融合指标分组的高维混合多目标进化优化

高维混合多目标优化问题因包含多个不同类型指标,目前尚缺乏有效求解该问题的进化优化方法。提出一种基于目标分组的高维混合多目标并行进化优化方法。采用深度学习神经网络预测种群隐式性能指标;基于指标相关性,将高维混合多目标优化问题分解为若干子优化问题;采用多种群并行进化算法,求解分解后的每一子优化问题,并基于各子种群的非被占优解构建外部保存集;采用聚合函数对外部保存集个体进一步优化,得到Pareto最优解集。在室内布局优化问题中验证所提方法,实验结果表明,所提方法的Pareto最优解在收敛性、分布性以及延展性等方面均优于对比方法。     

基于线性权重最优支配的高维多目标优化算法

在高维多目标优化问题中,Pareto支配关系存在非支配解随优化目标数增加呈指数级增长和种群选择压力下降等问题。针对这些问题,基于线性权重聚合函数和支配关系两种比较多目标解方法的思想,提出一种线性权重最优支配关系（LWM-dominance）,并理论证明了LWM非支配解集是Pareto非支配解集的子集,同时保留了种群中重要的角解。进一步地,基于LWM支配关系,实现了一个高维多目标进化优化算法,基于该算法的实验验证了LWM支配关系的性质。在随机解空间中的实验结果表明LWM支配关系适用于5~15个目标的高维多目标优化问题,通过DTLZ1~DTLZ7高维多目标优化问题进化过程中LWM非支配解集与Pareto非支配解集规模的对比实验,结果表明优化目标数为10和15时非支配解的比例平均下降了约17%。     

融入偏好的区间高维多目标集合进化优化方法

尽管区间参数高维多目标优化问题普遍存在且非常重要, 但是, 目前求解该问题的方法却很少. 本文提出一种有效解决该问题的集合进化优化方法, 通过在进化过程中融入决策者的偏好, 以得到符合决策者偏好的Pareto解集. 该方法将原优化问题转化为以超体积、不确定度、决策者满意度为新目标的确定型3目标优化问题; 为了求解转化后的优化问题, 采用集合Pareto占优关系比较个体, 并设计融入决策者偏好的延展性测度, 以进一步区分具有相同序值的个体; 此外, 还提出集合变异与重组策略, 以生成高性能的子代种群. 采用4个基准高维多目标优化问题和1个汽车驾驶室设计问题测试所提方法的性能, 并将其与另外3种方法进行对比. 实验结果验证, 该方法能得到收敛性、延展性、不确定度, 以及决策者满意度均衡的Pareto解集.     

基于Pareto解集分段预测策略的动态多目标进化算法

针对现有的动态多目标优化算法种群收敛速度慢、多样性难以保持等问题,提出了一种基于Pareto解集分段预测策略的动态多目标进化算法BPDMOP。当检测到环境变化时,对前一时刻进化得到的Pareto最优解根据任一子目标函数进行排序,并按照该子目标的大小均分为3段,分别计算出每一段Pareto解集中心点的移动方向;对每一段Pareto子集进行系统抽样得到Pareto前沿面的特征点,利用线性模型分段预测下一代种群;根据优化问题的难易程度,自适应地在预测的种群周围产生随机个体来增加种群的多样性。通过对3类标准测试函数的实验表明了该算法能够有效求解动态多目标优化问题。     

基于参考点的高维多目标粒子群算法

高维多目标优化问题一般指目标个数为4个 或以上时的多目标优化问题.由于种群中非支配解数量随着目标数量的增加而急剧增多,导致进化算法的进化压力严重降低,求解效率低.针对该问题,提出一种基于粒子群的高维多目标问题求解方法,在目标空间中引入一系列的参考点,根据参考点筛选出能兼顾多样性和收敛性的非支配解作为粒子的全局最优,以增大选择压力.同时,提出了基于参考点的外部档案维护策略,以保持最后所得解集的多样性.在标准测试函数DTLZ2上的仿真结果表明,所提方法在求解高维多目标问题时能够得到收敛性和分布性都较好的解集.     

求解多目标作业车间调度问题的混合变异杂草优化算法

针对多目标作业车间调度问题,提出一种混合变异杂草优化算法。该算法采用基于各子目标熵值权重的欧氏贴近度作为适应度值计算方法,引导种群向Pareto前端进化。在进化过程中,运用快速非支配排序策略构建Pareto档案,并利用进化种群中最优个体实时更新Pareto最优解集,提升算法的优化性能;同时通过引入变异算子增加种群多样性,避免算法陷入局部最优。最后,基于Benchmark算例的仿真实验,验证了该算法求解多目标作业车间调度问题的有效性。     

进化高维多目标优化研究进展

高维多目标优化问题是目标个数多于3的多目标优化问题.尽管进化优化方法在多目标优化问题求解中显示了卓越的性能,但是,对于高维多目标优化问题,已有方法存在目标维数难以扩展、Pareto占优关系无法区分进化个体,以及多样性维护策略失效等困难.因此,高维多目标优化问题的高效求解引起进化优化界的高度关注.本文将分别从新型占优关系、多样性维护策略、目标缩减、目标聚合、基于性能指标的选择、融入偏好、集合进化、变化算子、可视化技术,以及应用等10个方面分类总结近年来进化高维多目标优化的研究成果,通过分析已有研究存在的问题,指出今后可能的研究方向.     

区间参数高维多目标集合进化优化方法

区间参数高维多目标优化问题是现实生活中常见的一类优化问题,但其有效的求解方法并不是很多.对此,利用集合的概念,提出一种求解此类问题的新方法.首先,利用衡量解集收敛性、分布性、多样性的3种性能指标将原优化问题降为3目标优化问题;其次,采用集合Pareto占优关系和不确定测度来区分转化后优化问题解的优劣;再次,设计自适应变化的交叉、变异概率以提高种群的全局和局部搜索能力;最后,利用4种基准函数优化问题,对所提出方法和对比方法进行测试.测试结果显示,除了收敛性,所提出方法得到的Pareto解集的不确定性、多样性、分布性均优于对比方法.     

动态选择与替换策略的多目标约束优化进化算法

提出一种基于动态选择与替换策略的多目标优化进化算法用于求解约束优化问题.新算法首先将约束优化问题转化为两个目标的多目标优化问题,基于Parto支配关系,把初始种群分为Pareto子集和Non-Pareto子集,引入一种非劣个体保护偏好策略,动态选取一定比例的最优非劣个体直接进入下一代群体,剩下的非劣个体随机替代Pareto子集中的个体.Pareto子集和Non-Pareto子集分别进行单形交叉和多样性变异操作产生新的子种群.对13个标准测试问题的数值实验结果表明新算法的有效性.     

面向多目标流水车间调度的多种群多目标遗传算法

针对制造型企业普遍存在的流水车间调度问题,建立了以最小化最迟完成时间和总延迟时间为目标的多目标调度模型,并提出一种基于分解方法的多种群多目标遗传算法进行求解.该算法将多目标流水车间调度问题分解为多个单目标子问题,并分阶段地将这些子问题引入到算法迭代过程进行求解.算法在每次迭代时,依据种群的分布情况选择各子问题的最好解及与其相似的个体分别为当前求解的子问题构造子种群,通过多种群的进化完成对多个子问题最优解的并行搜索.通过对标准测试算例进行仿真实验,结果表明所提出的算法在求解该问题上能够获得较好的非支配解集.     

An objective reduction algorithm using representative Pareto solution search for many-objective optimization problems

In recent years, many-objective optimization problems (i.e. more than three objectives) have attracted the interests of many researchers. The main difficulties of many-objective optimization problems lie in high computational cost, stagnation in search process, etc. It is almost impossible to design an algorithm effective for all problems. However, for some problems, especially for problems with redundant objectives, it is possible to design effective algorithms by removing the redundant objectives and keeping the non-redundant objectives so that the original problem becomes the one with much fewer objectives. To do so, first, a multi-objective evolutionary algorithm-based decomposition is adopted to generate a smaller number of representative non-dominated solutions widely distributed on the Pareto front. Then the conflicting objective pairs are identified through these non-dominated solutions, and the redundant objectives are determined by these pairs and then removed. Based on these, a fast non-redundant objectives generation algorithm is proposed in this paper. Finally, the experiments are conducted on a set of benchmark test problems and the results indicate the effectiveness and efficiency of the proposed algorithm.     

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.     

基于估值不确定度排序顺序均值采样的昂贵高维多目标进化算法

模型管理,特别是训练样本的选择和填充采样准则,是影响昂贵多目标优化算法求解性能的重要因素.为此,选择样本库中具有较好目标函数值的若干个体作为样本训练目标函数的代理模型,使用基于参考向量的进化算法搜索模型的最优解集,并提出一种基于个体目标函数估值不确定度排序顺序均值的采样策略,从该最优解集中选择两个个体进行真实的目标函数评价.为了验证算法的有效性,将所提出算法在DTLZ和WFG多目标优化测试问题和两个实际工程优化问题上进行测试,并与其他5种优秀的同类型算法进行结果对比.实验结果表明,所提出算法在求解昂贵高维多目标优化问题上是有效的.     

融合张角拥挤控制策略的高维多目标优化

对于高维多目标优化问题,随着目标维数的增加,种群中非被支配解的比例剧增, 严重降低了种群的进化压力.为了对数量众多的非被支配解进行有效的拥挤控制并提升种群的多样性, 本文在提出张角概念的基础上设计了一种新的拥挤控制策略(Congestion control strategy based on open angle, CCSOA),它的时间复杂度并不会随着目标维数的增加而增大. 与目前优秀的进化多目标优化(Evolutionary multiobjective optimization, EMO)算法IBEA (Indicator-based evolutionary algorithm)、NSGAIII (Nondominated sorting genetic algorithm III)和GrEA (Grid-based evolutionary algorithm)的比较结果表明, 融合了CCSOA的高维多目标优化算法在收敛效果和解集分布的均匀性两个方面均有较大的优势.     

An angle based evolutionary algorithm with infeasibility information for constrained many-objective optimization

Recently, angle-based approaches have shown promising for unconstrained many-objective optimization problems (MaOPs), but few of them are extended to solve constrained MaOPs (CMaOPs). Moreover, due to the difficulty in searching for feasible solutions in high-dimensional objective space, the use of infeasible solutions comes to be more important in solving CMaOPs. In this paper, an angle based evolutionary algorithm with infeasibility information is proposed for constrained many-objective optimization, where different kinds of infeasible solutions are utilized in environmental selection and mating selection. To be specific, an angle-based constrained dominance relation is proposed for non-dominated sorting, which gives infeasible solutions with good diversity the same priority to feasible solutions for escaping from the locally feasible regions. As for diversity maintenance, an angle-based density estimation is developed to give the infeasible solutions with good convergence a chance to survive for next generation, which is helpful to get across the large infeasible barrier. In addition, in order to utilize the potential of infeasible solutions in creating high-quality offspring, a modified mating selection is designed by considering the convergence, diversity and feasibility of solutions simultaneously. Experimental results on two constrained many-objective optimization test suites demonstrate the competitiveness of the proposed algorithm in comparison with five existing constrained many-objective evolutionary algorithms for CMaOPs. Moreover, the effectiveness of the proposed algorithm on a real-world problem is showcased.     

采用放松支配关系的高维多目标微分进化算法

为了提高进化算法在求解高维多目标优化问题时的收敛性和多样性,提出了采用放松支配关系的高维多目标微分进化算法。该算法采用放松的Pareto支配关系,以增加个体的选择压力;采用群体和外部存储器协同进化的方案,并通过混合微分变异算子,生成子代群体;采用基于指标的方法计算个体的适应度并对群体进行更新;采用基于Lp范数（0相似文献   

A clustering-ranking method for many-objective optimization

In evolutionary multi-objective optimization, balancing convergence and diversity remains a challenge and especially for many-objective (three or more objectives) optimization problems (MaOPs). To improve convergence and diversity for MaOPs, we propose a new approach: clustering-ranking evolutionary algorithm (crEA), where the two procedures (clustering and ranking) are implemented sequentially. Clustering incorporates the recently proposed non-dominated sorting genetic algorithm III (NSGA-III), using a series of reference lines as the cluster centroid. The solutions are ranked according to the fitness value, which is considered to be the degree of closeness to the true Pareto front. An environmental selection operation is performed on every cluster to promote both convergence and diversity. The proposed algorithm has been tested extensively on nine widely used benchmark problems from the walking fish group (WFG) as well as combinatorial travelling salesman problem (TSP). An extensive comparison with six state-of-the-art algorithms indicates that the proposed crEA is capable of finding a better approximated and distributed solution set.     

模型辅助的计算费时进化高维多目标优化

代理模型能够辅助进化算法在计算资源有限的情况下加快找到问题的最优解集,因此建立高效的代理模型辅助多目标进化搜索逐渐受到了重视.然而随着目标数量的增加,对每个目标分别建立高斯过程模型时个体整体估值的不确定度会随之增加.因此通过对模型最优解集的搜索探索原问题潜在的非支配解集,并基于个体的收敛性,种群的多样性和估值的不确定度...