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.     

基于进化算法的多目标优化方法

进化算法在解决多目标优化问题中有其特有的优势.首先对多目标优化问题进行了描述;然后结合研究现状讨论了目前几种主要的基于进化算法的多目标优化方法,以及它们的优缺点;最后给出了多目标进化优化算法的一些应用,以及进化多目标优化算法的未来发展方向.     

多目标优化非支配集构造方法的研究进展

多目标优化非支配集的构造是多目标进化算法研究领域的一个重要步骤,旨在研究用多目标进化算法解决多目标优化问题的效率。对多目标优化问题进行了描述并且给出了求解算法的一般框架,结合研究现状讨论了目前该领域几种主要的基于Pareto非支配集的构造算法,以及它们的计算时间复杂度;总结并展望了该领域未来的发展趋势。     

多目标进化算法及其在控制领域中的应用综述

多目标进化算法在求解多目标优化问题方面具有独特的优势.对此,介绍了多目标进化算法的基本原理,讨论了多目标进化算法的一系列改进方法;论述了近年来多目标进化算法在自动控制领域中的最新研究成果,并对其未来的发展方向进行了展望.     

基于区间可信度下界的多目标优化算法研究及应用

旨在填补多目标优化算法研究的不足,以制造业中多因素耦合作用下的多目标优化问题为研究对象,首先提出区间可信度和占优关系等概念;其次基于区间可信度和占优关系建立基于区间可信度下界的多目标优化算法;最后通过多目标数值优化对所建立的优化算法进行探究。结果显示,在γ的取值相同时,H测度与进化代数呈现正相关,可以说明随着个体进化代数的增大,所提出的基于占优可信度下界的算法得到的γ-Pareto前沿越能反映真实的Pareto前沿;通过文中建立的算法与IP-MOEA和SPGA的比较可以看出,文中所建立的基于区间可信度下界的多目标优化算法与实际情况的吻合度更高,说明所建立的算法可以填补多目标优化算法的不足。     

时空视角下的动态多目标进化算法研究综述

现实中的多目标优化问题会随着时间或环境的变化而发生改变,因此在全周期优化过程中,环境变化检测和算法响应是求解动态多目标优化问题的两大关键步骤,为此重点对动态多目标进化算法方面的研究进行总结.为有效求解动态多目标优化问题,大量追踪性能优良的动态多目标进化算法在近20年里被提出,但是很少有文献从时空角度对已有研究进行分析和报道,鉴于此,从该视角对动态多目标进化算法研究进行综述.首先介绍动态多目标优化的基本概念、问题和性能指标;然后从时空视角对近5年提出的动态多目标进化算法研究进行分别介绍;最后列出目前动态多目标进化算法方面研究存在的一些挑战,并对未来研究进行展望.     

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。     

基于自适应划分的进化多目标优化非支配个体选择策略

进化多目标优化主要研究如何利用进化计算方法求解多目标优化问题,已经成为进化计算领域的研究热点之一.多目标优化问题解的多样性主要体现在两个方面,即分布的广度和均匀程度.在分析了已有多目标进化算法保持解的多样性策略的基础上,提出了一种基于自适应划分的非支配个体选取策略.新策略根据非支配个体在目标空间的相似性程度对由当前非支配个体构成的前沿面进行自适应划分,在划分出的各区域选择最具代表性的个体,实现对非支配个体的修剪操作.为了验证新策略的有效性,将此策略应用于两类典型的多目标进化算法中,基于13个标准测试问题的仿真结果表明,自适应划分策略使最优解的均匀性和广度得到了很好的提升.     

约束优化进化算法综述

约束优化进化算法主要研究如何利用进化计算方法求解约束优化问题,是进化计算领城的一个重要研究课题.约束优化问题求解存在约束区域离散、等式约束、非线性约束等挑战,其问题的本质是如何处理可行解与不可行解的关系才能使得算法更高效.本文首先介绍了约束优化问题的定义,然后系统地分析了目前存在的约束优化方法,同时基于约束处理机制将这些方法分为罚函数法、可行性法则、随机排序法、约束处理法、多目标优化法、混合法六类,并从约束处理方法的方面对约束优化进化算法的最新研究进展进行综述.最后,指出约束优化进化算法需进一步研究的方向与关键问题.     

多目标遗传算法及在过程优化综合中的应用

化工过程的多目标优化综合问题可归结为多目标混合整数非线性规划(MOMINLP)模型的求解,求解方法主要有数学规划法和多目标进化算法。以多目标遗传算法(MOGA)为代表的进化算法被认为是特别适合求解此类问题。遗传算法大多用于单目标问题的优化,近十几年来将遗传算法应用到多目标优化的研究得到了很大的发展。本文对多目标遗传算法的一些重要概念、发展历程进行了回顾。针对化工过程的模型特点,对MOGA在过程综合中的应用研究进行了讨论,并认为混合遗传算法应是求解此类问题的有效算法。     

基于多目标进化算法的MOEA/D权重向量产生方法

在进化多目标优化研究领域,多目标优化是指对含有2个及以上目标的多目标问题的同时优化,其在近些年来受到越来越多的关注。随着MOEA/D的提出,基于聚合的多目标进化算法得到越来越多的研究,对MOEA/D算法的改进已有较多成果,但是很少有成果研究MOEA/D中权重的产生方法。提出一种使用多目标进化算法产生任意多个均匀分布的权重向量的方法,将其应用到MOEA/D,MSOPS和NSGA-III中,对这3个经典的基于聚合的多目标进化算法进行系统的比较研究。通过该类算法在DTLZ测试集、多目标旅行商问题MOTSP上的优化结果来分别研究该类算法在连续性问题、组合优化问题上的优化能力,以及使用矩形测试问题使得多目标进化算法的优化结果在决策空间可视化。实验结果表明,没有一个算法能适用于所有特性的问题。然而,MOEA/D采用不同聚合函数的两个算法MOEA/D_Tchebycheff和MOEA/D_PBI在多数情况下的性能比MSOPS和NSGA-III更好。     

Pareto最优概念的多目标进化算法综述

群体搜索策略和群体间个体之间的信息交换是进化算法在解决多目标优化问题上的两大优势.目前,基于Pareto最优概念的多目标进化算法已成为多目标优化问题研究的主流方向.详细介绍了该领域的经典算法,特别对各种算法在种群快速收敛并均匀分布于问题的非劣最优域上所采取的策略进行了阐述,并归纳了算法性能评估中需要深入研究的问题.     

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.     

进化算法在复杂网络中的应用综述

复杂网络作为现今科学研究中的一个热点学科,在过去20年里得到了巨大的发展.现实中大量的复杂的交互系统,比如互联网、交通运输网、神经网络等都可以抽象为复杂网络,以进行系统的分析和研究.进化算法作为优化工具应用于复杂网络的不同领域的各个任务中,如网络社团结构的检测任务、网络动力学中的鲁棒性优化任务、网络传播中关键节点的搜寻任务等.本文首先对复杂网络和进化算法相关的基础知识进行了全面的概述,重点讨论了复杂网络中目标优化的研究进展,针对不同任务对优化目标及其具体应用展开了详细介绍,同时,对算法的性能评价指标进行了概述.此外,本文通过一系列实验展示了单/多目标优化算法在复杂网络优化问题上的性能表现,以及部分目标之间的相关性关系.最后对复杂网络中优化问题未来的研究动向进行了展望,为今后研究人员开展进化计算和复杂网络相结合的相关研究提供一些思路.     

A preference multi-objective optimization based on adaptive rank clone and differential evolution

Evolutionary multi-objective optimization (EMO) algorithms have been used in various real-world applications. However, most of the Pareto domination based multi-objective optimization evolutionary algorithms are not suitable for many-objective optimization. Recently, EMO algorithm incorporated decision maker’s preferences became a new trend for solving many-objective problems and showed a good performance. In this paper, we first use a new selection scheme and an adaptive rank based clone scheme to exploit the dynamic information of the online antibody population. Moreover, a special differential evolution (DE) scheme is combined with directional information by selecting parents for the DE calculation according to the ranks of individuals within a population. So the dominated solutions can learn the information of the non-dominated ones by using directional information. The proposed method has been extensively compared with two-archive algorithm, light beam search non-dominated sorting genetic algorithm II and preference rank immune memory clone selection algorithm over several benchmark multi-objective optimization problems with from two to ten objectives. The experimental results indicate that the proposed algorithm achieves competitive results.     

约束进化算法及其应用研究综述

约束优化问题广泛存在于科学研究和工程实践中,其对应的约束优化进化算法也成为了进化领域的重要研究方向。约束优化进化算法的本质问题是如何有效地利用不可行解和可行解的信息,平衡目标函数和约束条件,使得算法更加高效。首先对约束优化问题进行定义;然后详细分析了目前主流的约束进化算法,同时,基于不同的约束处理机制,将这些机制分为约束和目标分离法、惩罚函数法、多目标优化法、混合法和其他算法,并对这些方法进行了详细的分析和总结;接着指出约束进化算法亟待解决的问题,并明确指出未来需要进一步研究的方向;最后对约束进化算法在工程优化、电子和通信工程、机械设计、环境资源配置、科研领域和管理分配等方面的应用进行了介绍。     

Convergence of multi-objective evolutionary algorithms to a uniformly distributed representation of the Pareto front

In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent.     

A multi-objective differential evolutionary algorithm for constrained multi-objective optimization problems with low feasible ratio

Most current evolutionary multi-objective optimization (EMO) algorithms perform well on multi-objective optimization problems without constraints, but they encounter difficulties in their ability for constrained multi-objective optimization problems (CMOPs) with low feasible ratio. To tackle this problem, this paper proposes a multi-objective differential evolutionary algorithm named MODE-SaE based on an improved epsilon constraint-handling method. Firstly, MODE-SaE self-adaptively adjusts the epsilon level in line with the maximum and minimum constraint violation values of infeasible individuals. It can prevent epsilon level setting from being unreasonable. Then, the feasible solutions are saved to the external archive and take part in the population evolution by a co-evolution strategy. Finally, MODE-SaE switches the global search and local search by self-switching parameters of search engine to balance the convergence and distribution. With the aim of evaluating the performance of MODE-SaE, a real-world problem with low feasible ratio in decision space and fourteen bench-mark test problems, are used to test MODE-SaE and five other state-of-the-art constrained multi-objective evolution algorithms. The experimental results fully demonstrate the superiority of MODE-SaE on all mentioned test problems, which indicates the effectiveness of the proposed algorithm for CMOPs which have low feasible ratio in search space.     

一种基于Pareto最优概念和神经网络混合策略的多目标进化算法

基于Pareto最优的多目标进化算法得到了广泛地应用,但不适用于目标函数为非解析式的情况。基于神经网络和Pareto最优的联合策略,提出了一种解决此类问题的新方法：首先采用神经网络对历史数据进行学习,建立有效的神经网络模型来代替目标函数解析式;然后将神经网络模型嵌入多目标进化算法,进行进化计算;最后,将本文方法应用于卷烟配方比例掺配问题。实验结果表明,该方法优于传统方法,能较好地解决问题。     

Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling

This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Pareto front. On the other hand, the main negative effect is the increase in the computation time per generation. Thus, the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next, we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: the strength Pareto evolutionary algorithm and revised nondominated sorting genetic algorithm. Finally, we demonstrate that a local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.