Pareto-MEC算法及其收敛性分析

介绍了一种新的多目标进化算法——Pareto-MEC。将基本MEC和Pareto思想结合起来处理多目标问题。提出了局部Pareto最优解集与局部Pareto最优态集概念，并利用概率论的基本理论证明了趋同过程产生的序列强收敛于局部Pareto最优态集。数值试验验证了Pareto-MEC算法的有效性。     

基于粒子记忆体的多目标微粒群算法*

针对多目标微粒群算法(MOPSO)解的多样性分布问题,提出一种基于粒子记忆体的多目标微粒群算法(dp-MOPSO)。dp-MOPSO算法为每个微粒分配一个记忆体,保存寻优过程中搜索到的非支配pbest集,以避免搜索信息的丢失。采用外部存档保存种群搜索到的所有Pareto解,并引入动态邻域的策略从外部存档中选择全局最优解。利用几个典型的多目标测试函数对dp-MOPSO算法的性能进行测试,并与两种著名的多目标进化算法m-DNPSO、SPEA2进行比较。实验结果表明,dp-MOPSO算法可以更好地逼近真实Pareto沿,同时所得Pareto解分布更均匀。     

SP-MEC算法的收敛性分析

进化算法求解多目标优化问题具有独特的优势。SP-MEC是一种新的利用思维进化算法(MEC)解决多目标优化问题的算法,数值实验结果验证了它的可行性与有效性。文章利用概率论的基本理论对其收敛性进行分析,提出局部Pareto最优解集、局部Pareto最优态集及趋同过程产生的序列强收敛的概念,证明了在满足一定条件下趋同过程产生的序列强收敛于局部Pareto最优态集。     

混合多目标粒子群优化算法在热精轧负荷分配优化中的应用

通过对热精轧负荷分配过程的分析,选取负荷均衡、板形良好和轧制功率最低为目标,建立了热精轧负荷分配多目标优化模型.为了提高多目标优化算法解集的分布性和收敛性,提出了一种混合多目标粒子群优化算法(HMOPSO),该算法根据Pareto支配关系得到Pareto前沿进而保证种群收敛;采用分解策略维护外部存档,该策略首先根据Pareto前沿求出上界点对目标空间进行归一化处理,然后对种群进行分区处理进而保证种群的分布性能.仿真结果表明,HMOPSO的收敛性和分布性都好于MOPSO和d MOPSO;采用模糊多属性决策的方法从Pareto最优解集中选择一个Pareto最优解,通过与经验负荷分配方法相比,表明该Pareto最优解可以使轧制方案更加合理.     

基于动态拥挤距离的混合多目标免疫优化算法

多目标免疫优化算法的研究目标是种群均匀分布于优化问题的非劣最优域并使算法快速收敛。为进一步提高多目标优化问题非支配解集合的分布均匀性和收敛性,提出了一种基于动态拥挤距离的混合多目标免疫优化算法。该算法基于动态拥挤距离来对个体进行比较和更新操作,从而保持最终解集的均匀分布,同时借鉴经典差分进化算法中的变异引导算子来加强免疫优化算法的局部搜索能力并提高搜索精度。基于5个经典测试函数的仿真结果表明, 与其他几种有效的多目标优化算法相比,所提算法不仅在求得Pareto最优解集的逼近性、均匀性和宽广性上有明显优势,而且收敛速度也有较大的改进和提高。     

A multi-objective genetic algorithm for yard crane scheduling problem with multiple work lines

Due to increasing ships and quay cranes, container terminals operations become more and more busy. The traditional handling based on work line is converted into pool strategy, namely loading and unloading containers with multiple work lines are operating simultaneously. In the paper we discuss the yard crane scheduling problem with multiple work lines in container terminals. We develop a multi-objective 0-1 integer programming model considering the minimum total completion time of all yard cranes and the maximization balanced distribution of the completion time at the same time. With the application of adaptive weight GA approach, the problem can be solved by a multi-objective hybrid genetic algorithm and the Pareto solutions can be finally got. Using the compromised approach, the nearest feasible solution to ideal solution is chosen to be the best compromised Pareto optimal solution of the multi-objective model. The numerical example proves the applicability and effectiveness of the proposed method to the multi-objective yard crane scheduling problem.     

Multi-objective biogeography based optimization for optimal PMU placement

The paper proposes a multi-objective biogeography based optimization (MO-BBO) algorithm to design optimal placement of phasor measurement units (PMU) which makes the power system network completely observable. The simultaneous optimization of the two conflicting objectives such as minimization of the number of PMUs and maximization of measurement redundancy are performed. The Pareto optimal solution is obtained using the non-dominated sorting and crowding distance. The compromised solution is chosen using a fuzzy based mechanism from the Pareto optimal solution. Simulation results are compared with Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Non-dominated Sorting Differential Evolution (NSDE). Developed PMU placement method is illustrated using IEEE standard systems to demonstrate the effectiveness of the proposed algorithm.     

一种用于多目标优化的混合粒子群优化算法

将粒子群算法与局部优化方法相结合,提出了一种混合粒子群多目标优化算法（HMOPSO）。该算法针对粒子群局部优化性能较差的缺点,引入多目标线搜索与粒子群算法相结合的策略,以增强粒子群算法的局部搜索能力。HMOPSO首先运行PSO算法,得到近似的Pareto最优解;然后启动多目标线搜索,发挥传统数值优化算法的优势,对其进行进一步的优化。数值实验表明,HMOPSO具有良好的全局优化性能和较强的局部搜索能力,同时HMOPSO所得的非劣解集在分散性、错误率和逼近程度等量化指标上优于MOPSO。     

Multi-objective optimization of double suction centrifugal pump using Kriging metamodels

This paper proposes a new multi-objective optimization method for a family of double suction centrifugal pumps with various blade shapes, using a Simulation-Kriging model-Experiment (SKE) approach. The Kriging metamodel is established to approximate the characteristic performance functions of a pump, namely, the efficiency and required net positive suction head (NPSHr). Hence, the two objectives are to maximize the efficiency and simultaneously to minimize NPSHr. The Non-dominated Sorting Genetic Algorithm II (NSGA II) and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) have been applied to the multi-objective optimization problem, respectively. The Pareto solution set is obtained by a more effective and efficient manner of the two multi-objective optimization algorithms. A tradeoff optimal design point is selected from the Pareto solution set by means of a robust design based on Monte Carlo simulations, and the optimal solution is further compared with the value of the physical prototype test. The results show that the solution of the proposed multi-objective optimization method is in line with the experiment test.     

Approximate multi-objective optimization using conservative and feasible moving least squares method: application to automotive knuckle design

The original version of the moving least squares method (MLSM) does not always ensure solution feasibility for nonlinear and/or non-convex functions in the context of meta-model-based approximate optimization. The paper explores a new implementation of MLSM that ensures the conservative feasibility of Pareto optimal solutions in non-dominated sorting genetic algorithm (NSGA-II)-based approximate multi-objective optimization. We devised a ‘conservative and feasible MLSM’ (CF-MLSM) to realize the conservativeness and feasibility of multi-objective Pareto optimal solutions for both unconstrained and constrained problems. We verified the usefulness of our proposed approach by exploring strength-based sizing optimization of an automotive knuckle component under bump and brake loading constraints.     

Evolutionary multi criteria design optimization of robot grippers

This paper explores the use of intelligent techniques to obtain optimum geometrical dimensions of a robot gripper. The optimization problem considered is a non-linear, complex, multi-constraint and multicriterion one. Three robot gripper configurations are optimized. The aim is to find Pareto optimal front for a problem that has five objective functions, nine constraints and seven variables. The problem is divided into three cases. Case 1 has first two objective functions, the case 2 considers last three objective functions and case 3 deals all the five objective functions. Intelligent optimization algorithms namely Multi-objective Genetic Algorithm (MOGA), Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-objective Differential Evolution (MODE) are proposed to solve the problem. Normalized weighting objective functions method is used to select the best optimal solution from Pareto optimal front. Two multi-objective performance measures (solution spread measure (SSM) and ratio of non-dominated individuals (RNIs)) are used to evaluate the strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimizer overhead (OO) and algorithm effort are used to find the computational effort of MOGA, NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analyzed.     

多目标进化算法的污水处理过程优化控制

污水处理过程中,能耗与出水水质是两个相互矛盾的评价指标.为了找出这两个目标的最优解,本文在基于分解的多目标进化算法(MOEA/D)的基础上进行改进,期望用更少的进化次数得到分布均匀的近似帕累托前沿.针对MOEA/D算法每一次产生的新解,本文中改进的算法从所有子问题中找到最合适新解的子问题,并在其邻域范围内进行种群的更替,在原本子问题的基础上进行二次寻优,提高子代利用率,进而用更少的迭代次数找到优化问题中的近似帕累前沿.实验证明,该算法明显减少了找到帕累托前沿的步数,使得MOEA/D算法的性能明显提升,在污水处理过程优化问题中达到了优化目标的作用.     

Using the Manhattan distance for computing the multiobjective Markov chains problem

This paper presents a novel method for computing the multi-objective problem in the case of a metric state space using the Manhattan distance. The problem is restricted to a class of ergodic controllable finite Markov chains. This optimization approach is developed for converging to an optimal solution that corresponds to a strong Pareto optimal point in the Pareto front. The method consists of a two-step iterated procedure: (a) the first step consists on an approximation to a strong Pareto optimal point and, (b) the second step is a refinement of the previous approximation. We formulate the problem adding the Tikhonov's regularization method to ensure the convergence of the cost-functions to a unique strong point into the Pareto front. We prove that there exists an optimal solution that is a strong Pareto optimal solution and it is the closest solution to the utopian point of the Pareto front. The proposed solution is validated theoretically and by a numerical example considering the vehicle routing planning problem.     

结合Kriging和物理规划的多目标代理优化算法

遗传算法处理高耗时且具有黑箱性的工程优化问题效率不足。为了提高工程优化效率，结合Kriging代理优化和物理规划，提出了基于Kriging和物理规划的多目标代理优化算法。在处理多目标问题时，使用物理规划将多目标问题转换成单目标问题，再使用Kriging代理优化对单目标问题进行求解。通过两个多目标数值算例和一个工程实例对提出的算法进行验证。结果表明，提出的算法能够求出符合偏好设置的Pareto最优解，且算法的效率更高。     

Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Evolutionary multi-criterion optimization (EMO) algorithms emphasize non-dominated and less crowded solutions in a population iteratively until the population converges close to the Pareto optimal set. During the search process, non-dominated solutions are differentiated only by their local crowding or contribution to hypervolume or using a similar other metric. Thus, during evolution and even at the final iteration, the true convergence behavior of each non-dominated solutions from the Pareto optimal set is unknown. Recent studies have used Karush Kuhn Tucker (KKT) optimality conditions to develop a KKT Proximity Measure (KKTPM) for estimating proximity of a solution from Pareto optimal set for a multi-objective optimization problem. In this paper, we integrate KKTPM with a recently proposed EMO algorithm to enhance its convergence properties towards the true Pareto optimal front. Specifically, we use KKTPM to identify poorly converged non-dominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Assisted by the KKTPM, the modified algorithm is designed in a way that maintains the total number of function evaluations as low as possible while making use of local search where it is most needed. Simulations on both constrained and unconstrained multi- and many objectives optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms.     

基于MOPSO算法的卫星共形阵列天线多波束形成

针对共形阵列天线多波束方向图综合问题,提出一种基于最大方向性系数方法得到初始非劣解的多目标粒子群算法,求解满足多个期望波束和低副瓣要求的Pareto最优解。算法首先采用多目标分解策略,由多个单波束最优解的加权线性组合得到近最优解的非劣解。然后结合该非劣解,基于粒子空间和目标空间同时约束的局部搜寻策略,使用多目标粒子群算法优化多个波束,并降低副瓣。仿真结果表明,该算法有效地实现了卫星共形阵列天线的多波束形成和低副瓣,且能快速得到Pareto最优解分布。     

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。     

基于ADEMO/D-ENS的飞控系统性能指标分配方法

针对目前飞行控制系统设计中部件/组件性能参数的确定存在反复多次迭代的问题,对飞控系统性能指标的分配进行了研究。通过对性能指标分配过程进行建模,确定了分配过程属于多目标优化问题。基于Tchebycheff方法将多目标优化问题转化为单目标优化子问题集合,基于自适应差分进化算法得到的单目标优化子问题集合的最优解即为多目标优化问题Pareto最优解,同时采用惩罚因子保持差分进化算法种群的多样性。通过仿真与性能指标未分配的系统进行对比,结果表明分配后的系统具有更好的动态性和跟踪性,说明所提出的分配方法是正确的、可行的,并能够为工程应用提供一定的理论指导。     

基于随机黑洞和逐步淘汰策略的多目标粒子群优化算法

提出一种基于随机黑洞粒子群算法(RBH-PSO) 和逐步淘汰策略的多目标粒子群优化(MRBHPSO-SE) 算法. 利用RBH-PSO 全局优化能力强和收敛速度快的优点逼近Pareto 最优解; 为了避免拥挤距离排序策略的缺陷, 提出逐步淘汰策略, 并将其应用到下一代粒子的选择策略中. 同时, 动态选择领导粒子, 运用动态惯性权重系数和变异操作 来增强种群全局寻优能力, 以及避免早熟收敛. 利用具有不同特点的测试函数进行验证, 结果表明, 与同类算法相比, 该算法具有较高的精度并兼顾优化解的多样性.

     

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。