基于多点非均匀变异的多目标极值优化算法研究

多目标进化算法因其在解决含有多个矛盾目标函数的多目标优化问题中的强大处理能力,正受到越来越多的关注与研究。极值优化作为一种新型的进化算法,已在各种离散优化、连续优化测试函数以及工程优化问题中得到了较为成功的应用,但有关多目标EO算法的研究却十分有限。本文将采用Pareto优化的基本原理引入到极值优化算法中,提出一种求解连续多目标优化问题的基于多点非均匀变异的多目标极值优化算法。通过对六个国际公认的连续多目标优化测试函数的仿真实验结果表明：本文提出算法相比NSGA-II、 PAES、SPEA和SPEA2等经典多目标优化算法在收敛性和分布性方面均具有优势。     

Constrained multi-objective optimization algorithms: Review and comparison with application in reinforced concrete structures

Engineering design problems are often multi-objective in nature, which means trade-offs are required between conflicting objectives. In this study, we examine the multi-objective algorithms for the optimal design of reinforced concrete structures. We begin with a review of multi-objective optimization approaches in general and then present a more focused review on multi-objective optimization of reinforced concrete structures. We note that the existing literature uses metaheuristic algorithms as the most common approaches to solve the multi-objective optimization problems. Other efficient approaches, such as derivative-free optimization and gradient-based methods, are often ignored in structural engineering discipline. This paper presents a multi-objective model for the optimal design of reinforced concrete beams where the optimal solution is interested in trade-off between cost and deflection. We then examine the efficiency of six established multi-objective optimization algorithms, including one method based on purely random point selection, on the design problem. Ranking and consistency of the result reveals a derivative-free optimization algorithm as the most efficient one.     

Multi-objective immune algorithm with Baldwinian learning

By replacing the selection component, a well researched evolutionary algorithm for scalar optimization problems (SOPs) can be directly used to solve multi-objective optimization problems (MOPs). Therefore, in most of existing multi-objective evolutionary algorithms (MOEAs), selection and diversity maintenance have attracted a lot of research effort. However, conventional reproduction operators designed for SOPs might not be suitable for MOPs due to the different optima structures between them. At present, few works have been done to improve the searching efficiency of MOEAs according to the characteristic of MOPs. Based on the regularity of continues MOPs, a Baldwinian learning strategy is designed for improving the nondominated neighbor immune algorithm and a multi-objective immune algorithm with Baldwinian learning (MIAB) is proposed in this study. The Baldwinian learning strategy extracts the evolving environment of current population by building a probability distribution model and generates a predictive improving direction by combining the environment information and the evolving history of the parent individual. Experimental results based on ten representative benchmark problems indicate that, MIAB outperforms the original immune algorithm, it performs better or similarly the other two outstanding approached NSGAII and MOEA/D in solution quality on most of the eight testing MOPs. The efficiency of the proposed Baldwinian learning strategy has also been experimentally investigated in this work.     

一种新型约束多目标帝国竞争算法

针对约束多目标优化问题，提出了一种基于约束违背程度和Pareto支配的有效约束处理策略，并设计了一种新型多目标帝国竞争算法（MOICA）.该算法采用一种简化的初始帝国构建过程，在同化过程引入了向外部档案内非劣解学习的机制，并基于帝国势力新定义的帝国竞争新方法以获取问题高质量的解.选用了7个测试问题CF1~CF7进行计算实验并和多种算法进行对比.计算结果表明， MOICA在求解约束多目标优化问题方面具有较强的搜索能力和优势.     

基于混合预测策略与改进社会学习优化算法的动态多目标优化方法

近年来,国内外学者针对基于预测的动态多目标优化算法开展了深入研究,并提出了一系列有效的算法,然而已有的研究工作通常采用单一的预测策略,使得算法不能有效地应对剧烈的环境变化。针对上述问题,提出了一种基于混合预测策略与改进社会学习优化算法的动态多目标优化方法。具体地,当环境发生变化时,该方法首先基于代表性个体预测策略生成一部分群体;其次,基于拐点预测策略生成一部分新群体,特别地,为了提高种群的多样性,根据算法迭代的历史信息和环境变化情况随机地生成一定数量的新个体;为了提高问题的求解效率,对社会学习优化算法进行了改进,为每个进化空间设计了适用于动态多目标优化问题的算子;最后,将混合预测策略与改进的社会学习优化算法结合,构成了一种新的动态多目标优化方法。以FDA、DMOP和F函数集作为实验测试函数集,与四种代表性算法进行了性能对比;并以反向世代距离(inverted generational distance, IGD)对该方法的性能进行了深入的分析。实验结果表明所提方法具有较好的收敛性和鲁棒性。     

Multi-objective approach based on grammar-guided genetic programming for solving multiple instance problems

Multiple instance learning (MIL) is considered a generalization of traditional supervised learning which deals with uncertainty in the information. Together with the fact that, as in any other learning framework, the classifier performance evaluation maintains a trade-off relationship between different conflicting objectives, this makes the classification task less straightforward. This paper introduces a multi-objective proposal that works in a MIL scenario to obtain well-distributed Pareto solutions to multi-instance problems. The algorithm developed, Multi-Objective Grammar Guided Genetic Programming for Multiple Instances (MOG3P-MI), is based on grammar-guided genetic programming, which is a robust tool for classification. Thus, this proposal combines the advantages of the grammar-guided genetic programming with benefits provided by multi-objective approaches. First, a study of multi-objective optimization for MIL is carried out. To do this, three different extensions of MOG3P-MI are designed and implemented and their performance is compared. This study allows us on the one hand, to check the performance of multi-objective techniques in this learning paradigm and on the other hand, to determine the most appropriate evolutionary process for MOG3P-MI. Then, MOG3P-MI is compared with some of the most significant proposals developed throughout the years in MIL. Computational experiments show that MOG3P-MI often obtains consistently better results than the other algorithms, achieving the most accurate models. Moreover, the classifiers obtained are very comprehensible.     

一种基于偏好的多目标调和遗传算法

最近涌现了各种进化方法来解决多目标优化问题,多数方法使用Pareto优胜关系作为选择策略而没有采用偏好信息.这些算法不能有效处理目标数目许多时的优化问题.通过在不同准则之间引入偏好来解决该问题,提出一种多目标调和遗传算法MOCGA(multi-objective concordance genetic algorithm).当同时待优化的目标数目增加时,根据决策者提供的信息使用弱优胜关系进行个体优劣的比较.这种算法被证明为能收敛至全局最优.对于目标数目为很多的优化问题,测试实验结果表明了这种新算法的有效性.     

Hybrid multi-objective shape design optimization using Taguchi’s method and genetic algorithm

This research is based on a new hybrid approach, which deals with the improvement of shape optimization process. The objective is to contribute to the development of more efficient shape optimization approaches in an integrated optimal topology and shape optimization area with the help of genetic algorithms and robustness issues. An improved genetic algorithm is introduced to solve multi-objective shape design optimization problems. The specific issue of this research is to overcome the limitations caused by larger population of solutions in the pure multi-objective genetic algorithm. The combination of genetic algorithm with robust parameter design through a smaller population of individuals results in a solution that leads to better parameter values for design optimization problems. The effectiveness of the proposed hybrid approach is illustrated and evaluated with test problems taken from literature. It is also shown that the proposed approach can be used as first stage in other multi-objective genetic algorithms to enhance the performance of genetic algorithms. Finally, the shape optimization of a vehicle component is presented to illustrate how the present approach can be applied for solving multi-objective shape design optimization problems.     

一种求解多目标优化问题的进化算法混合框架

为了提高多目标优化算法的求解性能,提出一种启发式的基于种群的全局搜索与局部搜索相结合的多目标进化算法混合框架.该框架采用模块化、系统化的设计思想,不同模块可以采用不同策略构成不同的算法.采用经典的改进非支配排序遗传算法(NSGA-II)和基于分解的多目标进化算法(MOEA/D)作为进化算法的模块算法来验证所提混合框架的有效性.数值实验表明,所提混合框架具有良好性能,可以兼顾算法求解的多样性和收敛性,有效提升现有多目标进化算法的求解性能.     

A Multi-Objective Integer Melody Search Algorithm

There are a number of algorithms for the solution of continuous optimization problems. However, many practical design optimization problems use integer design variables instead of continuous. These types of problems cannot be handled by using continuous design variables-based algorithms. In this paper, we present a multi-objective integer melody search optimization algorithm (MO-IMS) for solving multi-objective integer optimization problems, which take design variables as integers. The proposed algorithm is a modified version of single-objective melody search (MS) algorithm, which is an innovative optimization algorithm, inspired by basic concepts applied in harmony search (HS) algorithm. Results show that MO-IMS has better performance in solving multi-objective integer problems than the existing multi-objective integer harmony search algorithm (MO-IHS). Performance of proposed algorithm is evaluated by using various performance metrics on test functions. The simulation results show that the proposed MO-IMS can be a better technique for solving multi-objective problems having integer decision variables.     

Hypervolume-based multi-objective local search

This paper presents a multi-objective local search, where the selection is realized according to the hypervolume contribution of solutions. The HBMOLS algorithm proposed is inspired from the IBEA algorithm, an indicator-based multi-objective evolutionary algorithm proposed by Zitzler and Künzli in 2004, where the optimization goal is defined in terms of a binary indicator defining the selection operator. In this paper, we use the indicator optimization principle, and we apply it to an iterated local search algorithm, using hypervolume contribution indicator as selection mechanism. The methodology proposed here has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on the multi-objective flow shop problem and the multi-objective quadratic assignment problem, using the hypervolume contribution selection as well as two different binary indicators which were initially proposed in the IBEA algorithm. Experimental results indicate that the HBMOLS algorithm is highly effective in comparison with the algorithms based on binary indicators.     

LeCMPSO算法求解异构无人机协同多任务重分配问题

无人机系统在军事领域有着广泛应用, 由于战场环境复杂多变, 无人机遭遇突发状况后需进行任务重分配.异构无人机是指多种类型的无人机, 可完成单一无人机无法完成的多类型复杂任务, 异构无人机协同多任务重分配问题约束条件复杂且包含混合变量, 现有多目标优化算法不能有效处理此类问题. 为高效求解上述问题, 本文构建多约束异构无人机协同多任务重分配问题模型, 提出一种学习引导的协同多目标粒子群优化算法(LeCMPSO), 该算法引入基于先验知识的初始化策略和基于历史信息学习的粒子更新策略, 能有效避免不可行解的产生并提升算法的搜索效率. 通过在4组实例上的仿真实验表明, 与其他典型的协同进化多目标优化算法相比, 所提算法在解集的多样性、收敛性及搜索时间方面均具有较好的性能.     

无参分组大规模变量的多目标算法研究

目前大多数多目标优化算法没有考虑到决策变量之间的交互性,只是将所有变量当作一个整体进行优化。随着决策变量的增加,多目标优化算法的性能会急剧下降。针对上述问题,提出一种无参变量分组的大规模变量的多目标优化算法(MOEA/DWPG)。该算法将协同优化与基于分解的多目标优化算法(MOEA/D)相结合,设计了一种不含参数的分组方式来提高交互变量分组的精确性,提高了算法处理含有大规模变量的多目标优化算法的性能。实验结果表明,该算法在大规模变量多目标问题上明显优于MOEA/D及其它先进算法。     

正交设计的E占优策略求解高维多目标优化问题研究

在实际应用中,传统多目标演化算法面临着高维多目标优化问题。针对这一缺陷,提出正交E占优(Orthogo-nality E-dominant,OE)策略。在OE策略的理论优越性设计的基础上,改进了当前5种具有代表性的演化多目标优化算法。改进前后的算法求解DTLZ1-6(20)测试问题的数值对比试验显示,OE策略改进后的算法在不同程度上提高了算法求解高维多目标优化问题的效果,从而证实了OE策略对演化多目标优化算法改进的有效性。     

Continuous probabilistic model building genetic network programming using reinforcement learning

Recently, a novel probabilistic model-building evolutionary algorithm (so called estimation of distribution algorithm, or EDA), named probabilistic model building genetic network programming (PMBGNP), has been proposed. PMBGNP uses graph structures for its individual representation, which shows higher expression ability than the classical EDAs. Hence, it extends EDAs to solve a range of problems, such as data mining and agent control. This paper is dedicated to propose a continuous version of PMBGNP for continuous optimization in agent control problems. Different from the other continuous EDAs, the proposed algorithm evolves the continuous variables by reinforcement learning (RL). We compare the performance with several state-of-the-art algorithms on a real mobile robot control problem. The results show that the proposed algorithm outperforms the others with statistically significant differences.     

基于反向学习和种群引导的多目标蝗虫优化算法

为了解决多目标优化的相关问题,提出了求解多目标的蝗虫优化算法,结合单个目标的蝗虫优化算法的搜寻机制、帕累托优势以及拥挤度策略,并在算法中应用种群引导和高斯变异算子,加入了反向学习机制。将所提出的算法与经典的MOPSO、MOCS、MOGOA和MOWOA算法进行了比较,比较结果表明,所提出的改进多目标蝗虫优化算法具有良好的鲁棒性,所求得的解分布更均匀,收敛更快速,是一种有着良好应用前景的多目标进化算法。     

A multi-objective membrane algorithm guided by the skin membrane

Multi-objective optimization problems exist widely in the field of engineering and science. Many nature-inspired methods, such as genetic algorithms, particle swarm optimization algorithms and membrane computing model based algorithms, were proposed to solve the problems. Among these methods, membrane computing model based algorithms, also termed membrane algorithms, are becoming a current research hotspot because the successful linkage of membrane computing and evolutionary algorithms. In the past years, a lot of effective multi-objective membrane algorithms have been designed, where the skin membrane was often only used as an archive to store good solutions. In this paper, we propose an effective multi-objective membrane algorithm guided by the skin membrane, named SMG-MOMA, where the information of solutions stored in the skin membrane is used to guide the evolution of internal membranes. A skin membrane guiding strategy is suggested by allocating the solutions in skin membrane to internal membranes. Experimental results on ZDT and DTLZ benchmark multi-objective problems show that the proposed algorithm outperforms the-state-of-the-art multi-objective optimization algorithms.     

Hybrid algorithms for the twin–screw extrusion configuration problem

The twin-screw configuration problem (TSCP) arises in the context of polymer processing, where twin-screw extruders are used to prepare polymer blends, compounds or composites. The goal of the TSCP is to define the configuration of a screw from a given set of screw elements. The TSCP can be seen as a sequencing problem as the order of the screw elements on the screw axis has to be defined. It is also inherently a multi-objective problem since processing has to optimize various conflicting parameters related to the degree of mixing, shear rate, or mechanical energy input among others. In this article, we develop hybrid algorithms to tackle the bi-objective TSCP. The hybrid algorithms combine different local search procedures, including Pareto local search and two phase local search algorithms, with two different population-based algorithms, namely a multi-objective evolutionary algorithm and a multi-objective ant colony optimization algorithm. The experimental evaluation of these approaches shows that the best hybrid designs, combining Pareto local search with a multi-objective ant colony optimization approach, outperform the best algorithms that have been previously proposed for the TSCP.     

A generalized learning algorithm for an automaton operating in amultiteacher environment

Learning algorithms for an automaton operating in a multiteacher environment are considered. These algorithms are classified based on the number of actions given as inputs to the environments and the number of responses (outputs) obtained from the environments. In this paper, we present a general class of learning algorithm for multi-input multi-output (MIMO) models. We show that the proposed learning algorithm is absolutely expedient and epsilon-optimal in the sense of average penalty. The proposed learning algorithm is a generalization of Baba's GAE algorithm and has applications in solving, in a parallel manner, multi-objective optimization problems in which each objective function is disturbed by noise.