Computational modification of neural systems using a novel stochastic search scheme,namely evaporation rate-based water cycle algorithm: an application in geotechnical issues

Recent studies have demonstrated the high efficiency of metaheuristic algorithms for various optimization engineering problems. The main focus of the present study is to apply a novel notion of stochastic search methods, namely evaporation rate-based water cycle algorithm (ER-WCA) to the problem of soil shear strength (SSS) prediction. The ER-WCA, as the name indicates, is a modified version of the water cycle algorithm that is used to computationally modify an artificial neural network (ANN) for the mentioned purpose. The sensitivity analysis showed that the most proper values for the number of rivers + sea and the population size are 5 and 300, respectively. The performance of the ER-WCA–ANN hybrid is compared to an ANN typically trained by the Levenberg–Marquardt algorithm to evaluate the effectiveness of the proposed metaheuristic technique. The findings showed that incorporation of the ER-WCA results in reducing the root-mean-square error by 5.87% and 4.92% in the training and testing phases, respectively. Meanwhile, the coefficient of determination rose from 84.27 to 86.11% and from 78.80 to 80.83% in these phases. It indicates that the weights and biases suggested by the ER-WCA can construct a considerably more reliable ANN. Therefore, the introduced method is recommended for practical uses in the early prediction of the SSS in civil engineering projects.

     

An efficient chaotic water cycle algorithm for optimization tasks

Water cycle algorithm (WCA) is a new population-based meta-heuristic technique. It is originally inspired by idealized hydrological cycle observed in natural environment. The conventional WCA is capable to demonstrate a superior performance compared to other well-established techniques in solving constrained and also unconstrained problems. Similar to other meta-heuristics, premature convergence to local optima may still be happened in dealing with some specific optimization tasks. Similar to chaos in real water cycle behavior, this article incorporates chaotic patterns into stochastic processes of WCA to improve the performance of conventional algorithm and to mitigate its premature convergence problem. First, different chaotic signal functions along with various chaotic-enhanced WCA strategies (totally 39 meta-heuristics) are implemented, and the best signal is preferred as the most appropriate chaotic technique for modification of WCA. Second, the chaotic algorithm is employed to tackle various benchmark problems published in the specialized literature and also training of neural networks. The comparative statistical results of new technique vividly demonstrate that premature convergence problem is relieved significantly. Chaotic WCA with sinusoidal map and chaotic-enhanced operators not only can exploit high-quality solutions efficiently but can outperform WCA optimizer and other investigated algorithms.

     

Spiral water cycle algorithm for solving multi-objective optimization and truss optimization problems

This paper addresses multi-objective optimization and the truss optimization problem employing a novel meta-heuristic that is based on the real-world water cycle behavior in rivers, rainfalls, streams, etc. This meta-heuristic is called multi-objective water cycle algorithm (MOWCA) which is receiving great attention from researchers due to the good performance in handling optimization problems in different fields. Additionally, the hyperbolic spiral movement is integrated into the basic MOWCA to guide the agents throughout the search space. Consequently, under this hyperbolic spiral movement, the exploitation ability of the proposed MOSWCA is promoted. To assess the robustness and coherence of the MOSWCA, the performance of the proposed MOSWCA is analysed on some multi-objective optimisation benchmark functions; and three truss structure optimization problems. The results obtained by the MOSWCA of all test problems were compared with various multi-objective meta-heuristic algorithms reported in the literature. From the empirical results, it is evident that the suggested approach reaches an excellent performance when solving multi-objective optimization and the truss optimization problems.

     

Hierarchical Learning Water Cycle Algorithm

In order to improve the global searching ability of Water Cycle Algorithm (WCA), the hierarchical learning concept is introduced and the Hierarchical Learning WCA (HLWCA) is proposed in this paper. The underlying idea of HLWCA is to divide the solutions into collections and give these collections with hierarchy differences. One of the collections has a higher hierarchy than others and utilizes an exploration-inclined updating mechanism. The solutions in this high hierarchy collection are the exemplars of other collections. The other collections are sorted according to the exemplars’ function value and the solutions in these collections actively choose whether to follow their own exemplar or not. Through different updating mechanisms of collections, the global searching ability is improved while the fast convergence and strong local search ability of WCA are retained. The proposed HLWCA is firstly experimented on IEEE CEC 2017 benchmark suite to testify its performance on complex numerical optimization tasks. Then, it is tested on four practical design benchmark problems to verify its ability of solving real-world problems. The experimental results illustrate the efficiency of the proposed algorithm.     

Grenade Explosion Method—A novel tool for optimization of multimodal functions

This work presents a new optimization technique called Grenade Explosion Method (GEM). The fundamental concepts and ideas which underlie the method are fully explained. It is seen that this simple and robust algorithm is quite powerful in finding all global and some local optima of multimodal functions. The method is tested with several multimodal benchmark functions and the results show it usually converges to the global minima faster than other evolutionary methods such as Genetic Algorithm (GA) and Artificial Bee Colony (ABC). Based on the performance on classical benchmark functions, the efficiency of the method in solving engineering applications can be highly appreciated.     

Gradient-based Water Cycle Algorithm with evaporation rate applied to chaos suppression

Water Cycle Algorithm (WCA) is a nature-inspired population-based metaheuristic algorithm, which has been successfully applied to solve a wide range of benchmarks and real-world optimization problems. In this paper, an extended version of WCA, namely Gradient-based Water Cycle Algorithm (GWCA) with evaporation rate, is introduced to enhance the performance of the standard WCA by incorporating a local optimization operator so-called gradient-based approach. The idea of GWCA is underlined using the concept of moving (flowing) individuals along the steepest direction slope under a certain criterion. In order to demonstrate parameters influence on the performance of GWCA, an extensive sensitivity analysis is also carried out. To verify the performance of the GWCA, twelve well-known benchmark functions are adopted from the literature in the experiments. Both value-based and ranked-based methods are conducted to compare the performance of reported algorithms on the whole test suite. To this reason, the mean best and standard deviation of the results are provided and the Friedman test is utilized to determine average ranking of the algorithms based on their performances in each experiment. Corresponding results indicate that the proposed GWCA has outstanding performance in comparison with some state-of-art optimization algorithms. Finally, the chaos suppression problem using backstepping control as a real case study was adopted to confirm the efficiency of GWCA. The experimental results demonstrate the feasibility and efficiency of the proposed GWCA.     

基于逻辑自映射的变尺度混沌粒子群优化算法*

针对基本粒子群优化算法的早熟收敛问题,提出了一种基于逻辑自映射的变尺度混沌粒子群优化算法。该算法在粒子群优化算法每次寻优结束时,采用逻辑自映射函数产生混沌序列,在已搜索到的精英粒子附近尝试搜索更优解并动态收缩搜索范围,在防止算法过早陷入局部最优的同时提高了算法搜索的精度。仿真结果表明,新算法在寻优成功率和平均最优值方面有很大提高,在求解包括欺骗性函数和高维函数在内的多种函数优化问题方面具有良好的效果。     

用于全局优化的一种新填充函数

填充函数法是一种寻求多变量、多峰值函数的总体最优的优化方法。鉴于提出过的填充函数,给出了一种形式简单的单参填充函数,计算中无需考虑函数出现不连续点的情况,且函数不受指数项影响。对一些标准函数的仿真结果比较表明构造的填充函数是有效的。     

一种引入单纯形法算子的新颖粒子群算法

提出一种将单纯形法SM与粒子群算法PSO混合的新颖优化算法,在10个著名测试函数上与其他已有算法进行了广泛的比较实验,并研究了不同参数选择对算法的影响.实验结果表明,这种混合算法对传统PSO求解的收敛率和解的质量有较明显的改善,在多峰函数优化问题上优势更突出.算法实现简单,具有很高的可靠性,是一种求解多峰连续函数极值的有效方法.     

最优化问题全局寻优的PSO-BFGS混合算法

针对利用粒子群优化算法进行多极值函数优化时存在早熟收敛和搜索效率低的问题,提出混合的PSO-BFGS算法,并增强了混合算法的变异能力使算法能逃出局部极值点.通过对三种Benchmark函数的测试结果表明,PSO-BFGS算法不仅具有有效的全局收敛性能,而且还具有较快的收敛速度,是求解最优化问题的一种有效算法.     

分数阶策略和带有Lévy飞行的螺旋蝙蝠算法

针对蝙蝠算法在求解多峰、复杂非线性问题时,搜索效率降低、易陷入局部最优等不足,提出了一种改进的蝙蝠算法。引入具有短期记忆特性的分数阶策略来更新蝙蝠位置,增加种群多样性,提高了算法收敛速度;用带有Lévy飞行的阿基米德螺旋策略产生局部新解,增强局部开发能力,同时有助于算法跳出局部最优;采用新的非线性动态机制调节响度和脉冲发射率,以平衡算法的探索和开发。选取CEC2014测试集,包括单峰、多峰、混合以及复合函数,对提出的算法和其他群智能算法进行仿真实验,测试结果表明提出的算法搜索效率和求解精度相较于对比算法得到提升,用Friedman统计分析验证了算法的优越性。将提出的算法用于求解机械工程减速器设计问题,与PSO-DE、WCA、APSO进行实验对比,验证该算法的有效性。     

FRPSO: Fletcher–Reeves based particle swarm optimization for multimodal function optimization

Particle swarm optimization (PSO) is a population-based optimization tool that is inspired by the collective intelligent behavior of birds seeking food. It can be easily implemented and applied to solve various function optimization problems. However, relatively few researchers have explored the potential of PSO for multimodal problems. Although PSO is a simple, easily implemented, and powerful technique, it has a tendency to get trapped in a local optimum. This premature convergence makes it difficult to find global optimum solutions for multimodal problems. A hybrid Fletcher–Reeves based PSO (FRPSO) method is proposed in this paper. It is based on the idea of increasing exploitation of the local optimum, while maintaining a good exploration capability for finding better solutions. In FRPSO, standard PSO is used to update the particle’s current position, which is then further refined by the Fletcher–Reeves conjugate gradient method. This enhances the performance of standard PSO. The results of experiments conducted on seventeen benchmark test functions demonstrate that the proposed method shows superior performance on a set of multimodal functions when compared with standard PSO, a genetic algorithm (GA) and fitness distance ratio PSO (FDRPSO).     

求解无约束优化问题的仿水循环算法

针对无约束优化问题,根据自然界水循环过程,提出一种仿水循环算法。其中包括汇流、分流、下渗、蒸发、降雨等粒子选优步骤,通过判断种群数量、粒子质量和位置,对种群和粒子进行相应调整,智能且动态地适应当前搜索的要求,同时采用新的相对重力粒子寻优机制,计算粒子相对重力的方向和大小,引导粒子持续向更优的位置移动。理论分析与仿真结果均表明,该算法能加快种群迭代速度,提高粒子搜索精度,防止粒子陷入局部最优。     

一种求解高维多模态复杂问题的差分文化算法

针对在求解高维多峰值复杂问题时种群容易陷入局部搜索、求解精度低的问题,提出了一种基于自适应差分进化算法和小生境高斯分布估计的文化算法。将差分进化算法用于种群空间的优化,利用动态小生境识别算法在种群空间中识别小生境群体。信度空间利用高斯分布估计算法在小生境内进行局部优化,并将小生境特征存入进化知识库,进化知识库进一步引导种群空间,有效地保证了种群的多样性,避免了局部的重复搜索。最后,通过仿真实验测试表明,算法具有收敛速度快、求解精度高、稳定性高和全局搜索能力强等优势。     

Improving the performance of differential evolution algorithm using Cauchy mutation

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real-valued, multimodal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence and/or slow convergence rate resulting in poor solution quality and/or larger number of function evaluation resulting in large CPU time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE) that enhances the convergence rate without compromising with the solution quality. The proposed MDE algorithm maintains a failure_counter (FC) to keep a tab on the performance of the algorithm by scanning or monitoring the individuals. Finally, the individuals that fail to show any improvement in the function value for a successive number of generations are subject to Cauchy mutation with the hope of pulling them out of a local attractor which may be the cause of their deteriorating performance. The performance of proposed MDE is investigated on a comprehensive set of 15 standard benchmark problems with varying degrees of complexities and 7 nontraditional problems suggested in the special session of CEC2008. Numerical results and statistical analysis show that the proposed modifications help in locating the global optimal solution in lesser numbers of function evaluation in comparison with basic DE and several other contemporary optimization algorithms.     

改进搜索策略的人工蜂群算法

针对人工蜂群(ABC)算法存在收敛速度慢、收敛精度低的问题,给出一种改进的人工蜂群算法用于数值函数优化问题。在ABC的邻域搜索公式中利用目标函数自适应调整步长,并根据迭代次数非线性减小侦查蜂的搜索范围。改进ABC算法提高了ABC算法的局部搜索能力,能够有效避免早熟收敛。基于6个标准测试函数的仿真实验表明,改进ABC算法的寻优能力有较大提高,对于多个高维多模态函数该算法可取得理论全局最优解。与对比算法相比,该算法具有更高的收敛精度,并且收敛速度更快。     

基于种群关系的多种群粒子群协同优化算法

传统粒子群优化算法容易陷入局部最优解,搜索效率不高,针对此问题,提出了一种基于种群关系和斥力因子的多种群粒子群优化算法SRB-PSO (Swarm-Relation-Based PSO).根据当前搜索结果定义种群之间统治、对等和被统治3种关系,通过引入斥力因子来保证种群间搜索的多样性,并通过统治和被统治关系提高算法的搜索效率,从而在改善算法的全局搜索性能的同时提高解的质量.将算法与其他几种主流粒子群优化改进算法在标准测试集上进行对比,实验结果证明了SRB-PSO算法能较好地保持粒子多样性,全局搜索能力强,在解决多峰函数时的性能优于其他几种主流粒子群优化改进算法.     

基于DE 和SA 的Memetic 高维全局优化算法

针对高维复杂多模态优化问题,传统的进化算法存在收敛速度慢,求解精度低等缺点,提出一种面向高维优化问题的Memetic全局优化算法。算法通过全局搜索和局部搜索结合的混合搜索策略,采用多模式并行差分进化算法进行全局搜索,基于高斯分布估计的模拟退火算法进行局部搜索。改进后的Memetic算法不仅继承了差分进化算法能发现全局最优解的优点,而且能大幅度提高搜索效率。最后,通过对4个高维多峰值Benchmark函数进行仿真实验,实验结果表明本文算法有效提高了算法的收敛速度和求解精度。     

基于反馈策略的引力搜索算法及其在支持向量机中应用

针对标准引力搜索算法(SGSA)在高维多峰函数寻优过程中容易出现早熟的问题,提出一种基于反馈策略的引力搜索算法(FGSA)。由于粒子在进化过程中群体多样性损失过快,采用粒子与最佳位置的距离和最邻近粒子的距离两个参数来均衡优化算法的勘探和开发能力,并将变异操作引入到FGSA中。通过对选取的四个基准函数测试,验证了FGSA和SGSA相比,在高维多峰函数寻优时,精确度和稳定性都有显著提高。同时,针对支持向量机(SVM)分类问题时,可有效地找出合适的特征子集及SVM参数,并取得较好的分类结果。     

Modified water cycle algorithm for optimal direction overcurrent relays coordination

The optimization model of Directional Over Current Relays (DOCRs) coordination is considered non-linear optimization problem with a large number of operating constraints. This paper proposes a modified version for Water Cycle Algorithm (WCA), referred to as MWCA to effectively solve the optimal coordination problem of DOCRs. The main goal is to minimize the summation of operating times of all relays when they act as primary protective devices. The operating time of a relay depends on time dial setting and pickup current setting or plug setting, which they are considered as decision variables. In the proposed technique, the search space has been reduced by increasing the C-value of traditional WCA, which effects on the balance between explorative and exploitative phases, gradually during the iterative process in order to find the global minimum. The performance of proposed algorithm is assessed using standard test systems; 8-bus, 9-bus, 15-bus, and 30-bus. The obtained results by the proposed algorithm are compared with those obtained by other well-known optimization techniques. In addition, the proposed algorithm has been validated using benchmark DIgSILENT PowerFactory. The results show the effectiveness and superiority of the proposed algorithm to solve DOCRs coordination problem, compared with traditional WCA and other optimization techniques.