Constrained differential evolution using generalized opposition-based learning

Differential evolution (DE) is a well-known optimization approach to deal with nonlinear and complex optimization problems. However, many real-world optimization problems are constrained problems that involve equality and inequality constraints. DE with constraint handling techniques, named constrained differential evolution (CDE), can be used to solve constrained optimization problems. In this paper, we propose a new CDE framework that uses generalized opposition-based learning (GOBL), named GOBL-CDE. In GOBL-CDE, firstly, the transformed population is generated using general opposition-based learning in the population initialization. Secondly, the transformed population and the initial population are merged and only half of the best individuals are selected to compose the new initial population to proceed mutation, crossover, and selection. Lastly, based on a jumping probability, the transformed population is calculated again after generating new populations, and the fittest individuals are selected to compose new population from the union of the current population and the transformed population. The GOBL-CDE framework can be applied to most CDE variants. As examples, in this study, the framework is applied to two popular representative CDE variants, i.e., rank-iMDDE and \(\varepsilon \)DEag. Experiment results on 24 benchmark functions from CEC’2006 and 18 benchmark functions from CEC’2010 show that the proposed framework is an effective approach to enhance the performance of CDE algorithms.     

Improving differential evolution with a new selection method of parents for mutation

In differential evolution (DE), the salient feature lies in its mutationmechanismthat distinguishes it from other evolutionary algorithms. Generally, for most of the DE algorithms, the parents for mutation are randomly chosen from the current population. Hence, all vectors of population have the equal chance to be selected as parents without selective pressure at all. In this way, the information of population cannot be fully exploited to guide the search. To alleviate this drawback and improve the performance of DE, we present a new selection method of parents that attempts to choose individuals for mutation by utilizing the population information effectively. The proposed method is referred as fitnessand- position based selection (FPS), which combines the fitness and position information of population simultaneously for selecting parents in mutation of DE. In order to evaluate the effectiveness of FPS, FPS is applied to the original DE algorithms, as well as several DE variants, for numerical optimization. Experimental results on a suite of benchmark functions indicate that FPS is able to enhance the performance of most DE algorithms studied. Compared with other selection methods, FPS is also shown to be more effective to utilize information of population for guiding the search of DE.     

Probabilistic properties of fitness-based quasi-reflection in evolutionary algorithms

Evolutionary algorithms (EAs) excel in optimizing systems with a large number of variables. Previous mathematical and empirical studies have shown that opposition-based algorithms can improve EA performance. We review existing opposition-based algorithms and introduce a new one. The proposed algorithm is named fitness-based quasi-reflection and employs the relative fitness of solution candidates to generate new individuals. We provide the probabilistic analysis to prove that among all the opposition-based methods that we investigate, fitness-based quasi-reflection has the highest probability of being closer to the solution of an optimization problem. We support our theoretical findings via Monte Carlo simulations and discuss the use of different reflection weights. We also demonstrate the benefits of fitness-based quasi-reflection on three state-of-the-art EAs that have competed at IEEE CEC competitions. The experimental results illustrate that fitness-based quasi-reflection enhances EA performance, particularly on problems with more challenging solution spaces. We found that competitive DE (CDE) which was ranked tenth in CEC 2013 competition benefited the most from opposition. CDE with fitness-based quasi-reflection improved on 21 out of the 28 problems in the CEC 2013 test suite and achieved 100% success rate on seven more problems than CDE.     

A novel adaptive cuckoo search algorithm for intrinsic discriminant analysis based face recognition

This paper presents a novel adaptive cuckoo search (ACS) algorithm for optimization. The step size is made adaptive from the knowledge of its fitness function value and its current position in the search space. The other important feature of the ACS algorithm is its speed, which is faster than the CS algorithm. Here, an attempt is made to make the cuckoo search (CS) algorithm parameter free, without a Levy step. The proposed algorithm is validated using twenty three standard benchmark test functions. The second part of the paper proposes an efficient face recognition algorithm using ACS, principal component analysis (PCA) and intrinsic discriminant analysis (IDA). The proposed algorithms are named as PCA + IDA and ACS–IDA. Interestingly, PCA + IDA offers us a perturbation free algorithm for dimension reduction while ACS + IDA is used to find the optimal feature vectors for classification of the face images based on the IDA. For the performance analysis, we use three standard face databases—YALE, ORL, and FERET. A comparison of the proposed method with the state-of-the-art methods reveals the effectiveness of our algorithm.     

基于新的适应度函数和多搜索策略的高维多目标进化算法

为提高高维多目标进化算法的性能,提出了一个基于新的适应度函数和多搜索策略的高维多目标进化算法。该算法提出了一个新的适应度函数来平衡多样性和收敛性,并且设计了一个多搜索策略来帮助交叉算子产生优秀的后代进而提高收敛性。该适应度函数首先从当前种群和新产生的后代中挑出收敛性较好的个体,然后计算这些个体的稀疏程度;该多搜索策略选择稀疏且收敛的解来执行全局和局部搜索。数值实验测试了CEC2018高维多目标竞赛的15个测试问题,每个测试问题的目标个数分别为5、10、15。实验结果表明,该算法能找到一组比四种代表性算法（如NSGAIII、MOEA/DD、KnEA、RVEA）具有更好的多样性和收敛性的解集。     

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using interval analysis combined with particle swarm optimization. A set inverter via interval analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a space cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified particle swarm optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100 000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.     

Intrinsic evolvable hardware platform for digital circuit design and repair using genetic algorithms

A hardware/software platform for intrinsic evolvable hardware is designed and evaluated for digital circuit design and repair on Xilinx Field Programmable Gate Arrays (FPGAs). Dynamic bitstream compilation for mutation and crossover operators is achieved by directly manipulating the bitstream using a layered framework. Experimental results on a case study have shown that benchmark circuit evolution from an unseeded initial population, as well as a complete recovery of a stuck-at fault is achievable using this platform. An average of 0.47 μs is required to perform the genetic mutation, 4.2 μs to perform the single point conventional crossover, 3.1 μs to perform Partial Match Crossover (PMX) as well as Order Crossover (OX), 2.8 μs to perform Cycle Crossover (CX), and 1.1 ms for one input pattern intrinsic evaluation. These represent a performance advantage of three orders of magnitude over the JBITS software framework and more than seven orders of magnitude over the Xilinx design tool driven flow for realizing intrinsic genetic operators on Xilinx Virtex Family devices.     

保存基因的2-Opt一般反向差分演化算法

为了进一步提高差分演化算法的性能,提出一种采用保存基因的2-Opt一般反向差分演化算法,并把它应用于函数优化问题中.新算法具有以下特征:(1)采用保存被选择个体基因的方式组成参加演化的新个体.保存基因的方法可以很好的保持种群多样性;(2)采用一般反向学习(GOBL)机制进行初始化,提高了初始化效率;(3)采用2-Opt算法加速差分演化算法的收敛速度,提高搜索效率.通过测试函数的实验,并与其他差分演化算法进行比较.实验结果证实了新算法的高效性,通用性和稳健性.     

Multiple Elite Individual Guided Piecewise Search-Based Differential Evolution

The differential evolution (DE) algorithm relies mainly on mutation strategy and control parameters’ selection. To take full advantage of top elite individuals in terms of fitness and success rates, a new mutation operator is proposed. The control parameters such as scale factor and crossover rate are tuned based on their success rates recorded over past evolutionary stages. The proposed DE variant, MIDE, performs the evolution in a piecewise manner, i.e., after every predefined evolutionary stages, MIDE adjusts its settings to enrich its diversity skills. The performance of the MIDE is validated on two different sets of benchmarks: CEC 2014 and CEC 2017 (special sessions & competitions on real-parameter single objective optimization) using different performance measures. In the end, MIDE is also applied to solve constrained engineering problems. The efficiency and effectiveness of the MIDE are further confirmed by a set of experiments.      

Optimization of constraint engineering problems using robust universal learning chimp optimization

Due to the challenging constraint search space of real-world engineering problems, a variation of the Chimp Optimization Algorithm (ChOA) called the Universal Learning Chimp Optimization Algorithm (ULChOA) is proposed in this paper, in which a unique learning method is applied to all previous best knowledge obtained by chimps (candid solutions) to update prey’s positions (best solution). This technique preserves the chimp’s variety, discouraging early convergence in multimodal optimization problems. Furthermore, ULChOA introduces a unique constraint management approach for dealing with the constraints in real-world constrained optimization issues. A total of fifteen commonly recognized multimodal functions, twelve real-world constrained optimization challenges, and ten IEEE CEC06-2019 suit tests are utilized to assess the ULChOA's performance. The results suggest that the ULChOA surpasses sixteen out of eighteen algorithms by an average Friedman rank of better than 78 percent for all 25 numerical functions and 12 engineering problems while outperforming jDE100 and DISHchain1e + 12 by 21% and 39%, respectively. According to Bonferroni-Dunn and Holm's tests, ULChOA is statistically superior to benchmark algorithms regarding test functions and engineering challenges. We believe that the ULChOA proposed here may be utilized to solve challenges requiring multimodal search spaces. Furthermore, ULChOA is more widely applicable to engineering applications than competitor benchmark algorithms.     

正交约束差分演化算法研究

提出一种适合求解约束问题的基于正交实验设计的差分演化算法。引入一种基于正交设计的杂交算子,并结合约束统计优生法产生最好子个体,采用决策变量分块策略,以减少正交实验次数,加快算法收敛速度。给出一种简单的多样性规则,以处理约束条件。提出基于非凸理论的多父体混合自适应杂交变异算子,以增强算法的非凸搜索能力和自适应能力。通过对13个标准测试函数进行实验,结果表明,该算法在解的精度、稳定性和收敛性上表现出较好的性能。     

基于种群多样性的可变种群缩减差分进化算法

为了更有效地避免早熟收敛,提高算法的全局搜索能力,提出了基于种群多样性的可变种群缩减差分进化算法(Dapr-DE)。首先,Dapr-DE使用群体多样性指标控制种群规模缩减;然后,使用聚类将种群分为不同类簇,在类簇中根据适应度值删除个体,既维持了种群的多样性,又减少了由于 存在过多相似个体而导致的局部收敛。最后在CEC14测试集的30个函数优化问题上进行了实验比较,验证了所提算法的有效性。     

Differential evolution in constrained numerical optimization: An empirical study

Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches.     

A novel hybrid multi-objective immune algorithm with adaptive differential evolution

In this paper, we propose a novel hybrid multi-objective immune algorithm with adaptive differential evolution, named ADE-MOIA, in which the introduction of differential evolution (DE) into multi-objective immune algorithm (MOIA) combines their respective advantages and thus enhances the robustness to solve various kinds of MOPs. In ADE-MOIA, in order to effectively cooperate DE with MOIA, we present a novel adaptive DE operator, which includes a suitable parent selection strategy and a novel adaptive parameter control approach. When performing DE operation, two parents are respectively picked from the current evolved and dominated population in order to provide a correct evolutionary direction. Moreover, based on the evolutionary progress and the success rate of offspring, the crossover rate and scaling factor in DE operator are adaptively varied for each individual. The proposed adaptive DE operator is able to improve both of the convergence speed and population diversity, which are validated by the experimental studies. When comparing ADE-MOIA with several nature-inspired heuristic algorithms, such as NSGA-II, SPEA2, AbYSS, MOEA/D-DE, MIMO and D²MOPSO, simulations show that ADE-MOIA performs better on most of 21 well-known benchmark problems.     

聚类佳点集交叉的约束优化混合进化算法

提出一种基于聚类佳点集多父代交叉和自适应约束处理技术的混合进化算法用于求解约束优化问题.新算法的主要特点是:在搜索机制方面,利用佳点集方法构造初始化种群,使个体能够均匀地分布在整个搜索空间.然后根据父代个体的相似度将种群个体进行聚类分析,从聚类中随机选择个体进行佳点集多父代交叉操作,利用多个父代个体所携带的信息产生新的具有代表性的子代个体,能够维持和增加种群的多样性.另外,引入局部搜索策略以提高算法局部搜索能力和收敛速度.在约束处理技术上,新算法引入了一个自适应约束处理技术,即根据当前种群中可行解的比例自适应选择不同的个体比较准则.通过15个标准测试函数验证了新算法的有效性.     

A hybrid memory-based dragonfly algorithm with differential evolution for engineering application

The dragonfly algorithm (DA) is a swarm-based stochastic algorithm which possesses static and dynamic behavior of swarm and is gaining meaningful popularity due to its low computational cost and fast convergence in solving complex optimization problems. However, it lacks internal memory and is thereby not able to keep track of its best solutions in previous generations. Furthermore, the solution also lacks in diversity and thereby has a propensity of getting trapped in the local optimal solution. In this paper, an iterative-level hybridization of dragonfly algorithm (DA) with differential evolution (DE) is proposed and named as hybrid memory-based dragonfly algorithm with differential evolution (DADE). The reason behind selecting DE is for its computational ability, fast convergence and capability in exploring the solution space through the use of crossover and mutation techniques. Unlike DA, in DADE the best solution in a particular iteration is stored in memory and proceeded with DE which enhances population diversity with improved mutation and accordingly increases the probability of reaching global optima efficiently. The efficiency of the proposed algorithm is measured based on its response to standard set of 74 benchmark functions including 23 standard mathematical benchmark functions, 6 composite benchmark function of CEC2005, 15 benchmark functions of CEC2015 and 30 benchmark function of CEC2017. The DADE algorithm is applied to engineering design problems such as welded beam deign, pressure vessel design, and tension/compression spring design. The algorithm is also applied to the emerging problem of secondary user throughput maximization in an energy-harvesting cognitive radio network. A comparative performance analysis between DADE and other most popular state-of-the-art optimization algorithms is carried out and significance of the results is deliberated. The result demonstrates significant improvement and prominent advantages of DADE compared to conventional DE, PSO and DA in terms of various performance measuring parameters. The results of the DADE algorithm applied on some important engineering design problems are encouraging and validate its appropriateness in the context of solving interesting practical engineering challenges. Lastly, the statistical analysis of the algorithm is also performed and is compared with other powerful optimization algorithms to establish its superiority.

     

Free Pattern Search for global optimization

An efficient algorithm named Pattern search (PS) has been used widely in various scientific and engineering fields. However, even though the global convergence of PS has been proved, it does not perform well on more complex and higher dimension problems nowadays. In order to improve the efficiency of PS and obtain a more powerful algorithm for global optimization, a new algorithm named Free Pattern Search (FPS) based on PS and Free Search (FS) is proposed in this paper. FPS inherits the global search from FS and the local search from PS. Two operators have been designed for accelerating the convergence speed and keeping the diversity of population. The acceleration operator inspired by FS uses a self-regular management to classify the population into two groups and accelerates all individuals in the first group, while the throw operator is designed to avoid the reduplicative search of population and keep the diversity. In order to verify the performance of FPS, two famous benchmark instances are conducted for the comparisons between FPS with Particle Swarm Optimization (PSO) variants and Differential Evolution (DE) variants. The results show that FPS obtains better solutions and achieves the higher convergence speed than other algorithms.     

An efficient hybrid technique for numerical optimization and applications

Real World Optimization Problems is one of the major concerns to show the potential and effectiveness of an optimization algorithm. In this context, a hybrid algorithm of two popular heuristics namely Differential Evolution (DE) and Particle Swarm Optimization (PSO) engaged on a ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups – Inferior Group, Mid Group and Superior Group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method is abbreviated as DPD as it uses DE–PSO–DE on a population. Two strategies namely Elitism (to retain the best obtained values so far) and Non-redundant search (to improve the solution quality) have been additionally employed in DPD cycle. Moreover, the robustness of the mutation strategies of DE have been well studied and suitable mutation strategies for both DEs (for DPD) are investigated over a set of existing 8 popular mutation strategies which results 64 variants of DPD. The top DPD is further tested through the test functions of CEC2006, CEC2010 and 5 Engineering Design Problems. Also it is used to solve CEC2011 Real World Optimization problems. An excellent efficiency of the recommended DPD is confirmed over the state-of-the-art algorithms.     

求解约束优化问题的一种新算法

提出了一种求解约束优化问题的微分进化算法。该算法使得种群在演化过程中能保持较好的多样性,且参数设置简单,不容易陷入局部最优,并能在较短时间内找到问题的最优解。在对多个测试函数的数值模拟中都得到了较好的结果,体现了该算法的有效性、通用性和稳健性。