Empirical analysis of five nature-inspired algorithms on real parameter optimization problems

In the past few years nature-inspired algorithms are seen as potential tools to solve computationally hard problems. Tremendous success of these algorithms in providing near optimal solutions has inspired the researchers to develop new algorithms. However, very limited efforts have been made to identify the best algorithms for diverse classes of problems. This work attempts to assess the efficacy of five contemporary nature-inspired algorithms i.e. bat algorithm (BA), artificial bee colony algorithm (ABC), cuckoo search algorithm (CS), firefly algorithm (FA) and flower pollination algorithm (FPA). The work evaluates the performance of these algorithms on CEC2014 30 benchmark functions which include unimodal, multimodal, hybrid and composite problems over 10, 30, 50 and 100 dimensions. Control parameters of all algorithms are self-adapted so as to obtain best results over benchmark functions. The algorithms have been evaluated along three perspectives (a) statistical significance using Wilcoxon rank sum test (b) computational time complexity (c) convergence rate of algorithms. Experimental results and analysis revealed that ABC algorithm perform best for majority of the problems on high dimension, while on small dimension, CS is the best choice. FPA attain the next best position follow by BA and FA for all kinds of functions. Self adaptation of above algorithms also revealed the best values of input parameters for various algorithms. This study may aid experts and scientists of computational intelligence to solve intricate optimization problems.     

混合花粉算法求解全局优化问题

元启发式算法可以用作寻找近似最优解的有效工具,因此,对元启发式算法进行改进,提高算法性能是有必要的。本文介绍花粉算法(Flower Pollination Algorithm, FPA)的增强变体,将花粉算法与极值优化算法(Extremal Optimization, EO)混合形成FPA-EO算法。FPA-EO算法综合利用了FPA的全局搜索能力和EO的局部搜索能力,并将其应用于11个基准测试函数来测试新算法。同时将该算法与其他4种著名优化算法（标准花粉算法(FPA)、蝙蝠算法(BAT)、萤火虫算法(FA)、模拟退火算法(SA)）进行比较。综合结果表明,本文算法能够找到比其他4种算法更精确的解。     

On the performances of the flower pollination algorithm – Qualitative and quantitative analyses

The flower pollination algorithm (FPA) is a recently proposed metaheuristic inspired by the natural phenomenon of flower pollination. Since its invention, this star-rising metaheuristic has gained a big interest in the community of metaheuristic optimisation. So, many works based on the FPA have already been proposed. However, these works have not given any deep analysis of the performances of the basic algorithm, neither of the variants already proposed. This makes it difficult to decide on the applicability of this new metaheuristic in real-world applications. This paper qualitatively and quantitatively analyses this metaheuristic. The qualitative analysis studies the basic variant of the FPA and some extensions of it. For quantitative analysis, the FPA is statistically examined through using it to solve the CEC 2013 benchmarks for real-parameter continuous optimisation, then by applying it on some of the CEC 2011 benchmarks for real-world optimisation problems. In addition, some extensions of the FPA, based on opposition-based learning and the modification of the movement equation in the global-pollination operator, are presented and also analysed in this paper. On the whole, the basic FPA has been found to offer less than average performances when compared to state-of-the-art algorithms, and the best of the proposed extensions has reached average results.     

A novel bat flower pollination algorithm for synthesis of linear antenna arrays

In this paper, a novel algorithm, namely bat flower pollination (BFP) is proposed for synthesis of unequally spaced linear antenna array (LAA). The new method is a combination of bat algorithm (BA) and flower pollination algorithm (FPA). In BFP, both BA and FPA interact with each other to escape from local minima. The results of BFP for solving a set of 13 benchmark functions demonstrate its superior performance as compared to variety of well-known algorithms available in the literature. The novel proposed method is also used for the synthesis of unequally spaced LAA for single and multi-objective design. Simulation results show that BFP is able to provide better synthesis results than wide range of popular techniques like genetic algorithm, differential evolution, cuckoo search, particle swarm optimization, back scattering algorithm and others.

     

Synthesis of linear antenna array using flower pollination algorithm

Linear antenna array (LAA) design is a classical electromagnetic problem. It has been extensively dealt by number of researchers in the past, and different optimization algorithms have been applied for the synthesis of LAA. This paper presents a relatively new optimization technique, namely flower pollination algorithm (FPA) for the design of LAA for reducing the maximum side lobe level (SLL) and null control. The desired antenna is achieved by controlling only amplitudes or positions of the array elements. FPA is a novel meta-heuristic optimization method based on the process of pollination of flowers. The effectiveness and capability of FPA have been proved by taking difficult instances of antenna array design with single and multiple objectives. It is found that FPA is able to provide SLL reduction and steering the nulls in the undesired interference directions. Numerical results of FPA are also compared with the available results in the literature of state-of-the-art algorithms like genetic algorithm, particle swarm optimization, cuckoo search, tabu search, biogeography based optimization (BBO) and others which also proves the better performance of the proposed method. Moreover, FPA is more consistent in giving optimum results as compared to BBO method reported recently in the literature.

     

基于单纯形法和自适应步长的花朵授粉算法

针对花朵授粉算法易陷入局部极值、后期收敛速度慢的不足,提出一种基于单纯形法和自适应步长的花朵授粉算法。该算法在基本花朵授粉算法的全局寻优部分采用自适应步长策略来更新个体位置,步长随迭代次数的增加而自适应地调整,避免局部极值;在局部寻优部分对进入下一次迭代的部分较差个体采用单纯形法的扩张、收缩/压缩操作,提高局部搜索能力,进而提高算法的寻优能力。通过八个CEC2005benchmark测试函数进行测试比较,结果表明,改进算法的寻优性能明显优于基本的花朵授粉算法,且其收敛速度、收敛精度、鲁棒性均较对比算法有较大提高。     

Social spiders optimization and flower pollination algorithm for multilevel image thresholding: A performance study

In this paper, we investigate the ability of two new nature-inspired metaheuristics namely the flower pollination (FP) and the social spiders optimization (SSO) algorithms to solve the image segmentation problem via multilevel thresholding. The FP algorithm is inspired from the biological process of flower pollination. It relies on two basic mechanisms to generate new solutions. The first one is the global pollination modeled in terms of a Levy distribution while the second one is the local pollination that is based on random selection of local solutions. For its part, the SSO algorithm mimics different natural cooperative behaviors of a spider colony. It considers male and female search agents subject to different evolutionary operators. In the two proposed algorithms, candidate solutions are firstly generated using the image histogram. Then, they are evolved according to the dynamics of their corresponding operators. During the optimization process, solutions are evaluated using the between-class variance or Kapur's method. The performance of each of the two proposed approaches has been assessed using a variety of benchmark images and compared against two other nature inspired algorithms from the literature namely PSO and BAT algorithms. Results have been analyzed both qualitatively and quantitatively based on the fitness values of obtained best solutions and two popular performance measures namely PSNR and SSIM indices as well. Experimental results have shown that both SSO and FP algorithms outperform PSO and BAT algorithms while exhibiting equal performance for small numbers of thresholds. For large numbers of thresholds, it was observed that the performance of FP algorithm decreases as it is often trapped in local minima. In contrary, the SSO algorithm provides a good balance between exploration and exploitation and has shown to be the most efficient and the most stable for all images even with the increase of the threshold number. These promising results suggest that the SSO algorithm can be effectively considered as an attractive alternative for the multilevel image thresholding problem.     

t-分布扰动策略和变异策略的花授粉算法

为了解决传统花授粉算法(FPA)收敛速度慢、易陷入局部最优、寻优精度低等缺陷,提出了一种t-分布扰动策略和变异策略的花授粉算法(t MFPA).首先利用混沌映射初始化花朵个体的位置,然后在全局授粉过程中,利用t-分布扰动的随机个体和莱维飞行共同实现个体位置更新,加快收敛速度的同时提高搜索空间的多样性;在局部授粉过程中,加入具有两个差分向量的变异策略和小概率策略,结合两种策略使算法能够跳出局部最优.实验结果表明,t MFPA相比于FPA和其他启发式智能算法具有更好的寻优精度和收敛速度,相对于其他改进算法具有更好的收敛性能.     

Hybridization of Chaos and Flower Pollination Algorithm over K-Means for data clustering

Classical clustering algorithms like K-means often converge to local optima and have slow convergence rates for larger datasets. To overcome such situations in clustering, swarm based algorithms have been proposed. Swarm based approaches attempt to achieve the optimal solution for such problems in reasonable time. Many swarm based algorithms such as Flower Pollination Algorithm (FPA), Cuckoo Search Algorithm (CSA), Black Hole Algorithm (BHA), Bat Algorithm (BA) Particle Swarm Optimization (PSO), Firefly Algorithm (FFA), Artificial Bee Colony (ABC) etc have been successfully applied to many non-linear optimization problems. In this paper, an algorithm is proposed which hybridizes Chaos Optimization and Flower Pollination over K-means to improve the efficiency of minimizing the cluster integrity. The proposed algorithm referred as Chaotic FPA (CFPA) is compared with FPA, CSA, BHA, BA, FFA, and PSO over K-Means for data clustering problem. Experiments are conducted on sixteen benchmark datasets. Algorithms are compared on four different performance parameters — cluster integrity, execution time, number of iterations to converge (NIC) and stability. Results obtained are analyzed statistically using Non-parametric Friedman test. If Friedman test rejects the Null hypothesis then pair wise comparison is done using Nemenyi test. Experimental Result demonstrates the following: (a) CFPA and BHA have better performance on the basis of cluster integrity as compared to other algorithms; (b) Prove the superiority of CFPA and CSA over others on the basis of execution time; (c) CFPA and FPA converges earlier than other algorithms to evaluate optimal cluster integrity; (d) CFPA and BHA produce more stable results than other algorithms.     

A Modified Flower Pollination Algorithm for Global Optimization

Expert and intelligent systems try to simulate intelligent human experts in solving complex real-world problems. The domain of problems varies from engineering and industry to medicine and education. In most situations, the system is required to take decisions based on multiple inputs, but the search space is usually very huge so that it will be very hard to use the traditional algorithms to take a decision; at this point, the metaheuristic algorithms can be used as an alternative tool to find near-optimal solutions. Thus, inventing new metaheuristic techniques and enhancing the current algorithms is necessary. In this paper, we introduced an enhanced variant of the Flower Pollination Algorithm (FPA). We hybridized the standard FPA with the Clonal Selection Algorithm (CSA) and tested the new algorithm by applying it to 23 optimization benchmark problems. The proposed algorithm is compared with five famous optimization algorithms, namely, Simulated Annealing, Genetic Algorithm, Flower Pollination Algorithm, Bat Algorithm, and Firefly Algorithm. The results show that the proposed algorithm is able to find more accurate solutions than the standard FPA and the other four techniques. The superiority of the proposed algorithm nominates it for being a part of intelligent and expert systems.     

Group Search Optimizer: An Optimization Algorithm Inspired by Animal Searching Behavior

Nature-inspired optimization algorithms, notably evolutionary algorithms (EAs), have been widely used to solve various scientific and engineering problems because of to their simplicity and flexibility. Here we report a novel optimization algorithm, group search optimizer (GSO), which is inspired by animal behavior, especially animal searching behavior. The framework is mainly based on the producer-scrounger model, which assumes that group members search either for ldquofindingrdquo (producer) or for ldquojoiningrdquo (scrounger) opportunities. Based on this framework, concepts from animal searching behavior, e.g., animal scanning mechanisms, are employed metaphorically to design optimum searching strategies for solving continuous optimization problems. When tested against benchmark functions, in low and high dimensions, the GSO algorithm has competitive performance to other EAs in terms of accuracy and convergence speed, especially on high-dimensional multimodal problems. The GSO algorithm is also applied to train artificial neural networks. The promising results on three real-world benchmark problems show the applicability of GSO for problem solving.     

LADPSO: using fuzzy logic to conduct PSO algorithm

Optimization plays a critical role in human modern life. Nowadays, optimization is used in many aspects of human modern life including engineering, medicine, agriculture and economy. Due to the growing number of optimization problems and their growing complexity, we need to improve and develop theoretical and practical optimization methods. Stochastic population based optimization algorithms like genetic algorithms and particle swarm optimization are good candidates for solving complex problems efficiently. Particle swarm optimization (PSO) is an optimization algorithm that has received much attention in recent years. PSO is a simple and computationally inexpensive algorithm inspired by the social behavior of bird flocks and fish schools. However, PSO suffers from premature convergence, especially in high dimensional multi-modal functions. In this paper, a new method for improving PSO has been introduced. The Proposed method which has been named Light Adaptive Particle Swarm Optimization is a novel method that uses a fuzzy control system to conduct the standard algorithm. The suggested method uses two adjunct operators along with the fuzzy system in order to improve the base algorithm on global optimization problems. Our approach is validated using a number of common complex uni-modal/multi-modal benchmark functions and results have been compared with the results of Standard PSO (SPSO2011) and some other methods. The simulation results demonstrate that results of the proposed approach is promising for improving the standard PSO algorithm on global optimization problems and also improving performance of the algorithm.     

新授粉方式的花授粉算法

为了解决因花授粉算法搜索方程存在的不足所导致的易早熟、后期收敛速度慢和寻优精度低的问题,提出了一种新授粉方式的花授粉算法（Flower Pollination Algorithm with New pollination Methods,NMFPA）。该算法把惯性权重和两组随机个体差异矢量融入到全局搜索,组成新的全局授粉,以保持种群的差异性,提高算法的全局探索能力;利用信息共享机制与两种新的变异策略构建新局部授粉策略,增强算法的局部开发能力;为了减少个体进化的盲目性,提高算法的收敛速度和精度,采用基于高斯变异的最优个体来引导其他种群个体的进化方向,并且引入非均匀变异机制增加种群的多样性,避免算法易陷入局部极值点,提升算法的全局优化性能。在22个测试函数上进行数值仿真实验,实验结果和统计分析验证了新算法较标准FPA算法,在收敛精度和速度上有明显提升,且能够较好地解决早熟问题。此外,与已有改进的FPA算法从多角度进行对比分析,实验结果表明改进算法是一种富有竞争力的新算法。同时,运用NMFPA算法求解置换流水车间调度问题,实验结果验证了新算法用于解决实际工程问题是可行的,且具有一定的优势。     

A particle swarm inspired cuckoo search algorithm for real parameter optimization

The cuckoo search algorithm (CS) is a simple and effective global optimization algorithm. It has been successfully applied to solve a wide range of real-world optimization problems. In this paper, inspired by the particle swarm optimization (PSO), the proposed algorithm uses the best individuals among the entire population to enhance the convergence rate of the standard cuckoo search algorithm. While the PSO directly uses the global best solution of the population to determine new positions for the particles at the each iteration, agents of the CS do not directly use this information but the global best solution in the CS is stored at the each iteration. The global best solutions are used to add into the Information flow between the nest helps increase global and local search abilities of the new approach. Therefore, in the first component, the neighborhood information is added into the new population to enhance the diversity of the algorithm. In the second component, two new search strategies are used to balance the exploitation and exploration of the algorithm through a random probability rule. In other aspect, our algorithm has a very simple structure and thus is easy to implement. To verify the performance of PSCS, 30 benchmark functions chosen from literature are employed. The results show that the proposed PSCS algorithm clearly outperforms the basic CS and PSO algorithm. Compared with some evolution algorithms (CLPSO, CMA-ES, GL-25, DE, OXDE, ABC, GOABC, FA, FPA, CoDE, BA, BSA, BDS and SDS) from literature, experimental results indicate that the proposed algorithm performs better than, or at least comparable to state-of-the-art approaches from literature when considering the quality of the solution obtained. In the last part, experiments have been conducted on two real-world optimization problems including the spread spectrum radar poly-phase code design problem and the chaotic system. Simulation results demonstrate that the proposed algorithm is very effective.     

Artificial algae algorithm (AAA) for nonlinear global optimization

In this study, a novel bio-inspired metaheuristic optimization algorithm called artificial algae algorithm (AAA) inspired by the living behaviors of microalgae, photosynthetic species, is introduced. The algorithm is based on evolutionary process, adaptation process and the movement of microalgae. The performance of the algorithm has been verified on various benchmark functions and a real-world design optimization problem. The CEC’05 function set was employed as benchmark functions and the test results were compared with the algorithms of Artificial Bee Colony (ABC), Bee Algorithm (BA), Differential Evolution (DE), Ant Colony Optimization for continuous domain (ACO_R) and Harmony Search (HS_POP). The pressure vessel design optimization problem, which is one of the widely used optimization problems, was used as a sample real-world design optimization problem to test the algorithm. In order to compare the results on the mentioned problem, the methods including ABC and Standard PSO (SPSO2011) were used. Mean, best, standard deviation values and convergence curves were employed for the analyses of performance. Furthermore, mean square error (MSE), root mean square error (RMSE) and mean absolute percentage error (MAPE), which are computed as a result of using the errors of algorithms on functions, were used for the general performance comparison. AAA produced successful and balanced results over different dimensions of the benchmark functions. It is a consistent algorithm having balanced search qualifications. Because of the contribution of adaptation and evolutionary process, semi-random selection employed while choosing the source of light in order to avoid local minima, and balancing of helical movement methods each other. Moreover, in tested real-world application AAA produced consistent results and it is a stable algorithm.     

The improvement of glowworm swarm optimization for continuous optimization problems

Glowworm swarm optimization (GSO) algorithm is the one of the newest nature inspired heuristics for optimization problems. In order to enhances accuracy and convergence rate of the GSO, two strategies about the movement phase of GSO are proposed. One is the greedy acceptance criteria for the glowworms update their position one-dimension by one-dimension. The other is the new movement formulas which are inspired by artificial bee colony algorithm (ABC) and particle swarm optimization (PSO). To compare and analyze the performance of our proposed improvement GSO, a number of experiments are carried out on a set of well-known benchmark global optimization problems. The effects of the parameters about the improvement algorithms are discussed by uniform design experiment. Numerical results reveal that the proposed algorithms can find better solutions when compared to classical GSO and other heuristic algorithms and are powerful search algorithms for various global optimization problems.     

A binary ABC algorithm based on advanced similarity scheme for feature selection

Feature selection is the basic pre-processing task of eliminating irrelevant or redundant features through investigating complicated interactions among features in a feature set. Due to its critical role in classification and computational time, it has attracted researchers’ attention for the last five decades. However, it still remains a challenge. This paper proposes a binary artificial bee colony (ABC) algorithm for the feature selection problems, which is developed by integrating evolutionary based similarity search mechanisms into an existing binary ABC variant. The performance analysis of the proposed algorithm is demonstrated by comparing it with some well-known variants of the particle swarm optimization (PSO) and ABC algorithms, including standard binary PSO, new velocity based binary PSO, quantum inspired binary PSO, discrete ABC, modification rate based ABC, angle modulated ABC, and genetic algorithms on 10 benchmark datasets. The results show that the proposed algorithm can obtain higher classification performance in both training and test sets, and can eliminate irrelevant and redundant features more effectively than the other approaches. Note that all the algorithms used in this paper except for standard binary PSO and GA are employed for the first time in feature selection.     

基于萤火虫算法的自适应花授粉优化算法

花授粉算法是一种新的启发式算法,由于存在易陷入局部最优且演化后期收敛速度慢等缺陷,导致算法的寻优能力受到限制。针对该算法存在的不足,在局部授粉过程中引入自适应的变异因子,并对花授粉算法中的转换概率进行自适应调整后,将其与萤火虫算法相结合,提出了一种基于萤火虫算法的改进花授粉算法;最后,通过经典的标准测试函数对新提出的算法与DE-FPA、PSO-FPA做比较实验。实验结果表明,改进后的算法比基本花授粉算法具有更高的收敛精度和稳定性。     

基于花授粉算法的PID参数优化

PID参数优化对PID控制性能起着决定性作用,针对PID参数寻优问题,提出运用一种花授粉算法（FPA）。该算法启发于自然界中花粉的传播授粉过程,以三个PID参数组成每个花粉单元的位置坐标,根据一定的全局授粉与局部授粉规则更新花粉单元的位置,使其向最优解迭代。仿真结果表明,与粒子群算法和人群搜索算法相比,花授粉算法优化参数使系统具备更短的响应时间、更高的系统控制精度以及更好的鲁棒性,为PID控制系统的参数整定提供了参考。     

Cells to Switches Assignment in Cellular Mobile Networks Using Metaheuristics

Cabling, handoff, and switching costs play pivotal roles in the design and development of cellular mobile networks. The assignment pattern consisting of which cell is to be connected to which switch can have a significant impact on the individual cost. In the presence of the limitation on the number of cells that can be assigned to a switch, the problem of the cell to switch assignment (CSA) becomes nondeterministic polynomial time hard to solve with all effective solutions being based on metaheuristic optimization algorithms (MOA) approach. This article applies three recently evolved MOA, namely, flower pollination algorithm (FPA), hunting search (HuS), and wolf search algorithm (WSA) for solving CSA problem. Comprehensive computational experiments conducted to collate the performance of the three algorithms indicate that FPA is superior to both HuS and WSA with respect to attaining the global best value and faster convergence with desired CSA.