A Differential Covariance Matrix Adaptation Evolutionary Algorithm for real parameter optimization

Hybridization in context to Evolutionary Computation (EC) aims at combining the operators and methodologies from different EC paradigms to form a single algorithm that may enjoy a statistically superior performance on a wide variety of optimization problems. In this article we propose an efficient hybrid evolutionary algorithm that embeds the difference vector-based mutation scheme, the crossover and the selection strategy of Differential Evolution (DE) into another recently developed global optimization algorithm known as Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES). CMA-ES is a stochastic method for real parameter (continuous domain) optimization of non-linear, non-convex functions. The algorithm includes adaptation of covariance matrix which is basically an alternative method of traditional Quasi-Newton method for optimization based on gradient method. The hybrid algorithm, referred by us as Differential Covariance Matrix Adaptation Evolutionary Algorithm (DCMA-EA), turns out to possess a better blending of the explorative and exploitative behaviors as compared to the original DE and original CMA-ES, through empirical simulations. Though CMA-ES has emerged itself as a very efficient global optimizer, its performance deteriorates when it comes to dealing with complicated fitness landscapes, especially landscapes associated with noisy, hybrid composition functions and many real world optimization problems. In order to improve the overall performance of CMA-ES, the mutation, crossover and selection operators of DE have been incorporated into CMA-ES to synthesize the hybrid algorithm DCMA-EA. We compare DCMA-EA with original DE and CMA-EA, two best known DE-variants: SaDE and JADE, and two state-of-the-art real optimizers: IPOP-CMA-ES (Restart Covariance Matrix Adaptation Evolution Strategy with increasing population size) and DMS-PSO (Dynamic Multi Swarm Particle Swarm Optimization) over a test-suite of 20 shifted, rotated, and compositional benchmark functions and also two engineering optimization problems. Our comparative study indicates that although the hybridization scheme does not impose any serious burden on DCMA-EA in terms of number of Function Evaluations (FEs), DCMA-EA still enjoys a statistically superior performance over most of the tested benchmarks and especially over the multi-modal, rotated, and compositional ones in comparison to the other algorithms considered here.     

一种改进的基于差分进化的多目标进化算法

近年来运用进化算法（EAs）解决多目标优化问题（Multi-objective Optimization Problems MOPs）引起了各国学者们的关注。作为一种基于种群的优化方法,EAs提供了一种在一次运行后得到一组优化的解的方法。差分进化（DE）算法是EA的一个分支,最开始是用来解决连续函数空间的问题。提出了一种改进的基于差分进化的多目标进化算法（CDE）,并且将它与另外两个经典的多目标进化算法（MOEAs）NSGA-II和SPEA2进行了对比实验。     

基于量子行为粒子群优化方法的随机规划算法

在不断变化的金融市场中,多阶段投资组合优化通过周期性地重组投资对象来追求回报最大,风险最小。提出了使用基于量子化行为的粒子群优化算法（Quantum-behaved Particle Swarm Optimization,QPSO）解决多阶段投资优化问题,并使用经典的利润风险函数作为目标函数,通过算法对标准普尔指数100的不同股票和现金进行投资组合的优化研究。根据实验得出的期望收益率与方差表明,QPSO算法在寻找全局最优解方面要优于粒子群算法（Particle Swarm Optimization,PSO）和遗传算法（Genetic Algorithm,GA）。     

Constrained self-adaptive differential evolution based design of robust optimal fixed structure controller

This paper presents a constrained Self-adaptive Differential Evolution (SaDE) algorithm for the design of robust optimal fixed structure controllers with uncertainties and disturbance. Almost all real world optimization problems have constraints which should be satisfied along with the best optimal solution for the problem. In evolutionary algorithms (EAs) the presence of constraints reduces the feasible region and complicates the search process. Therefore, a suitable method to handle the constraints must also be executed. In the SaDE algorithm, four mutation strategies and the control parameter CR are self-adapted. Self-adaptive Penalty (SP) method is introduced into the SaDE algorithm for constraint handling. The performance of SaDE algorithm is demonstrated on the design of robust optimal fixed structure controller of three systems, namely the linearized magnetic levitation system, F-8 aircraft linearized model and a SISO plant. For the comparison purpose, reported results of constrained PSO algorithm and five DE algorithms with different strategies and parameter values are taken into account. Statistical performance in 20 independent runs is considered to compare the performance of algorithms. From the obtained results, it is observed that SaDE algorithm is able to self-adapt the mutation strategy and the crossover rate and hence performs better than the other variants of DE and the constrained PSO algorithm. Better performance of SaDE is achieved by sustained maintenance of diversity throughout the evolutionary process thus producing better individuals consistently. This also aids the algorithm to escape from local optima thereby avoiding premature convergence.     

The spherical search algorithm for bound-constrained global optimization problems

In this paper, a new optimization algorithm called Spherical Search (SS) is proposed to solve the bound-constrained non-linear global optimization problems. The main operations of SS are the calculation of spherical boundary and generation of new trial solution on the surface of the spherical boundary. These operations are mathematically modeled with some more basic level operators: Initialization of solution, greedy selection and parameter adaptation, and are employed on the 30 black-box bound constrained global optimization problems. This study also analyzes the applicability of the proposed algorithm on a set of real-life optimization problems. Meanwhile, to show the robustness and proficiency of SS, the obtained results of the proposed algorithm are compared with the results of other well-known optimization algorithms and their advanced variants: Particle Swarm Optimization (PSO), Differential Evolution (DE), and Covariance Matrix Adapted Evolution Strategy (CMA-ES). The comparative analysis reveals that the performance of SS is quite competitive with respect to the other peer algorithms.     

演化信息协助的动态协同随机漂移粒子群优化算法

为了改善随机漂移粒子群算法的群体多样性,通过演化信息的协助,提出动态协同随机漂移粒子群优化（CRDPSO）算法。利用上下文粒子的向量信息,粒子之间的动态协作增加了种群多样性,这有助于提高群体的搜索能力,并使整个群体协同搜索全局最优值。同时在演化过程中的每次迭代,利用二维空间分割树结构来存储算法中的估计解的位置和适应度值,从而实现快速适应度函数逼近。由于适应度函数逼近增强了变异策略,因此变异是自适应且无参数的。通过典型测试函数将CRDPSO算法和差分进化算法（DE）、协方差矩阵适应进化策略算法（CMA-ES）、非重复访问遗传算法（cNrGA）以及三种改进的量子行为粒子群算法（QPSO）进行比较。实验结果表明,不管是对于单峰还是多峰测试函数,CRDPSO的性能均是最优的,证明了该算法的有效性。     

演化信息协助的动态协同随机漂移粒子群优化算法

为了改善随机漂移粒子群算法的群体多样性，通过演化信息的协助，提出动态协同随机漂移粒子群优化（CRDPSO）算法。利用上下文粒子的向量信息，粒子之间的动态协作增加了种群多样性，这有助于提高群体的搜索能力，并使整个群体协同搜索全局最优值。同时在演化过程中的每次迭代，利用二维空间分割树结构来存储算法中的估计解的位置和适应度值，从而实现快速适应度函数逼近。由于适应度函数逼近增强了变异策略，因此变异是自适应且无参数的。通过典型测试函数将CRDPSO算法和差分进化算法（DE）、协方差矩阵适应进化策略算法（CMA-ES）、非重复访问遗传算法（cNrGA）以及三种改进的量子行为粒子群算法（QPSO）进行比较。实验结果表明，不管是对于单峰还是多峰测试函数，CRDPSO的性能均是最优的，证明了该算法的有效性。     

A comparison between optimization algorithms applied to synchronization of bilateral teleoperation systems against time delay and modeling uncertainties

The goal of this paper is to achieve optimal performance for synchronization of bilateral teleoperation systems against time delay and modeling uncertainties, in both free and contact motions. Time delay in bilateral teleoperation systems imposes a delicate tradeoff between the conflicting requirements of stability and transparency. To this reason, in this paper, population-based optimization algorithms are employed to tuning the proposed controller parameters. The performance of tuned controllers is compared with the gains obtained by Cuckoo Optimization Algorithm (COA), Biogeography-Based Optimization (BBO), Imperialist Competitive Algorithm (ICA), Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Ant Colony Optimization with continuous domain (ACOR), Self-adaptive Differential Evolution with Neighborhood Search (SaNSDE), Adaptive Differential Evolution with Optional External Archive (JADE), Differential Evolution with Ensemble of Parameters and mutation strategies (EPSDE) and Cuckoo Search (CS). Through numerical simulations, the validity of the proposed method is illustrated. It is also shown that the COA algorithm is able to solve synchronization problem with high performance in stable transparent bilateral teleoperation systems.     

Adaptive simulation budget allocation in Simulation assisted Differential Evolution algorithm

Recently, the literature on simulation assisted optimization for solving stochastic optimization problems has been considerably growing. In the optimization context, the population based meta-heuristics algorithms, such as, Differential Evolutionary (DE), has shown tremendous success in solving continuous optimization problems. While in the simulation context, Monte-Carlo Simulation for sample average approximation is one of the successful approaches in handling the stochastic parameters of such problems. However, the intertwined computational burden, when combining these two approaches is amplified, and that encourages new research in this topic. In this problem, the challenge is to maintain high quality stochastic solutions by minimizing the computational cost to a reasonable level. To deal with this challenge, we propose a novel Adaptive Segment Based Scheme (ASBS) algorithm, for allocating the MCS budget in a Simulation assisted Differential Evolution (Sim-DE) Algorithm. This allows the algorithm to adaptively control the simulation budget based on a performance measure. The performance of the proposed ASBS algorithm is compared with other simulation budget allocation techniques while using the same base algorithm. The experimental study has been conducted by solving a modified set of IEEE-CEC’2006 test problems and a wind-thermal power systems application. The experimental results reveal that the ASBS algorithm is able to substantially reduce the simulation budget, with an insignificant effect in solution quality.     

Improving the multi-objective evolutionary optimization algorithm for hydropower reservoir operations in the California Oroville–Thermalito complex

This study demonstrates the application of an improved Evolutionary optimization Algorithm (EA), titled Multi-Objective Complex Evolution Global Optimization Method with Principal Component Analysis and Crowding Distance Operator (MOSPD), for the hydropower reservoir operation of the Oroville–Thermalito Complex (OTC) – a crucial head-water resource for the California State Water Project (SWP). In the OTC's water-hydropower joint management study, the nonlinearity of hydropower generation and the reservoir's water elevation–storage relationship are explicitly formulated by polynomial function in order to closely match realistic situations and reduce linearization approximation errors. Comparison among different curve-fitting methods is conducted to understand the impact of the simplification of reservoir topography. In the optimization algorithm development, techniques of crowding distance and principal component analysis are implemented to improve the diversity and convergence of the optimal solutions towards and along the Pareto optimal set in the objective space. A comparative evaluation among the new algorithm MOSPD, the original Multi-Objective Complex Evolution Global Optimization Method (MOCOM), the Multi-Objective Differential Evolution method (MODE), the Multi-Objective Genetic Algorithm (MOGA), the Multi-Objective Simulated Annealing approach (MOSA), and the Multi-Objective Particle Swarm Optimization scheme (MOPSO) is conducted using the benchmark functions. The results show that best the MOSPD algorithm demonstrated the best and most consistent performance when compared with other algorithms on the test problems. The newly developed algorithm (MOSPD) is further applied to the OTC reservoir releasing problem during the snow melting season in 1998 (wet year), 2000 (normal year) and 2001 (dry year), in which the more spreading and converged non-dominated solutions of MOSPD provide decision makers with better operational alternatives for effectively and efficiently managing the OTC reservoirs in response to the different climates, especially drought, which has become more and more severe and frequent in California.     

基于量子粒子群算法的多方法协作优化方法

介绍粒子群算法和具有量子行为的粒子群优化算法QPSO(Quantum-behaved Particle Swarm Optimization).针对QPSO在处理高维复杂函数时存在的收敛速度慢、易陷入局部极小等问题,提出了基于QPSO算法的多方法协作优化算法,将QPSO算法与进化规划EP(Evolutionary Programming)算法协作.实验结果表明,改进算法在收敛性和取得最优值方面优于PSO算法和QPSO算法.     

A novel hybrid approach for feature selection in software product lines

Software Product Line (SPL) customizes software by combining various existing features of the software with multiple variants. The main challenge is selecting valid features considering the constraints of the feature model. To solve this challenge, a hybrid approach is proposed to optimize the feature selection problem in software product lines. The Hybrid approach ‘Hyper-PSOBBO’ is a combination of Particle Swarm Optimization (PSO), Biogeography-Based Optimization (BBO) and hyper-heuristic algorithms. The proposed algorithm has been compared with Bird Swarm Algorithm (BSA), PSO, BBO, Firefly, Genetic Algorithm (GA) and Hyper-heuristic. All these algorithms are performed in a set of 10 feature models that vary from a small set of 100 to a high-quality data set of 5000. The detailed empirical analysis in terms of performance has been carried out on these feature models. The results of the study indicate that the performance of the proposed method is higher to other state-of-the-art algorithms.

     

An Integrated Optimization Enabled Sensor Deployment Model in Wireless Sensor Network

ABSTRACT

Target coverage (TCOV) and network connectivity (NCON) are the most basic problems affecting robust data communication and environmental sensing in a wireless sensor network (WSN) application. This article proposes an intelligent Context Aware Sensor Network (CASN) for the process of sensor deployment in WSNs. Accordingly, the process is sub-divided into two phases. In the initial phase, optimal TCOV is performed; whereas, in the second phase, the proposed algorithm establishes NCON among the sensors. The objective model that meets both TCOV and NCON is evaluated as the minimization problem. This problem is solved by a new method that hybridizes the Artificial Bee Colony (ABC) algorithm and the Whale Optimization Algorithm (WOA) together, which is known as the Onlooker Probability-based WOA (OP-WOA) for the determination of optimal sensor locations. In addition, the adopted OP-WOA model is compared with the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), the ABC algorithm, Differential Evolution (DE), FireFly (FF), the WOA, and the Evolutionary Algorithm (EA)-based TCOV and NCON models. Finally, the results attained from the execution demonstrate the enhanced performance of the implemented OP-WOA technique.     

An artificial bee colony algorithm for learning Bayesian networks

One basic approach to learn Bayesian networks (BNs) from data is to apply a search procedure to explore the set of candidate networks for the database in light of a scoring metric, where the most popular stochastic methods are based on some meta-heuristic mechanisms, such as Genetic Algorithm, Evolutionary Programming and Ant Colony Optimization. In this paper, we have developed a new algorithm for learning BNs which employs a recently introduced meta-heuristic: artificial bee colony (ABC). All the phases necessary to tackle our learning problem using this meta-heuristic are described, and some experimental results to compare the performance of our ABC-based algorithm with other algorithms are given in the paper.     

Chaotic antlion algorithm for parameter optimization of support vector machine

Support Vector Machine (SVM) is one of the well-known classifiers. SVM parameters such as kernel parameters and penalty parameter (C) significantly influence the classification accuracy. In this paper, a novel Chaotic Antlion Optimization (CALO) algorithm has been proposed to optimize the parameters of SVM classifier, so that the classification error can be reduced. To evaluate the proposed algorithm (CALO-SVM), the experiment adopted six standard datasets which are obtained from UCI machine learning data repository. For verification, the results of the CALO-SVM algorithm are compared with grid search, which is a conventional method of searching parameter values, standard Ant Lion Optimization (ALO) SVM, and three well-known optimization algorithms: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Social Emotional Optimization Algorithm (SEOA). The experimental results proved that the proposed algorithm is capable of finding the optimal values of the SVM parameters and avoids the local optima problem. The results also demonstrated lower classification error rates compared with GA, PSO, and SEOA algorithms.     

应用改进PSO算法求解待约束优化问题

为解决高维复杂CO问题,可将进化算法中保持物种多样性的思想引入基本PSO算法的方法。针对基本PSO算法在迭代后期粒子活性减弱的问题,引入‘吸引’和‘扩散’两个算子,对基本PSO算法的速度更新公式进行改进和考虑固定惩罚函数无法有效引导粒子向可行解方向搜索的缺点,提出LPFM方法替代固定惩罚函数法,以有效引导粒子进入可行解域,并在迭代后期加强对粒子的约束,使其不至因违背约束所获的收益大于所受的惩罚而收敛到不可行解域。最后对改进的PSO算法进行了试验,试验结果表明改进PSO算法对解决高维复杂CO问题是有效的。     

Optimal foraging algorithm for global optimization

An optimization algorithm, inspired by the animal Behavioral Ecology Theory—Optimal Foraging Theory, named the Optimal Foraging Algorithm (OFA) has been developed. As a new stochastic search algorithm, OFA is used to solve the global optimization problems following the animal foraging behavior. During foraging, animals know how to find the best pitch with abundant prey; in establishing OFA, the basic operator of OFA was constructed following this foraging strategy. During foraging, an individual of the foraging swarms obtained more opportunities to capture prey through recruitment; in OFA the recruitment was adopted to ensure the algorithm has a higher chance to receive the optimal solution. Meanwhile, the precise model of prey choices proposed by Krebs et al. was modified and adopted to establish the optimal solution choosing strategy of OFA. The OFA was tested on the benchmark functions that present difficulties common to many global optimization problems. The performance comparisons among the OFA, real coded genetic algorithms (RCGAs), Differential Evolution (DE), Particle Swarm Optimization (PSO) algorithm, Bees Algorithm (BA), Bacteria Foraging Optimization Algorithm (BFOA) and Shuffled Frog-leaping Algorithm (SFLA) are carried out through experiments. The parameter of OFA and the dimensions of the multi-functions are researched. The results obtained by experiments and Kruskal-Wallis test indicate that the performance of OFA is better than the other six algorithms in terms of the ability to converge to the optimal or the near-optimal solutions, and the performance of OFA is the second-best one from the view of the statistical analysis.     

多核环境下并行粒子群算法

针对串行粒子群算法在解决大任务耗时过长的问题,提出一种共享并行粒子群(Shared-PSO)算法。充分利用多核处理能力缩短问题处理运行时间,设置共享区和采取粒子随机替换策略有效促进粒子信息的交流,其算法流程具有较好的通用性,允许利用多种串行粒子群算法完成粒子信息更新工作。在标准优化测试集CEC 2014上的实验结果显示新算法的执行时间是串行算法的1/4。新算法能够有效地改善串行粒子群的执行效率,扩展粒子群算法的应用范围。     

An algorithm comparison for dynamic optimization problems

This work presents a study on the performance of several algorithms on different continuous dynamic optimization problems. Eight algorithms have been used: SORIGA (an Evolutionary Algorithm), an agents-based algorithm, the mQSO (a widely used multi-population PSO) as well as three heuristic-rule-based variations of it, and two trajectory-based cooperative strategies. The algorithms have been tested on the Moving Peaks Benchmark and the dynamic version of the Ackley, Griewank and Rastrigin functions. For each problem, a wide variety of configuration variations have been used, emphasizing the influence of dynamism, and using a full-factorial experimental design. The results give an interesting overview of the properties of the algorithms and their applicability, and provide useful hints to face new problems of this type with the best algorithmic approach. Additionally, a recently introduced methodology for comparing a high number of experimental results in a graphical way is used.     

混合量子算法及其在flow shop问题中的应用

量子进化算法（QEA）是目前较为独特的优化算法,它的理论基础是量子计算。算法充分借鉴了量子比特的干涉性、并行性,使得QEA求解组合优化问题具备了可行性。由于在求解排序问题中,算法本身存在收敛慢,没有利用其它未成熟个体等缺陷,将微粒群算法（PSO）及进化计算思想融入QEA中,构成了混合量子算法（HQA）。采用flow shop经典问题对算法进行了测试,结果证明混合算法克服了QEA的缺陷,对于求解排序问题具有一定的普适性。