一个用于多目标优化的进化规划算法

进化计算的群体搜索机制为多目标优化问题的直接求解提供了途径。本文将多目标遗传算法中的一些技术用于进化规划,提出一个多目标进化规划算法,并给出计算实例。     

一种快速的双目标非支配排序算法

提出一种快速的双目标非支配排序算法(BNSA)。设计了前向比较操作,以便快速识别非支配个体。提出了按需排序策略,避免生成多余的非支配前沿。论证BNSA算法的正确性,分析其时间复杂度为O(NlogN)。在9个标准的双目标优化测试问题上进行了比较实验。实验结果表明与其它3种非支配排序算法相比,BNSA算法在大多数测试问题上具有更快速的性能。当进化代数超过400代时,BNSA在所有的测试问题上都具有最好的加速效果。此外,BNSA算法简明、易于编程实现,可集成到任何基于非支配排序的多目标进化算法中,能较大程度地提高双目标优化的运行速度。     

Convergence analysis of a self-adaptive multi-objective evolutionary algorithm based on grids

Evolutionary algorithms have been successfully applied to various multi-objective optimization problems. However, theoretical studies on multi-objective evolutionary algorithms, especially with self-adaption, are relatively scarce. This paper analyzes the convergence properties of a self-adaptive (μ+1)-algorithm. The convergence of the algorithm is defined, and general convergence conditions are studied. Under these conditions, it is proven that the proposed self-adaptive (μ+1)-algorithm converges in probability or almost surely to the Pareto-optimal front.     

一种求解约束优化问题的线性进化算法

提出一种基于实数编码处理约束优化问题的线性算法,并对其复杂度和收敛性进行分析.该算法将约束优化问题的高维搜索空间通过线性变换映射到二维空间,在二维空间中探索原优化问题的解,从数学分析的角度给出一种线性适应度函数.算法中融入一种基于密度函数的交叉算子和变异算法,采用基于分级聚类的平均联接方式以维持Pareto最优解集个体数目.3组典型优化问题的测试表明,该算法是可行和有效的,解集分布的均匀性与多样性均较理想.     

混沌云模型多目标布谷鸟搜索算法

针对多目标布谷鸟搜索算法（MOCS）迭代后期寻优速度慢,并且容易造成局部最优等缺点,提出一种混沌云模型多目标布谷鸟搜索算法（CCMMOCS）。首先在进化过程中通过混沌理论对一般的布谷鸟巢位置在全局中寻求优化,以防落入局部最优;然后利用云模型对较好的布谷鸟巢位置局部优化来提高精度;最后将两种方法对比得到相对更好的解作为最优值以完成优化。对比误差估计值及多样性指标,由5个常用多目标测试函数仿真结果可知,CCMMOCS比传统多目标布谷鸟搜索算法、多目标粒子群算法（MOPSO）及多目标遗传（NSGA-Ⅱ）算法性能更好,Pareto前沿更接近理想曲线,分布也更均匀。     

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.     

一种基于新型差分进化模型的MOEA/D改进算法

针对MOEA/D算法中差分进化操作收敛精度不高且速度较慢的不足,提出了一种综合基于可控支配域的向量差生成策略和基于主成分的动态缩放因子的新型差分进化模型,均衡显性与隐性搜索引导;并实现了一种基于新型差分进化模型的MOEA/D改进算法（MOEA/D-iDE）。新型差分进化是借助基于可控支配域的非支配排序对邻域进行分层,根据分层信息生成与不同进化阶段相匹配的向量差,实现对种群收敛速度的显性引导;同时对决策空间进行主成分分析,动态调整差分进化缩放因子,实现对种群收敛精度的隐性引导。实验选取ZDT、DTLZ和WFG等为测试问题,以IGD+,ER作为评价指标,将MOEA/D-iDE算法与6个同类算法进行对比实验,结果表明新算法在保证多样性的同时具有更好的收敛速度与精度,从而验证了新型差分进化模型的有效性。     

量子多目标进化算法研究

本文首次将量子计算的理论用于多目标优化,提出量子多目标进化算法（QMOEA）,其采用量子位染色体表示法,利用量子门旋转策略和量子变异实现群体的进化,使用ε支配关系构造外部种群以此保持算法的较好分布性,提出基于快速排序的非劣最优解构造方法加快算法运行效率,实验表明,这种方法与经典的多目标进化算法SPEA2相比,其收敛性更好且分布更均匀     

基于IGD+S指标的高维多目标进化算法

如何有效评价个体是处理高维多目标优化问题的关键.文中提出改进的反世代距离(IGD⁺S)指标,以反世代距离(IGD)指标为原型,融合修改的反世代距离(IGD⁺)指标的弱支配性,增加无贡献个体概念,可综合评价解集收敛性和多样性.将IGD⁺S指标嵌入进化算法框架中,提出基于IGD⁺S指标的高维多目标进化算法.在环境选择过程中,根据IGD⁺S选择优良个体.实验表明,文中算法在处理DTLZ问题和WFG问题上具有良好的竞争力.     

基于Delaunay三角剖分的多目标进化算法解集分布度评价指标

系统分析目前多目标进化算法(MOEAs)分布度评价指标的特点和不足,提出一种基于Delaunay三角剖分的分布度评价指标。该指标将基于邻域和基于距离的评价思想相结合,利用Delaunay三角网最近邻与邻接性的特点实现自主邻域划分。采用空间映射的方法,有效减少MOEAs解集非支配关系对种群分布度评价的影响。测试结果表明该指标能准确反映MOEAs解集的分布性。     

Solving a tri-objective supply chain problem with modified NSGA-II algorithm

In this paper, we propose the modification of an existing Multi-Objective Evolutionary Algorithm (MOEA) known as Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The proposed algorithm has been applied on a tri-objective problem for a two echelon serial supply chain. The objectives considered are: (1) minimization of the total cost of a two-echelon serial supply chain and (2) minimization of the variance of order quantity and (3) minimization of the total inventory. The variance of order quantity is an important factor to consider since the variance of order quantity is used to measure the bullwhip effect which is one of the performance measures of a supply chain. The supply chain under consideration is assumed to consist of buyers and supplier. The production process at the supplier is an imperfect production process and thus produces defective items. A percentage of defective items are sold at a secondary market and the remaining defective items are repaired. We have introduced a mutation algorithm which has been embedded in the proposed algorithm. Since the proposed mutation algorithm is performed over the entire population, thus the mutation algorithm has caused the modification of the parts of the original NSGA-II. The results of the modified algorithm have been compared with those of the original NSGA-II and SPEA2 (Strength Pareto Evolutionary Algorithm 2) evolutionary algorithms for varying values of probability of crossover. The experimental results show that the proposed algorithm performs significantly better than the original NSGA-II and SPEA2.     

基于隐马尔可夫链的自适应MODE及应用

不同的控制参数设定和生成策略（交叉和变异）都会对多目标差分进化算法的性能产生显著影响。为实现其控制参数和变异策略的实时自适应调整,提出一种基于隐马尔可夫链的自适应多目标差分进化算法。该算法利用隐马尔可夫模型对种群信息进行分析并得到最优序列,通过最优序列与实际状态序列的对比得出变异缩放因子[F]与交叉概率[CR]的最大似然估计值,从而实现控制参数的自适应调整;同时,通过隐马尔可夫模型得到一组策略链来辅助多目标差分进化算法来选择合适的变异策略。通过与其他9种多目标进化算法在16个测试函数上的对比研究,结果表明所提算法的整体性能优于其他比较算法。最后,将该算法用于求解海铁联运能耗优化问题,所得结果能够为决策者提供多种可行方案。     

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。     

A charging-scheme decision model for electric vehicle battery swapping station using varied population evolutionary algorithms

This paper proposes a new battery swapping station (BSS) model to determine the optimized charging scheme for each incoming Electric Vehicle (EV) battery. The objective is to maximize the BSS’s battery stock level and minimize the average charging damage with the use of different types of chargers. An integrated objective function is defined for the multi-objective optimization problem. The genetic algorithm (GA), differential evolution (DE) algorithm and three versions of particle swarm optimization (PSO) algorithms have been implemented to solve the problem, and the results show that GA and DE perform better than the PSO algorithms, but the computational time of GA and DE are longer than using PSO. Hence, the varied population genetic algorithm (VPGA) and varied population differential evolution (VPDE) algorithm are proposed to determine the optimal solution and reduce the computational time of typical evolutionary algorithms. The simulation results show that the performances of the proposed algorithms are comparable with the typical GA and DE, but the computational times of the VPGA and VPDE are significantly shorter. A 24-h simulation study is carried out to examine the feasibility of the model.     

基于自适应算子的混合进化算法及其应用

提出了一种求解多目标优化最短路径问题的混合进化算法。算法中依据小生境机制生成若干个实数编码染色体的子群,各子群分别利用自适应算子的局域搜索能力找出优化解。协同进化机制能更好地保证进化的方向性和种群的多样性,基于路径表示的染色体十进制编码方法以及染色体的交叉和变异具有新颖性。该算法用于解决智能交通系统的公共交通线路换乘问题,实验结果表明了其优越性。还运用Markov随机过程理论证明了算法的收敛性。     

一种基于云模型的多目标进化算法

在多目标进化算法的基础上,提出了一种基于云模型的多目标进化算法(CMOEA).算法设计了一种新的变异算子来自适应地调整变异概率,使得算法具有良好的局部搜索能力.算法采用小生境技术,其半径按X条件云发生器非线性动态地调整以便于保持解的多样性,同时动态计算个体的拥挤距离并采用云模型参数来估计个体的拥挤度,逐个删除种群中超出的非劣解以保持解的分布性.将该算法用于多目标0/1背包问题来测试CMOEA的性能,并与目前最流行且有效的多目标进化算法NSGA-II及SPEA2进行了比较.结果表明,CMOEA具有良好的搜索性能,并能很好地维持种群的多样性,快速收敛到Pareto前沿,所获得的Pareto最优解集具有更好的收敛性与分布性.     

一种基于局部收敛估计的多目标进化算法

采用了一种基于局部收敛估计的多目标进化算法（MOEAE/LC）。在进化过程中计算连续两代归档集合群体之间的种群相似度,若在算法运行的早期其连续两代归档集的相似度小于预先设置的阈值,则认为算法有一定概率局部收敛。这时以一定概率重新初始化内部种群并且对归档集的部分个体进行变异,这样能在算法有可能陷入局部最优时产生新个体,从而提高了解集的收敛性和多样性。通过与经典的多目标算法（MOEAs）进行对比实验,实验结果表明了该算法的有效性。     

Tourism Route Recommendation Based on A Multi-Objective Evolutionary Algorithm Using Two-Stage Decomposition and Pareto Layering

Tourism route planning is widely applied in the smart tourism field. The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails, sharp peaks and disconnected regions problems, which leads to uneven distribution and weak diversity of optimization solutions of tourism routes. Inspired by these limitations, we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR) with two-stage and Pareto layering based on decom...     

基于自适应机制的多宇宙并行量子衍生进化算法

进化参量的选取对量子衍生进化算法(QEA)的优化性能有极大的影响,传统QEA在选择进化参量时并未考虑种群中个体间的差异,种群中所有个体采用相同的进化参量完成更新,导致算法在解决组合优化问题中存在收敛速度慢、容易陷入局部最优解等问题。针对这一问题,采用自适应机制调整QEA的旋转角步长和量子变异概率,算法中任意一代的任一个体的进化参量均由该个体自身适应度确定,从而保证尽可能多的进化个体能够朝着最优解方向不断靠近。此外,由于自适应量子进化算法需要评估个体的适应度,导致运算时间较长,针对这一问题则采用多宇宙机制将算法分布于多个宇宙中并行实现,从而提高算法的执行效率。通过搜索多峰函数最优解和求解背包问题测试算法性能,结果表明,与传统QEA相比,所提出算法在收敛速度、搜索全局最优解及执行速度方面具有较好的表现。     

Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure

A self-adaptive differential evolution algorithm incorporate Pareto dominance to solve multi-objective optimization problems is presented. The proposed approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. The experiments were performed using eighteen benchmark test functions. The experiment results show that, compared with three other multi-objective optimization evolutionary algorithms, the proposed MOSADE is able to find better spread of solutions with better convergence to the Pareto front and preserve the diversity of Pareto optimal solutions more efficiently.