基于多目标粒子群算法的PID控制器设计

随着对控制系统的要求越来越高,进行比例积分微分(Proortion Integration Differentiation,PID)控制器的设计的时候应该同时考虑到系统时域指标和频域指标,常规的PID整定方法往往很难实现.为解决上述问题,采用多目标粒子群算法进行PID控制器参数的设计,算法将系统的超调量、上升时间和稳定时间作为目标函数,频域指标作为约束条件.算法的运算结果为一组Pareto最优解,运行者可以根据当前对系统的要求从中选取合适的解.通过与常规PID整定方法和采用单目标粒子群算法的方法进行比较,证明了改进方法的有效性.     

基于Pareto熵的多目标粒子群优化算法

粒子群优化算法因形式简洁、收敛快速和参数调节机制灵活等优点,同时一次运行可得到多个解,且能逼近非凸或不连续的Pareto最优前端,因而被认为是求解多目标优化问题最具潜力的方法之一.但当粒子群优化算法从单目标问题扩展到多目标问题时,Pareto最优解集的存储与维护、全局和个体最优解的选择以及开发与开采的平衡等问题亦随之出现.通过目标空间变换方法,采用Pareto前端在被称为平行格坐标系统的新目标空间中的分布熵及差熵评估种群的多样性及进化状态,并以此为反馈信息来设计进化策略,使得算法能够兼顾近似Pareto前端的收敛性和多样性.同时,引入格占优和格距离密度的概念来评估Pareto最优解的个体环境适应度,以此建立外部档案更新方法和全局最优解选择机制,最终形成了基于Pareto熵的多目标粒子群优化算法.实验结果表明：在IGD性能指标上,与另外8种对等算法相比,该算法在由ZDT和DTLZ系列组成的12个多目标测试问题集中表现出了显著的性能优势.     

基于多目标粒子群的非线性系统PID控制器设计

PID控制器自产生以来,一直是工业生产过程中应用最广泛、最成熟的控制器。随着控制品质的要求越来越高,综合考虑系统的准确性、稳定性、快速性等多个性能指标,基于改进的Pareto最优排序多目标粒子群算法,给出一个适用于一类非线性系统的PID控制器设计方法。采用经典的非线性倒立摆系统作为PID被控对象进行仿真,将超调量和调节时间两个目标作为多目标粒子群算法的目标,求出一组Pareto最优控制参数,通过跟踪控制得到精确稳定的控制效果。     

基于差分进化粒子群算法的多目标无功优化

针对电力系统有功网损最小、电压水平最好和电压稳定裕度最大的多目标无功优化问题,提出一种基于差分进化的改进多目标粒子群优化算法。该算法通过对Pareto最优解集的差分进化来增加Pareto最优解的多样性,通过拥挤距离来控制精英集中非支配解的分布,以提高对种群空间的均匀采集;采用擂台赛法则构造多目标Pareto最优解集,较大程度的提高了算法的运行效率;自适应惯性权重和加速度因子的动态变化可增强算法的全局搜索能力。将该算法在IEEE14、IEEE30节点标准测试系统上进行了无功优化仿真,结果表明,基于差分进化的改进多目标粒子群优化算法能够在保持Pareto最优解的多样性的同时具有较好的收敛性能,为多目标无功优化提供了一种新的方法。     

支持向量机算法多目标模型选择

为适应支持向量机（Support Vector Machine,SVM）算法应用过程中的不同性能指标要求,将SVM算法的模型选择问题作为一个多目标优化（Multi-Object Optimization,MOO）问题进行处理。以改进的粒子群优化（Particle Swarm Optimization,PSO）算法对该多目标优化问题进行求解,得到其Pareto解集,在具体应用中根据实际需要从Pareto解集中选择适合的最优解作为支持向量机算法参数,实现支持向量机算法的模型选择。在几个数据集上的仿真实验表明,该方法能够较快地得到Pareto解集,解集中的参数组合能够满足对支持向量机算法速度和泛化能力的不同要求。     

具有约束多目标优化的进化算法

针对带有约束多目标优化问题,提出一种多目标优化进化算法。在选择过程中,采用约束的Pareto支配和聚集距离定义适应值,根据适应值挑选出有代表性的个体。在变异过程中,沿着权重梯度方向搜索来寻找可行的Pareto最优解。最后,采用两个数值算例测草算法的性能,结果表明该算法能获得多目标约束优化问题的可行Pareto最优解并且具有较好的分散性。     

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。     

基于最大最小适应度函数的多目标粒子群算法

针对多目标优化问题提出了一种基于最大最小适应度函数（F_maximin）的粒子群算法，将此算法简称为IMPSO。它在求解多目标问题的非劣解前沿（Pareto Front）时表现出很好的性能。通过经典测试函数计算表明该算法保证收敛到多目标优化问题的Pareto最优前沿；同时，使用两个性能指标（GD和Diversity）验证了此算法优于其他的多目标粒子群优化算法。     

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.     

CMOPSO/D算法的发酵过程补料优化控制

为了改善发酵过程补料优化控制的性能指标,提出一种基于改进的分解多目标粒子群优化算法的发酵过程补料优化控制方法。将发酵过程的多目标优化问题分解为若干单目标优化问题,对每个单目标优化问题应用2个粒子群协同搜索最优解,其中一个种群对连接向量进行搜索,改进了连接向量的更新方式,另一个种群将决策空间分解,使用不同种群对不同维度的解向量进行优化,并在进化过程中使用前一个种群的最优解构成完整的解向量评价每个子群的最优解,提高了最优解评价的准确性,保证算法收敛到全局最优解。将该算法用到在工业酵母发酵过程模型中,对补料速率进行优化控制,并同时优化2个性能指标,即菌体浓度最大化和乙醇浓度最小化,并与基本的分解粒子群优化算法的优化结果作对比,该算法获得的Pareto前沿在基本分解粒子群优化算法获得的Pareto前沿下方,并且分布更加完整。实验证明该算法能够获得最优补料速率,使工业酵母发酵过程的菌体浓度提高了约9%,乙醇浓度降低了约为15%,为发酵过程补料优化控制提供了一种有效方法。     

一类新型动态多目标鲁棒进化优化方法

传统动态多目标优化问题（Dynamic multi-objective optimization problems,DMOPs）的求解方法,通常需要在新环境下,通过重新激发寻优过程,获得适应该环境的Pareto最优解.这可能导致较高的计算代价和资源成本,甚至无法在有限时间内执行该优化解.由此,提出一类寻找动态鲁棒Pareto最优解集的进化优化方法.动态鲁棒Pareto解集是指某一时刻下的Pareto较优解可以以一定稳定性阈值,逼近未来多个连续动态环境下的真实前沿,从而直接作为这些环境下的Pareto解集,以减小计算代价.为合理度量Pareto解的环境适应性,给出了时间鲁棒性和性能鲁棒性定义,并将其转化为两类鲁棒优化模型.引入基于分解的多目标进化优化方法和无惩罚约束处理方法,构建了动态多目标分解鲁棒进化优化方法.特别是基于移动平均预测模型实现了未来动态环境下适应值的多维时间序列预测.基于提出的两类新型性能评价测度,针对8个典型动态测试函数的仿真实验,结果表明该方法得到满足决策者精度要求,且具有较长平均生存时间的动态鲁棒Pareto最优解.     

Applying multi-objective ant colony optimization algorithm for solving the unequal area facility layout problems

The unequal area facility layout problem (UA-FLP) which deals with the layout of departments in a facility comprises of a class of extremely difficult and widely applicable multi-objective optimization problems with constraints arising in diverse areas and meeting the requirements for real-world applications. Based on the heuristic strategy, the problem is first converted into an unconstrained optimization problem. Then, we use a modified version of the multi-objective ant colony optimization (MOACO) algorithm which is a heuristic global optimization algorithm and has shown promising performances in solving many optimization problems to solve the multi-objective UA-FLP. In the modified MOACO algorithm, the ACO with heuristic layout updating strategy which is proposed to update the layouts and add the diversity of solutions is a discrete ACO algorithm, with a difference from general ACO algorithms for discrete domains which perform an incremental construction of solutions but the ACO in this paper does not. We propose a novel pheromone update method and combine the Pareto optimization based on the local pheromone communication and the global search based on the niche technology to obtain Pareto-optimal solutions of the problem. In addition, the combination of the local search based on the adaptive gradient method and the heuristic department deformation strategy is applied to deal with the non-overlapping constraint between departments so as to obtain feasible solutions. Ten benchmark instances from the literature are tested. The experimental results show that the proposed MOACO algorithm is an effective method for solving the UA-FLP.     

Differential evolution based on ε-domination and orthogonal design method for power environmentally-friendly dispatch

This paper proposes a differential evolution algorithm based on ε-domination and orthogonal design method (ε-ODEMO) to solve power dispatch problem considering environment protection and saving energy. Besides the operation costs of thermal power plant, contaminative gas emission is also optimized as an objective. In the proposed algorithm, ε-dominance is adopted to make genetic algorithm obtain a good distribution of Pareto-optimal solutions in a small computational time, and the orthogonal design method can generate an initial population of points that are scattered uniformly over the feasible solution space, these modify the differential evolution algorithm (DE) to make it suit for multi-objective optimization (MOO) problems and improve its performance. A test hydrothermal system is used to verify the feasibility and effectiveness of the proposed method. Compared with other methods, the results obtained demonstrate the effectiveness of the proposed algorithm for solving the power environmentally-friendly dispatch problem.     

Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm

Selection of optimum machining parameters is vital to the machining processes in order to ensure the quality of the product, reduce the machining cost, increasing the productivity and conserve resources for sustainability. Hence, in this work a posteriori multi-objective optimization algorithm named as Non-dominated Sorting Teaching–Learning-Based Optimization (NSTLBO) is applied to solve the multi-objective optimization problems of three machining processes namely, turning, wire-electric-discharge machining and laser cutting process and two micro-machining processes namely, focused ion beam micro-milling and micro wire-electric-discharge machining. The NSTLBO algorithm is incorporated with non-dominated sorting approach and crowding distance computation mechanism to maintain a diverse set of solutions in order to provide a Pareto-optimal set of solutions in a single simulation run. The results of the NSTLBO algorithm are compared with the results obtained using GA, NSGA-II, PSO, iterative search method and MOTLBO and are found to be competitive. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal set of solutions will help the decision maker in volatile scenarios and are useful for real production systems.     

基于幂变换的多目标进化算法MOEA?D权重设计方法

在多目标最优化问题中,如何求解一组均匀散布在前沿界面上的有效解具有重要意义.MOEA?D是最近出现的一种杰出的多目标进化算法,当前沿界面的形状是某种已知的类型时,MOEA?D使用高级分解的方法容易求出均匀散布在前沿界面上的有效解.然而,多目标优化问题的前沿界面的形状通常是未知的.为了使MOEA?D能求出一般多目标优化问题的均匀散布的有效解,利用幂函数对目标进行数学变换,使变换后的多目标优化问题的前沿界面在算法的进化过程中逐渐接近希望得到的形状,提出了一种求解一般的多目标优化问题的MOEA?D算法的权重设计方法,并且讨论了经过数学变换后前沿界面的保距性问题.采用建议的权重设计方法,MOEA?D更容易求出一般的多目标优化问题均匀散布的有效解.数值结果验证了算法的有效性.     

A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems

This paper proposes a self-organized speciation based multi-objective particle swarm optimizer (SS-MOPSO) to locate multiple Pareto optimal solutions for solving multimodal multi-objective problems. In the proposed method, the speciation strategy is used to form stable niches and these niches/subpopulations are optimized to search and maintain Pareto-optimal solutions in parallel. Moreover, a self-organized mechanism is proposed to improve the efficiency of the species formulation as well as the performance of the algorithm. To maintain the diversity of the solutions in both the decision and objective spaces, SS-MOPSO is incorporated with the non-dominated sorting scheme and special crowding distance techniques. The performance of SS-MOPSO is compared with a number of the state-of-the-art multi-objective optimization algorithms on fourteen test problems. Moreover, the proposed SS-MOSPO is also employed to solve a real-life problem. The experimental results suggest that the proposed algorithm is able to solve the multimodal multi-objective problems effectively and shows superior performance by finding more and better distributed Pareto solutions.     

An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.     

Conservative multi-objective optimization considering design robustness and tolerance: a quality engineering design approach

Methods of multi-objective optimization are proposed to account for tolerance of design variable and variation in problem parameter. The post-optimization effort is initiated from deterministic Pareto-optimal solutions that were obtained from NSGA-II. The successive process to determine search directions and step sizes toward conservative multi-objective solutions was conducted by design of experiments to determine the worst design that had the highest constraint violation. The signal-to-noise (S/N) ratio was also employed to represent the robustness of constrained objective functions under parameter variation. Structural optimization was explored to accommodate both design tolerance and parameter variation and further apply S/N ratio in conservative multi-objective optimization.     

动态多目标优化:测试函数和算法比较

生活中存在大量的动态多目标优化问题,应用进化算法求解动态多目标优化问题受到越来越多的关注,而动态多目标测试函数对算法的评估起着重要的作用.在已有动态多目标测试函数的基础上,设计一组新的动态多目标测试函数.Pareto最优解集和Pareto前沿面的不同变化形式影响着动态多目标测试函数的难易程度,通过引入Pareto最优解集形状的变化,结合已有的Pareto最优解集移动模式,设计一组测试函数集.基于提出的测试函数集,对3个算法进行测试,仿真实验结果表明,所设计的函数给3个算法带来了挑战,并展现出算法的优劣.     

Development of Pareto-based evolutionary model integrated with dynamic goal programming and successive linear objective reduction

This study investigates the coupling effects of objective-reduction and preference-ordering schemes on the search efficiency in the evolutionary process of multi-objective optimization. The difficulty in solving a many-objective problem increases with the number of conflicting objectives. Degenerated objective space can enhance the multi-directional search toward the multi-dimensional Pareto-optimal front by eliminating redundant objectives, but it is difficult to capture the true Pareto-relation among objectives in the non-optimal solution domain. Successive linear objective-reduction for the dimensionality-reduction and dynamic goal programming for preference-ordering are developed individually and combined with a multi-objective genetic algorithm in order to reflect the aspiration levels for the essential objectives adaptively during optimization. The performance of the proposed framework is demonstrated in redundant and non-redundant benchmark test problems. The preference-ordering approach induces the non-dominated solutions near the front despite enduring a small loss in diversity of the solutions. The induced solutions facilitate a degeneration of the Pareto-optimal front using successive linear objective-reduction, which updates the set of essential objectives by excluding non-conflicting objectives from the set of total objectives based on a principal component analysis. Salient issues related to real-world problems are discussed based on the results of an oil-field application.