基于种群个体可行性的约束优化进化算法

提出一种新的求解约束优化问题的进化算法.该算法在处理约束时不引入惩罚因子,使约束处理问题简单化.基于种群中个体的可行性,分别采用3种不同的交叉方式和混合变异机制用于指导算法快速搜索过程.为了求解位于边界附近的全局最优解,引入一种不可行解保存和替换机制,允许一定比例的最好不可行解进入下一代种群.标准测试问题的实验结果表明了该算法的可行性和有效性.     

面向多目标优化的适应度共享免疫克隆算法

多目标优化的日标在于使得解集能够快速的逼近真实Pareto前沿.针对解的分布性问题,以免疫克隆算法为框架,引入适应度共享策略,提出了一种新的具有良好分布性保持的多目标优化进化算法;算法建立外部群体以保存非支配解,以Pareto优和共亨适应度作为外部群体更新与激活抗体选择的双重标准.为了增强算法对决策空间的开发能力,引入...     

A novel two-archive strategy for evolutionary many-objective optimization algorithm based on reference points

Current evolutionary many-objective optimization algorithms face two challenges: one is to ensure population diversity for searching the entire solution space. The other is to ensure quick convergence to the optimal solution set. In this paper, we propose a novel two-archive strategy for evolutionary many-objective optimization algorithm. The uniform archive strategy, based on reference points, is used to keep population diversity in the evolutionary process, and to ensure that an evolutionary algorithm is able to search the entire solution space. The single elite archive strategy is used to ensure that individuals with the best single objective value are able to evolve into the next generation and have more opportunities to generate offspring. This strategy aims to improve the convergence rate. Then this novel two-archive strategy is applied to improving the Non-dominated Sorting Genetic Algorithm (NSGA-III). Simulation experiments are conducted on benchmark test sets and experimental results show that our proposed algorithm with the two-archive strategy has a better performance than other state-of-art algorithms.     

Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm

Surrogate-assisted evolutionary optimization has proved to be effective in reducing optimization time, as surrogates, or meta-models can approximate expensive fitness functions in the optimization run. While this is a successful strategy to improve optimization efficiency, challenges arise when constructing surrogate models in higher dimensional function space, where the trade space between multiple conflicting objectives is increasingly complex. This complexity makes it difficult to ensure the accuracy of the surrogates. In this article, a new surrogate management strategy is presented to address this problem. A k-means clustering algorithm is employed to partition model data into local surrogate models. The variable fidelity optimization scheme proposed in the author's previous work is revised to incorporate this clustering algorithm for surrogate model construction. The applicability of the proposed algorithm is illustrated on six standard test problems. The presented algorithm is also examined in a three-objective stiffened panel optimization design problem to show its superiority in surrogate-assisted multi-objective optimization in higher dimensional objective function space. Performance metrics show that the proposed surrogate handling strategy clearly outperforms the single surrogate strategy as the surrogate size increases.     

基于小波精英解学习和多角度搜索的新型阴阳平衡优化算法

针对基本阴阳平衡优化算法计算精度低和优化速度慢等问题,提出一种新型阴阳平衡优化算法.首先,设计小波精英解学习策略,充分利用精英解的进化信息产生高质量的解,用于算法的全局勘探和局部开发;然后,将搜索角度引入解更新方程中,以实现对算法搜索空间的全方位搜索,并对所提出算法的收敛性进行理论分析;最后,采用连续优化测试函数和瓶颈旅行商问题进行数值实验,并将所提出算法与多种智能优化方法进行比较.实验结果表明,所提出算法具有更好的优化性能.     

一种新的基于进化策略的多目标优化算法

用进化策略求解多目标优化问题时，为了提高解在决策变量空间中的搜索能力和保证Pareto前沿的多样性，提出了一种新的基于进化策略的多目标优化算法。运用自适应变异步长的进化策略，使解在决策变量空间中进行全局和局部搜索；并引入非劣解按一定比例进入下一代的方法，使完全被占优的个体有机会参与到下一代的繁殖，保持了解在Pareto前沿的多样性。该算法在保证解在决策空间多样性的同时，也保持了Pareto前沿的多样性。仿真实验表明，该算法具有良好的搜索性能。     

Dynamic partition search algorithm for global numerical optimization

This paper presents a novel evolutionary algorithm entitled Dynamic Partition Search Algorithm (DPSA) for global optimization problems with continuous variables. The DPSA is a population-based stochastic search algorithm in nature, which mainly consists of initialization process and evolution process. In the initialization process, the DPSA randomly generates an initial population of members from a specific search space and finds a leader. In the evolution process, the DPSA applies two groups to balance exploration ability and exploitation ability, in which one group is in charge of exploring new region via a dynamic partition strategy, and the other group relies on Cauchy distributions to exploit the region around the best member. Later, numerical experiments are conducted for 24 classical benchmark functions with 100, 1000 or even 10000 dimensions. And the performance of the proposed DPSA is compared with a state-of-the-art cooperative coevolving particle swarm optimization (CCPSO2), and two existing differential evolution (DE) algorithms. The experimental results show that DPSA has a better performance than the algorithms used for comparison, especially for high dimensional optimization problems. In addition, the numerical computational results also demonstrate that the DPSA has good scalability, and it is an effective evolutionary algorithm for solving large-scale global optimization problems.     

基于灰支持向量回归机预测适应值的交互式集合进化计算

个体适应值的高精度预测和高效的进化策略对于提高进化优化算法性能至关重要.针对现有大规模种群交互式进化计算个体适应值估计误差较大以及传统进化策略搜索效率较低的问题,提出一种基于灰支持向量回归机的个体适应值预测方法和大规模种群集合进化策略.建立基于灰支持向量回归机的适应值预测模型,给出4种集合进化个体比较测度,同时提出新的集合进化个体自适应交叉和变异概率.基于上述策略,采用NSGA-II范式设计一种交互式集合进化优化算法.将该算法应用于RGB颜色One-max优化问题,以表明所提出个体适应值预测方法和集合进化策略的有效性.     

一种多目标人工蜂群算法

为将标准人工蜂群算法有效应用到多目标优化问题中,设计了一种多目标人工蜂群算法。其进化策略在利用精英解引导搜索的同时结合正弦函数搜索操作来平衡算法对解空间的开发与开采行为。另外,算法借助了外部集合来记录与维护种群进化过程中产生的Pareto最优解。理论分析表明:针对多目标优化问题,本算法能收敛到理论最优解集合。对典型多目标测试问题的仿真实验结果表明:本算法能有效逼近理论最优,具有较好的收敛性和均匀性,并且与同类型算法相比,本算法具有良好的求解性能。     

A Bi-population Cooperative Optimization Algorithm Assisted by an Autoencoder for Medium-scale Expensive Problems

This study presents an autoencoder-embedded optimization (AEO) algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems (MEPs). A huge search space can be compressed to an informative low-dimensional space by using an autoencoder as a dimension reduction tool. The search operation conducted in this low space facilitates the population with fast convergence towards the optima. To strike the balance between exploration and exploitation during optimization, two phases of a tailored teaching-learning-based optimization (TTLBO) are adopted to coevolve solutions in a distributed fashion, wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process. Also, a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed. The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200. As indicated in our experiments, TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer. Compared with the state-of-the-art algorithms for MEPs, AEO shows extraordinarily high efficiency for these challenging problems, thus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.      

Hybridizing electromagnetism-like mechanism algorithm with migration strategy for layout and size optimization of truss structures with frequency constraints

The optimal design of a truss structure with dynamic frequency constraints is a highly nonlinear optimization problem with several local optimums in its search space. In this type of structural optimization problems, the optimization methods should have a high capability to escape from the traps of the local optimums in the search space. This paper presents hybrid electromagnetism-like mechanism algorithm and migration strategy (EM–MS) for layout and size optimization of truss structures with multiple frequency constraints. The electromagnetism-like mechanism (EM) algorithm simulates the attraction and repulsion mechanism between the charged particles in the field of the electromagnetism to find optimal solutions, in which each particle is a solution candidate for the optimization problem. In the proposed EM–MS algorithm, two mechanisms are utilized to update the position of particles: modified EM algorithm and a new migration strategy. The modified EM algorithm is proposed to effectively guide the particles toward the region of the global optimum in the search space, and a new migration strategy is used to provide efficient exploitation between the particles. In order to test the performance of the proposed algorithm, this study utilizes five benchmark truss design examples with frequency constraints. The numerical results show that the EM–MS algorithm is an alternative and competitive optimizer for size and layout optimization of truss structures with frequency constraints.     

A new real-coded quantum-inspired evolutionary algorithm for continuous optimization

This paper presents a recursive deepening hybrid strategy to solve real-parameter optimization problems. It couples a local search technique with a quantum-inspired evolutionary algorithm. In order to adapt the quantum-inspired evolutionary algorithm for continuous optimization without losing the states superposition property, a suitable sampling of the search space that tightens recursively and an integration of a uniformly generated random part after measurement have been utilized. The use of local search provides, for each search window, a good exploitation of the quantum inspired generated solution's neighbourhood. The proposed approach has been tested through the reference black-box optimization benchmarking framework. The comparison of the obtained results with those of some state-of-the-art algorithms has shown its actual effectiveness.     

基于径向空间划分的昂贵多目标进化算法

为了解决难以建立精确数学模型或者真实评估实验成本高昂的多目标优化问题, 提出了一种基于径向空间划分的昂贵多目标进化算法. 首先算法使用高斯回归作为代理模型逼近目标函数; 然后将目标空间的个体投影到径向空间, 结合目标空间和径向空间信息保留对种群贡献更高的个体; 之后由径向空间中个体的位置分布决定下一步应该选择哪些个体进行真实评估; 最后, 采用一种双档案管理策略维护代理模型的质量. 数值实验和现实问题上的结果表明, 与5种先进算法相比, 该算法在解决昂贵多目标优化问题时能够提供更高质量的解.     

HMOFA:一种混合型多目标萤火虫算法

现实中不断涌现出数目众多且日益复杂的多目标优化问题,迫切需要发展新型多目标优化算法以应对挑战.将基本萤火虫算法拓展至多目标优化领域,提出一种混合型多目标萤火虫算法HMOFA（hybrid multi-objective firefly algorithm）.该算法提出使用混合水平正交实验设计和连续决策空间量化的方法生成接近于用户指定规模且均匀分布于搜索空间的初始种群,为后续的进化提供良好的起始点;利用外部档案中的精英解个体引导萤火虫移动,促使算法较快收敛;运用3点最短路径方法维持外部档案的多样性.HMOFA算法与另外5种代表性多目标进化算法一同在17个基准多目标测试题上进行性能比较,实验结果表明,HMOFA算法在收敛性、多样性和鲁棒性方面总体上具有较显著的性能优势.     

A radial space division based evolutionary algorithm for many-objective optimization

In evolutionary many-objective optimization, diversity maintenance plays an important role in pushing the population towards the Pareto optimal front. Existing many-objective evolutionary algorithms mainly focus on convergence enhancement, but pay less attention to diversity enhancement, which may fail to obtain uniformly distributed solutions or fall into local optima. This paper proposes a radial space division based evolutionary algorithm for many-objective optimization, where the solutions in high-dimensional objective space are projected into the grid divided 2-dimensional radial space for diversity maintenance and convergence enhancement. Specifically, the diversity of the population is emphasized by selecting solutions from different grids, where an adaptive penalty based approach is proposed to select a better converged solution from the grid with multiple solutions for convergence enhancement. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on a variety of benchmark test problems. Experimental results demonstrate the competitiveness of the proposed algorithm in terms of both convergence enhancement and diversity maintenance.     

Multi-modal function optimization with the ZEDS (zoomed evolutionary dual strategy) algorithmzoomed evolutionary algorithm

This article introduces a new evolutionary algorithm for multi-modal function optimization called ZEDS (zoomed evolutionary dual strategy). ZEDS employs a two-step, zoomed (global to local), evolutionary approach. In the first (global) step, an improved ‘GT algorithm’ is employed to perform a global recombinatory search that divides the search space into niches according to the positions of its approximate solutions. In the second (local) step, a ‘niche evolutionary strategy’ performs a local search in the niches obtained from the first step, which is repeated until acceptable solutions are found. The ZEDS algorithm was applied to some challenging problems with good results, as shown in this article.     

变邻域量子烟花算法求解CVRP

针对带容量约束的车辆路径问题，提出一种融合量子进化算法和变邻域优化策略的变邻域量子烟花算法。该算法采用等分随机键与最大位置法结合的实数编码方式，通过量子旋转门和非门变异提高算法全局搜索能力，同时运用结合2-Opt的变邻域优化策略加强局部搜索能力。选取17个基准算例进行参数实验和对比实验，实验结果表明，相对于对比算法，所提出的算法具有较好的寻优能力和收敛速度。     

基于目标空间划分的自适应多目标进化算法

目前,多目标进化算法在众多领域具有极高的应用价值,是优化领域的研究热点之一.分析已有多目标进化算法在保持种群多样性方面的不足并提出一种基于解空间划分的自适应多目标进化算法（space division basedadaptive multiobjective evolutionary algorithm,简称SDA-MOEA）来解决多目标优化问题.该方法首先将多目标优化问题的解空间划分为大量子空间,在算法进化过程中,每个子空间都保留一个非支配解集,以保证种群的多样性.另外,该方法根据每个子空间推进种群前进的距离,自适应地为每个子空间分配进化机会,以提高种群的进化速度.最后,利用3组共14个多目标优化问题检验SDA-MOEA的性能,并将SDA-MOEA与其他5个已有多目标进化算法进行对比分析.实验结果表明：在10个问题上,算法SDA-MOEA显著优于其他对比算法.     

差分型复杂过程全局进化方法

复杂过程全局进化算法是一种具有类似分散搜索的通用框架结构,能够高效完成全局搜索的新型进化算法。在该算法的基础上,提出了差分型复杂过程全局进化算法。差分型算法采用拉丁超立方体抽样生成多样性种群,并应用“最小欧几里德距离的最大值法”产生参考集Refset2,以保证参考集的多样性。采用差分变异和交叉策略替代原算法的线性合并,兼顾算法的收敛速度和种群的多样性。应用Nelder-Mead直接搜索法进行局部搜索,防止搜索过程在局部最优点附近反复。仿真结果表明差分型复杂过程全局进化算法,具有较高的搜索效率。     

PSO-Based Multiobjective Optimization With Dynamic Population Size and Adaptive Local Archives

Recently, various multiobjective particle swarm optimization (MOPSO) algorithms have been developed to efficiently and effectively solve multiobjective optimization problems. However, the existing MOPSO designs generally adopt a notion to “estimate” a fixed population size sufficiently to explore the search space without incurring excessive computational complexity. To address the issue, this paper proposes the integration of a dynamic population strategy within the multiple-swarm MOPSO. The proposed algorithm is named dynamic population multiple-swarm MOPSO. An additional feature, adaptive local archives, is designed to improve the diversity within each swarm. Performance metrics and benchmark test functions are used to examine the performance of the proposed algorithm compared with that of five selected MOPSOs and two selected multiobjective evolutionary algorithms. In addition, the computational cost of the proposed algorithm is quantified and compared with that of the selected MOPSOs. The proposed algorithm shows competitive results with improved diversity and convergence and demands less computational cost.