基于改进混沌优化的多目标遗传算法

针对多目标遗传算法存在的缺陷,提出了基于改进混沌优化的多目标遗传算法．引入基于改Tent映射的自适应变尺度混沌优化方法细化搜索空间和高效寻优,结合非支配排序的群体分级机制和精英保留等多目标优化策略,保持种群多样性的同时保证了进化向Pareto优解集的方向进行．多目标测试函数的数值仿真和电力系统无功优化的算例分析表明了该算法的有效性和可行性．     

求解多目标最小生成树的一种新的遗传算法

在改进的非支配排序遗传算法（NSGA-II）的基础上,提出了一种新的基于生成树边集合编码的繁殖算子求解多目标最小生成树问题的遗传算法。通过快速非支配排序法,降低了算法的计算复杂度,引入保存精英策略,扩大采样空间。实验结果表明：对于多目标最小生成树问题,边集合编码具有较好的遗传性和局部性,而且基于此繁殖算子的遗传算法在求解效率和解的质量方面都优于基于PrimRST的遗传算法。     

一种求解多目标组合优化的遗传局部搜索算法

为改善遗传算法求解多目标组合优化问题的搜索效率,提出一种新的遗传局部搜索算法.算法采取非劣解并行局部搜索策略以及基于分散度的精英选择策略,并采用基于NSGA-Ⅱ的适应度赋值方式和二元赌轮选择操作,以提高算法收敛性,保持群体多样性.实验结果表明,新算法能够产生数量较多分布较广的近似Pareto最优解.     

数据驱动选择策略的多目标差分进化算法

针对多目标差分进化算法求解复杂多目标优化问题时,最优解选择策略中非支配排序计算复杂度高的问题,提出一种数据驱动选择策略的多目标差分进化(MODE-DDSS)算法.首先,设计多目标差分进化算法的优化解排序等级评估准则,建立基于评估准则的优化解排序等级评估库;其次,设计基于优化解双向搜索机制和无重复比较机制的数据驱动选择策略,实现优化解的高效搜索和快速排序;最后,构建数据驱动选择策略的多目标差分进化算法,降低算法在最优解选择操作中的时间复杂度,提高算法的寻优效率.实验结果表明,所提出的MODE-DDSS算法能够有效减少最优解在选择过程中的比较次数,提升多目标差分进化算法解决复杂多目标优化问题的寻优效率.     

Multi-objective evolutionary algorithms based on the summation of normalized objectives and diversified selection

Most multi-objective evolutionary algorithms (MOEAs) use the concept of dominance in the search process to select the top solutions as parents in an elitist manner. However, as MOEAs are probabilistic search methods, some useful information may be wasted, if the dominated solutions are completely disregarded. In addition, the diversity may be lost during the early stages of the search process leading to a locally optimal or partial Pareto-front. Beside this, the non-domination sorting process is complex and time consuming. To overcome these problems, this paper proposes multi-objective evolutionary algorithms based on Summation of normalized objective values and diversified selection (SNOV-DS). The performance of this algorithm is tested on a set of benchmark problems using both multi-objective evolutionary programming (MOEP) and multi-objective differential evolution (MODE). With the proposed method, the performance metric has improved significantly and the speed of the parent selection process has also increased when compared with the non-domination sorting. In addition, the proposed algorithm also outperforms ten other algorithms.     

A covariance matrix adaptation evolution strategy variant and its engineering application

This paper proposes a novel covariance matrix adaptation evolution strategy (CMA-ES) variant, named AEALSCE, for single-objective numerical optimization problems in the continuous domain. To avoid premature convergence and strengthen the exploration capacity of the basic CMA-ES, AEALSCE is obtained by integrating the CMA-ES with two strategies that can adjust the evolutionary directions and enrich the population diversity. The first strategy is named the anisotropic eigenvalue adaptation (AEA) technique, which adapts the search scope towards the optimal evolutionary directions. It scales the eigenvalues of the covariance matrix anisotropically based on local fitness landscape detection. The other strategy is named the local search (LS) strategy, which is executed under the eigen coordinate system and can be subdivided into two parts. In the first part, the new candidates of superior solutions are sampled around the best solution to perform local exploration. In the other part, the new candidates of inferior solutions are generated using a modified mean point along the fitness descent direction. The proposed AEALSCE algorithm is compared with other top competitors, including the CEC 2014 champion, L-SHADE, and the promising NBIPOP-aCMA-ES, by benchmarking the CEC 2014 testbed. Moreover, AEALSCE is applied in solving three constrained engineering design problems and parameter estimation of photovoltaic (PV) models. According to the statistical results of the experiments, our proposed AEALSCE is competitive with other algorithms in convergence efficiency and accuracy. AEALSCE benefits from a good balance of exploration and exploitation, and it exhibits a potential to address real-world optimization problems.     

Multi-objective topology and sizing optimization of truss structures based on adaptive multi-island search strategy

This paper uses genetic algorithm to handle the topology and sizing optimization of truss structures, in which a sparse node matrix encoding approach is used and individual identification technique is employed to avoid duplicate structural analysis to save computation time. It is observed that NSGA-II could not improve the convergence of non-dominated front at latter generations when solving multi-objective topology and sizing optimization of truss structures. Therefore, an adaptive multi-island search strategy for multi-objective optimization problem (AMISS-MOP) is developed to enhance the convergence. Meanwhile, an elitist strategy based on archive set is introduced to reduce the size of non-dominated sorting to improve computation efficiency. Two numeric examples are presented to demonstrate the performance of AMISS-MOP. Results show that the global Pareto front could be found by AMISS-MOP, the convergence is improved as generation increases, and the time spent on non-dominated sorting is reduced.     

基于分形维数和多目标遗传算法的特征选择

在文本分类系统中,特征的优劣往往极大地影响着分类器的设计和性能。提出一种利用分形维数和带精英策略的非劣支配排序遗传算法进行特征选择的方法。在该方法中分形维数作为特征选择的一个评价机制,利用NSGA-II算法将特征子集选择问题视为多目标优化问题来处理。为了分析结果的有效性,利用SVM分类算法对复旦大学语料库进行测试。实验结果表明该方法具有较好的性能,它可以有效去除无效特征并提高分类准确性。     

网络社区发现的多目标分解粒子群优化算法

通过分析社会网络中社区发现问题的优化目标,构造了社区发现的多目标优化模型,提出一种网络社区发现的多目标分解粒子群优化算法。该算法采用切比雪夫法将多目标优化问题分解为多个单目标优化子问题,使用粒子群优化(PSO)算法对社区结构进行挖掘,并引入了一种新颖的基于局部搜索的变异策略以提高算法的搜索效率和收敛速度,该算法克服了单目标优化算法存在的解单一以及难以发现社区层次结构的缺陷。人工网络及真实网络上的实验结果表明,该算法能够快速准确地挖掘网络社区并揭示社区的层次结构。     

基于改进K 支配排序的高维多目标进化算法

为提高4目标以上高维多目标优化问题的求解性能,提出一种基于改进K支配排序的高维多目标进化算法(KS-MODE).该算法针对K支配的支配关系和排序方法进行改进,避免循环支配并增强选择压力;设计新的全局密度估计方法提高局部密度估计精确性;设计新的精英选择策略和适应度值评价函数;采用CAO局部搜索算子加速收敛.在4～30个目标标准测试函数上的实验结果表明,KS-MODE能够在保证解集分布性的同时大幅提升收敛性和稳定性,能够有效求解高维多目标优化问题.     

Multi-objective sine-cosine algorithm (MO-SCA) for multi-objective engineering design problems

This paper proposes a novel and an effective multi-objective optimization algorithm named multi-objective sine-cosine algorithm (MO-SCA) which is based on the search technique of sine-cosine algorithm (SCA). MO-SCA employs the elitist non-dominated sorting and crowding distance approach for obtaining different non-domination levels and to preserve the diversity among the optimal set of solutions, respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as convex, non-convex and discrete. This proposed algorithm is also checked for the multi-objective engineering design problems with distinctive features. Furthermore, we show the proposed algorithm effectively generates the Pareto front and is easy to implement and algorithmically simple.

     

基于支配强度的NSGA2改进算法

NSGA2是一种简单、高效且被广泛使用的多目标进化算法(Multi-objective Evolutionary Algorithm,MoEA),但在求解实际工程领域中的高维、复杂非线性多目标优化问题(Multi-objective Optimization Problems,MOP)时,存在无法有效识别伪非支配解、计算效率低、解集收敛性和分布性较差等设计缺陷。对此,文中提出一种基于支配强度的NSGA2改进算法(INSGA2-DS)。新算法采用快速支配强度排序法构造非支配集,引入了考虑方差的拥挤距离公式,并通过自适应精英保留策略动态调整精英保留规模。基于标准测试函数的仿真实验表明,INSGA2-DS算法较好地改善了NSGA2算法的收敛性和分布性。     

Efficient covariance matrix update for variable metric evolution strategies

Randomized direct search algorithms for continuous domains, such as evolution strategies, are basic tools in machine learning. They are especially needed when the gradient of an objective function (e.g., loss, energy, or reward function) cannot be computed or estimated efficiently. Application areas include supervised and reinforcement learning as well as model selection. These randomized search strategies often rely on normally distributed additive variations of candidate solutions. In order to efficiently search in non-separable and ill-conditioned landscapes the covariance matrix of the normal distribution must be adapted, amounting to a variable metric method. Consequently, covariance matrix adaptation (CMA) is considered state-of-the-art in evolution strategies. In order to sample the normal distribution, the adapted covariance matrix needs to be decomposed, requiring in general Θ(n ³) operations, where n is the search space dimension. We propose a new update mechanism which can replace a rank-one covariance matrix update and the computationally expensive decomposition of the covariance matrix. The newly developed update rule reduces the computational complexity of the rank-one covariance matrix adaptation to Θ(n ²) without resorting to outdated distributions. We derive new versions of the elitist covariance matrix adaptation evolution strategy (CMA-ES) and the multi-objective CMA-ES. These algorithms are equivalent to the original procedures except that the update step for the variable metric distribution scales better in the problem dimension. We also introduce a simplified variant of the non-elitist CMA-ES with the incremental covariance matrix update and investigate its performance. Apart from the reduced time-complexity of the distribution update, the algebraic computations involved in all new algorithms are simpler compared to the original versions. The new update rule improves the performance of the CMA-ES for large scale machine learning problems in which the objective function can be evaluated fast.     

一种基于多样性度量的多目标化进化算法

针对如何通过附加的方法对多目标化问题进行理论分析,提出并证明了选择附加函数的3个前提条件.提出一种多目标化进化算法,根据种群中个体的多样性度量进行多目标化,并采用改进的非劣分类遗传算法对构造所得的多目标优化问题进行多目标优化.在静态和动态两种环境下进行算法性能验证,结果表明,在种群多样性保持、处理欺骗问题、动态环境下的适应能力等方面,所提算法明显优于其他同类算法.     

A preference multi-objective optimization based on adaptive rank clone and differential evolution

Evolutionary multi-objective optimization (EMO) algorithms have been used in various real-world applications. However, most of the Pareto domination based multi-objective optimization evolutionary algorithms are not suitable for many-objective optimization. Recently, EMO algorithm incorporated decision maker’s preferences became a new trend for solving many-objective problems and showed a good performance. In this paper, we first use a new selection scheme and an adaptive rank based clone scheme to exploit the dynamic information of the online antibody population. Moreover, a special differential evolution (DE) scheme is combined with directional information by selecting parents for the DE calculation according to the ranks of individuals within a population. So the dominated solutions can learn the information of the non-dominated ones by using directional information. The proposed method has been extensively compared with two-archive algorithm, light beam search non-dominated sorting genetic algorithm II and preference rank immune memory clone selection algorithm over several benchmark multi-objective optimization problems with from two to ten objectives. The experimental results indicate that the proposed algorithm achieves competitive results.     

基于全局排序的高维多目标优化研究

目标数超过4的高维多目标优化是目前进化多目标优化领域求解难度最大的问题之一,现有的多目标进化算法求解该类问题时,存在收敛性和解集分布性上的缺陷,难以满足实际工程优化需求.提出一种基于全局排序的高维多目标进化算法GR-MODE,首先,采用一种新的全局排序策略增强选择压力,无需用户偏好及目标主次信息,且避免宽松Pareto支配在排序结果合理性与可信性上的损失;其次,采用Harmonic平均拥挤距离对个体进行全局密度估计,提高现有局部密度估计方法的精确性;最后,针对高维多目标复杂空间搜索需求,设计新的精英选择策略及适应度值评价函数.将该算法与国内外现有的5种高性能多目标进化算法在标准测试函数集DTLZ{1,2, 4,5}上进行对比实验,结果表明,该算法具有明显的性能优势,大幅提升了4~30维高维多目标优化的收敛性和分布性.     

基于多策略的多目标粒子群优化算法

针对目前多目标粒子群优化算法的收敛性能和非劣解的多样性不能同时得到满足等缺陷,提出一种基于多策略的多目标粒子群优化算法（Multi-Objective Particle Swarm Optimization algorithm for Multi-Strategy,MS-MOPSO）。采用非支配排序和拥挤距离排序相结合策略,重新划分外部种群和进化种群;采用小生境选择策略,在外部种群中选择最佳粒子作为领导粒子,用于领导进化种群中粒子的进化;在进化种群中利用多尺度高斯变异策略,平衡算法的全局搜索和局部精确搜索;采用邻域认知个体极值更新策略,不断更新个体极值。将该算法应用到典型的多目标测试函数,并与其他多目标优化算法进行对比分析,测试结果表明该算法中四个策略的有效性和互补性,同时验证了该算法不但具有较好的收敛性和收敛速度,而且该算法最优解的分布具有良好的均匀性和多样性。     

基于NSGA-II的扩展置信规则库激活规则多目标优化方法

针对扩展置信规则库（extended belief rule base,EBRB）系统在不一致的激活规则过多时推理准确性不高的问题,引入带精英策略的快速非支配排序遗传算法（NSGA-Ⅱ）,提出一种基于NSGA-Ⅱ的激活规则多目标优化方法。该方法首先将激活权重大于零的规则（即激活规则）进行二进制编码,把最终参与合成推理的激活规则集合的不一致性以及激活权重和作为多目标优化问题的目标函数,通过带精英策略的快速非支配排序遗传算法求解不一致性更小的激活规则集合,从而降低不一致激活规则对于EBRB系统推理准确性的影响。为了验证本文方法的有效性和可行性,引入非线性函数和输油管道检漏实例进行测试。实验结果表明,基于NSGA-Ⅱ的扩展置信规则库激活规则多目标优化方法能够有效提高EBRB系统的推理能力。     

基于新型非支配排序的多目标麻雀优化算法

针对麻雀搜索算法在求解多目标问题中的不足,并且在求解过程中易陷入局部最优与收敛性差的问题,提出了一种改进的多目标麻雀搜索算法。首先,引入了新型非支配排序,找到最优前沿面;其次,将多项式变异和正余弦算法融合到种群进化策略中,增强其搜索能力,通过竞争机制的种群选择方法,降低搜索过程中局部最优粒子和全局最优粒子导致的误差;最后,将改进算法与多种多目标算法在标准测试函数上进行对比,仿真结果表明,改进算法的收敛性与搜索能力均优于其他算法。由此说明该算法具有可靠的多目标寻优能力,能够有效解决多目标优化问题。     

A hybrid CMA-ES and HDE optimisation algorithm with application to solar energy potential

This paper describes the results of initial experiments to apply computational algorithms to explore a large parameter space containing many variables in the search for an optimal solution for the sustainable design of an urban development using a potentially complicated fitness function. This initial work concentrates on varying the placement of buildings to optimise solar irradiation availability. For this we propose a hybrid of the covariance matrix adaptation evolution strategy (CMA-ES) and hybrid differential evolution (HDE) algorithms coupled with an efficient backwards ray tracing technique. In this paper we concentrate on the formulation of the new hybrid algorithm and its testing using standard benchmarks as well as a solar optimisation problem. The new algorithm outperforms both the standalone CMA-ES and HDE algorithms in benchmark tests and an alternative multi-objective optimisation tool in the case of the solar optimisation problem.