MCEDA: A novel many-objective optimization approach based on model and clustering

To solve many-objective optimization problems (MaOPs) by evolutionary algorithms (EAs), the maintenance of convergence and diversity is essential and difficult. Improved multi-objective optimization evolutionary algorithms (MOEAs), usually based on the genetic algorithm (GA), have been applied to MaOPs, which use the crossover and mutation operators of GAs to generate new solutions. In this paper, a new approach, based on decomposition and the MOEA/D framework, is proposed: model and clustering based estimation of distribution algorithm (MCEDA). MOEA/D means the multi-objective evolutionary algorithm based on decomposition. The proposed MCEDA is a new estimation of distribution algorithm (EDA) framework, which is intended to extend the application of estimation of distribution algorithm to MaOPs. MCEDA was implemented by two similar algorithm, MCEDA/B (based on bits model) and MCEDA/RM (based on regular model) to deal with MaOPs. In MCEDA, the problem is decomposed into several subproblems. For each subproblem, clustering algorithm is applied to divide the population into several subgroups. On each subgroup, an estimation model is created to generate the new population. In this work, two kinds of models are adopted, the new proposed bits model and the regular model used in RM-MEDA (a regularity model based multi-objective estimation of distribution algorithm). The non-dominated selection operator is applied to improve convergence. The proposed algorithms have been tested on the benchmark test suite for evolutionary algorithms (DTLZ). The comparison with several state-of-the-art algorithms indicates that the proposed MCEDA is a competitive and promising approach.     

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.     

DAV-MOEA:一种采用动态角度向量支配关系的高维多目标进化算法

现实中不断涌现的高维多目标优化问题对传统的基于Pareto支配的多目标进化算法构成巨大挑战.一些研究者提出了若干改进的支配关系,但仍难以有效地平衡高维多目标进化算法的收敛性和多样性.提出一种动态角度向量支配关系动态地刻画进化种群在高维目标空间的分布状况,以较好地在收敛性与多样性之间取得平衡;另外,提出一种改进的基于Lp...     

Many objective cooperative bat searching algorithm

In this paper, a many objective cooperative bat searching algorithm (MOCBA) is proposed to solve many-objective optimization problems by using the balanceable fitness estimation method. Similar to the particle swarm optimization (PSO) algorithm and the evolutionary algorithm (EA), the cooperative bat searching algorithm (CBA) is a recently developed swarm intelligence optimization algorithm to efficiently solve single-objective optimization problems. With the balanceable fitness estimation method, the MOCBA balances the diversity ability and convergence ability of the algorithm during searching process. Moreover, the convergence issue for MOCBA is also studied. The results on convergence in mean and convergence in probability of the MCOBA are presented. Experimental results are provided to demonstrate the effectiveness of the proposed MOCBA by comparing with fourteen state-of-the-art many-objective optimization algorithms by solving benchmark functions: DTLZ1–DTLZ5 and WFG1–WFG9. By calculating the means, standard deviations and running the Wilcoxon rank sum tests and the Friedmans tests of 100 algorithm executions, the proposed MOCBA shows superior performance among all the fifteen algorithms.     

Research on a new optimization algorithm simulating multi- states of matter inspired by finite element analysis approach

A new optimization algorithm is proposed, since a huge problem that many algorithms faced was not being able to effectively balance the global and local search ability. Matter exists in three states: solid, liquid, and gas, which presents different motion characteristics. Inspired by multi- states of matter, individuals of optimization algorithm have different motion characteristics of matter, which could present different search ability. The Finite Element Analysis (FEA) approach can simulate multi- states of matter, which can be adopted to effectively balance the global search ability and local search ability in new optimization algorithm. The new algorithm is creative application of Finite Element Analysis at optimization algorithm field. Artificial Physics Optimization (APO) and Gravitational Search Algorithm (GSA) belongs to the algorithm types defined by force and mass. According to FEA approach, node displacement caused by force and stiffness could be equivalent to motion caused by force and mass of APO and GSA. In the new algorithm framework, stiffness replaces mass of APO and GSA algorithm. This paper performs research on two different algorithms based on APO and GSA respectively. The individuals of new optimization algorithm are divided into solid state, liquid state, and gas state. The effects of main parameters on the performance were studied through experiments of 6 static test functions. The performance is compared with PSO, basic APO, or GSA for four complex models which made up of solid individual, liquid individual, and gas individual in iterative process. The reasonable complex model can be confirmed experimentally. Based on the reasonable complex model, the article conducted complete experiments against Enhancing artificial bee colony algorithm with multi-elite guidance (MGABC), Artificial bee colony algorithm with an adaptive greedy position update strategy (AABC), Multi-strategy ensemble artificial bee colony (MEABC), Self-adaptive heterogeneous PSO (fk-PSO), and APO with 28 CEC2013 test problem. Experimental results show that the proposed method achieves a good performance in comparison to its counterparts as a consequence of its better exploration– exploitation balance. The algorithm supplies a new method to improve physics optimization algorithm.

     

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.     

Bollinger bands approach on boosting ABC algorithm and its variants

In this study, a new algorithm that will improve the performance and the solution quality of the ABC (artificial bee colony) algorithm, a swarm intelligence based optimization algorithm is proposed. ABC updates one parameter of the individuals before the fitness evaluation. Bollinger bands is a powerful statistical indicator which is used to predict future stock price trends. By the proposed method an additional update equation for all ABC-based optimization algorithms is developed to speed up the convergence utilizing the statistical power of the Bollinger bands. The proposed algorithm was tested against classical ABC algorithm and recent ABC variants. The results of the proposed method show better performance in comparison with ABC-based algorithm with one parameter update in convergence speed and solution quality.     

A new particle swarm optimization algorithm with adaptive inertia weight based on Bayesian techniques

Particle swarm optimization is a stochastic population-based algorithm based on social interaction of bird flocking or fish schooling. In this paper, a new adaptive inertia weight adjusting approach is proposed based on Bayesian techniques in PSO, which is used to set up a sound tradeoff between the exploration and exploitation characteristics. It applies the Bayesian techniques to enhance the PSO's searching ability in the exploitation of past particle positions and uses the cauchy mutation for exploring the better solution. A suite of benchmark functions are employed to test the performance of the proposed method. The results demonstrate that the new method exhibits higher accuracy and faster convergence rate than other inertia weight adjusting methods in multimodal and unimodal functions. Furthermore, to show the generalization ability of BPSO method, it is compared with other types of improved PSO algorithms, which also performs well.     

一种基于分解和协同的高维多目标进化算法

现实中高维多目标优化问题普遍存在，而且其巨大的目标空间使得经典的多目标进化算法面临严峻挑战，提出一种基于分解和协同策略的高维多目标进化算法MaOEA/DCE.该算法利用混合水平正交实验设计方法产生接近于指定规模且均匀分布于聚合系数空间的权重向量，提高种群的分布性；其次，算法将差分进化算子和自适应SBX算子进行协同进化以产生高质量的子代个体，改善算法的收敛性.该算法与另外五种高性能的多目标进化算法在基准测试函数集DTLZ{1，2，4，5}上进行IGD⁺性能指标实验，结果表明MaOEA/DCE在收敛性、多样性和稳定性方面总体具有显著的性能优势.     

具有自适应全局最优引导快速搜索策略的人工蜂群算法

针对人工蜂群算法存在开发与探索能力不平衡的缺点,提出了具有自适应全局最优引导快速搜索策略的改进算法.在该策略中,首先采蜜蜂利用自适应搜索方程平衡了不同搜索方法的探索和开发能力;其次跟随蜂利用全局最优引导邻域搜索方程对蜜源进行精细化搜索,以提高其收敛精度和全局搜索能力.14个标准测试函数的仿真结果表明,相比其他算法,所提出的改进算法有效平衡了算法的开发与探索能力,并提高了其最优解的精度及收敛速度.     

MOPSO算法及其在水库优化调度中的应用

提出了一种新的多目标粒子群优化(MOPSO)算法，该算法采用自适应网格方法来估计非劣解集中粒子的密度信息、平衡全局和局部搜索能力的Pareto最优解的搜索机制、删除品质差的多余粒子的Archive集的修剪技术。通过对三峡梯级多目标优化调度问题的计算，表明该算法是求解大规模复杂多目标优化问题的一种有效手段。     

一种狼群智能算法及收敛性分析

针对狼群算法求解复杂函数时容易陷入局部极值、计算耗费大、学习能力差等局限性, 提出一种狼群智能算法. 首先, 通过构建智能猎杀行为提高算法自适应学习能力, 降低算法的计算耗费, 构建双高斯函数更新法以增强算法全局搜索能力; 然后, 运用马尔科夫过程证明狼群智能算法的收敛性; 最后, 对多种典型测试函数进行仿真实验并与多种智能算法进行对比分析. 实验结果表明, 所提出算法具有全局收敛性强、计算耗费低、寻优精度高等优势.     

空间优化选址中的增强型人工蜂群算法

公共服务设施选址是一种复杂的空间优化问题,选址的好坏关系到公共服务设施能否发挥其最大作用。利用穷举算法难以对高维的数据问题进行求解。针对空间优化选址的特点及人工蜂群算法收敛速度慢的问题,提出了适合空间选址的邻域搜索新公式,并将交叉的思想引入到了算法中,加快了全局最优解的寻优速度。对算法的可行性和有效性进行了验证,实验表明增强型人工蜂群算法比基本的人工蜂群算法取得了较优的效果。     

Tent 混沌人工蜂群与粒子群混合算法

针对人工蜂群和粒子群算法的优势与缺陷,提出一种Tent混沌人工蜂群粒子群混合算法.首先利用Tent混沌反向学习策略初始化种群;然后划分双子群,利用Tent混沌人工蜂群算法和粒子群算法协同进化;最后应用重组算子选择最优个体作为跟随蜂的邻域蜜源和粒子群的全局极值.仿真结果表明,该算法不仅能有效避免早熟收敛,而且能有效跳出局部极值,与其他最新人工蜂群和粒子群算法相比具有较强的全局搜索能力和局部搜索能力.     

融合BFGS的自适应蜂群算法在谐波平衡分析中的应用

针对谐波平衡分析中传统算法存在初值限制,以及智能算法收敛速度慢的缺点,提出一种基于BFGS（Broyden-Fleteher-Goldfarl-Shanno）算法局部搜索策略的自适应蜂群算法。该算法在基本蜂群算法的基础上引入非线性的动态调整因子代替蜂群算法搜索公式中的随机变量,增加搜索的自适应性,并将BFGS算法运用到自适应蜂群算法后期求解,提高其局部搜索能力。实验结果表明,改进算法较标准蜂群算法迭代次数减少51.9%,相对于传统BFGS算法和部分改进智能算法均表现出较好收敛性能。     

进化超多目标优化研究进展及展望

近年来,超多目标优化逐渐成为多目标优化研究的热点之一,由于超多目标优化问题具有难以寻优的高维目标空间,其研究颇有挑战性,因此受到广泛关注.现有综述性文献通常只是针对某个特定方面,缺乏系统性考察.鉴于此,首先从问题定义出发,综合考虑超多目标优化问题范畴,进行超多目标优化问题的概念辨析;其次通过对近些年的相关文献整理,系统分析超多目标优化问题进展并对其中部分经典方法加以介绍,通过对基准测试函数和性能指标的说明,围绕超多目标优化研究方法展开综合性论述;接着选取5个典型的超多目标进化算法,在2组基准测试函数和4个实际问题上分别展开仿真实验,通过性能指标和非参数检验对不同类别的算法进行理论分析;最后在明确超多目标优化研究领域的若干前沿问题的基础上,对今后的研究工作进行展望.     

A modified artificial bee colony approach for the 0-1 knapsack problem

The 0-1 knapsack problem (KP01) is one of the classical NP-hard problems in operation research and has a number of engineering applications. In this paper, the BABC-DE (binary artificial bee colony algorithm with differential evolution), a modified artificial bee colony algorithm, is proposed to solve KP01. In BABC-DE, a new binary searching operator which comprehensively considers the memory and neighbour information is designed in the employed bee phase, and the mutation and crossover operations of differential evolution are adopted in the onlooker bee phase. In order to make the searching solution feasible, a repair operator based on greedy strategy is employed. Experimental results on different dimensional KP01s verify the efficiency of the proposed method, and it gets superior performance compared with other five metaheuristic algorithms.     

基于高斯变异的量子粒子群算法

粒子群算法相对于其他优化算法来说有着较强的寻优能力以及收敛速度快等特点,但是在多峰值函数优化中,基本粒子群算法存在着早熟收敛现象。针对粒子群算法易于陷入局部最小的弱点,提出了一种基于高斯变异的量子粒子群算法。该算法使粒子同时具有良好的全局搜索能力以及快速收敛能力。典型函数优化的仿真结果表明,该算法具有寻优能力强、搜索精度高、稳定性好等优点,适合于工程应用中的函数优化问题。     

深层加速搜索的蜂群算法

蜂群(ABC)算法是近年来提出的一种求解优化问题的较新型的仿生进化算法。针对蜂群算法的不足,依据反向搜索的思想,提出一种改进的蜂群算法。在改进算法中,每次邻域搜索之后,通过比较新旧食物源位置的花蜜值(而非适应度)来选择保留较优解。同时,在采蜜蜂采蜜后以一定概率进行反向搜索,保留较优解。邻域搜索的维数也不再限定某一维。基于五个标准测试函数的仿真结果表明,本算法能有效加快收敛速度,提高最优解的精度,其性能明显优于基本的蜂群算法。     

A food source-updating information-guided artificial bee colony algorithm

Artificial bee colony algorithm simulates the foraging behavior of honey bees, which has shown good performance in many application problems and large-scale optimization problems. To model the bees foraging behavior more accurately, a food source-updating information-guided artificial bee colony algorithm is proposed in this paper. In this algorithm, some food source-updating information obtained during optimizing time is introduced to redefine the foraging strategies of artificial bees. The proposed algorithm has been tested on a set of test functions with dimension 30, 100, 1000 and compared with some recently proposed related algorithms. The experimental results show that the performance of artificial bee colony algorithm is significantly improved for both rotated problems and large-scale problems. Compared with the related algorithms, the proposed algorithm can achieve better or competitive performance on most test functions and greatly better performance on parts of test functions.