. For the purpose of the experiments, six versions are thoroughly investigated to determine the best version for solving the text clustering. Eight benchmark text datasets are used for the evaluation process available at the Laboratory of Computational Intelligence (LABIC). Seven evaluation measures are utilized to validate the proposed algorithms, namely, ASDC, accuracy, precision, recall, F-measure, purity, and entropy. The proposed algorithms are compared with the other successful algorithms published in the literature. The results proved that the proposed improved krill herd algorithm with hybrid function achieved almost all the best results for all datasets in comparison with the other comparative algorithms.     

基于混合混沌磷虾算法的短期水火电调度研究

Short-Term Hydrothermal Scheduling (STHS) is a nonlinear, multi-constrained and time-varying optimization problem. When the valve point effect is considered, the problem becomes non- convex and more complicated. In order to improve the search ability of the Krill Herd Algorithm (KHA) in the STHS problem, the hybrid chaotic map is introduced to improve the global convergence speed of KHA. In order to avoid premature convergence of the algorithm, by recording the number of times that the fuel cost values of the best individual in each generation remain unchanged and making the decision that a positional mutation in the non-positionally dominant individual within its feasible domain, a hybrid chaotic krill herd algorithm (HCKHA) is proposed. HCKHA and KHA, CKHA were applied to the standard STHS test systems such as "four hydro and three thermal plants" and "four hydro and ten thermal plants", independently. The simulation results show that HCKHA has better optimization ability, fuel cost values and transmission loss values than KHA, CKHA and the optimization methods in other related literatures.     

Chaotic krill herd algorithm for optimal reactive power dispatch considering FACTS devices

Conventionally, optimal reactive power dispatch (ORPD) is described as the minimization of active power transmission losses and/or total voltage deviation by controlling a number of control variables while satisfying certain equality and inequality constraints. This article presents a newly developed meta-heuristic approach, chaotic krill herd algorithm (CKHA), for the solution of the ORPD problem of power system incorporating flexible AC transmission systems (FACTS) devices. The proposed CKHA is implemented and its performance is tested, successfully, on standard IEEE 30-bus test power system. The considered power system models are equipped with two types of FACTS controllers (namely, thyristor controlled series capacitor and thyristor controlled phase shifter). Simulation results indicate that the proposed approach yields superior solution over other popular methods surfaced in the recent state-of-the-art literature including chaos embedded few newly developed optimization techniques. The obtained results indicate the effectiveness for the solution of ORPD problem of power system considering FACTS devices. Finally, simulation is extended to some large-scale power system models like IEEE 57-bus and IEEE 118-bus test power systems for the same objectives to emphasis on the scalability of the proposed CKHA technique. The scalability, the robustness and the superiority of the proposed CKHA are established in this paper.     

全局优化的蝴蝶优化算法

针对基本蝴蝶优化算法中存在的易陷入局部最优值、收敛速度慢等问题,提出一种全局优化的蝴蝶算法,引入limit阈值来限定蝴蝶优化算法陷入局部最优解的次数,从而改变算法易陷入早熟的问题,结合单纯形策略优化迭代后期位置较差的蝴蝶使种群能够较快地找到全局最优解;将正弦余弦算法作为局部算子融入BOA中,改善迭代后期种群多样性下降的缺陷,加快算法跳出局部最优。在仿真模拟实验中与多个算法进行对比,结果表明改进算法的寻优性能更好。     

A robust stochastic genetic algorithm (StGA) for global numerical optimization

Many real-life problems can be formulated as numerical optimization of certain objective functions. However, often an objective function possesses numerous local optima, which could trap an algorithm from moving toward the desired global solution. Evolutionary algorithms (EAs) have emerged to enable global optimization; however, at the present stage, EAs are basically limited to solving small-scale problems due to the constraint of computational efficiency. To improve the search efficiency, this paper presents a stochastic genetic algorithm (StGA). A novel stochastic coding strategy is employed so that the search space is dynamically divided into regions using a stochastic method and explored region-by-region. In each region, a number of children are produced through random sampling, and the best child is chosen to represent the region. The variance values are decreased if at least one of five generated children results in improved fitness, otherwise, the variance values are increased. Experiments on 20 test functions of diverse complexities show that the StGA is able to find the near-optimal solution in all cases. Compared with several other algorithms, StGA achieves not only an improved accuracy, but also a considerable reduction of the computational effort. On average, the computational cost required by StGA is about one order less than the other algorithms. The StGA is also shown to be able to solve large-scale problems.