基于自变量简约的大规模稀疏多目标优化

现有的大多数进化算法在求解大规模优化问题时性能会随决策变量维数的增长而下降。通常,多目标优化的Pareto有效解集是自变量空间的一个低维流形,该流形的维度远小于自变量空间的维度。鉴于此,提出一种基于自变量简约的多目标进化算法求解大规模稀疏多目标优化问题。该算法通过引入局部保持投影降维,保留原始自变量空间中的局部近邻关系,并设计一个归档集,将寻找到的非劣解存入其中进行训练,以提高投影的准确性。将该算法与四种流行的多目标进化算法在一系列测试问题和实际应用问题上进行了比较。实验结果表明,所提算法在解决稀疏多目标问题上具有较好的效果。因此,通过自变量简约能降低问题的求解难度,提高算法的搜索效率,在解决大规模稀疏多目标问题方面具有显著的优势。     

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.     

多目标自适应和声搜索算法

提出了一种利用Pareto支配来求解多目标优化问题的自适应和声搜索算法（MOSAHS）。该算法利用外部种群来保存非支配解,为了保持非支配解的多样性,提出了一种基于拥挤度的删除策略,这个策略能较好地度量个体的拥挤程度。用5个标准测试函数对其进行测试,并与其他多目标优化算法相比较。实验结果表明,与其他的算法相比,提出的算法在逼近性和均匀性两方面都有很好的表现,是一种有效的多目标和声搜索算法。     

An iterated local search for the multi-objective permutation flowshop scheduling problem with sequence-dependent setup times

Due to its simplicity yet powerful search ability, iterated local search (ILS) has been widely used to tackle a variety of single-objective combinatorial optimization problems. However, applying ILS to solve multi-objective combinatorial optimization problems is scanty. In this paper we design a multi-objective ILS (MOILS) to solve the multi-objective permutation flowshop scheduling problem with sequence-dependent setup times to minimize the makespan and total weighted tardiness of all jobs. In the MOILS, we design a Pareto-based variable depth search in the multi-objective local search phase. The search depth is dynamically adjusted during the search process of the MOILS to strike a balance between exploration and exploitation. We incorporate an external archive into the MOILS to store the non-dominated solutions and provide initial search points for the MOILS to escape from local optima traps. We compare the MOILS with several multi-objective evolutionary algorithms (MOEAs) shown to be effective for treating the multi-objective permutation flowshop scheduling problem in the literature. The computational results show that the proposed MOILS outperforms the MOEAs.     

基于决策变量关系的动态多目标优化算法

动态多目标优化问题(DMOPs)需要进化算法跟踪不断变化的Pareto最优前沿,从而在检测到环境变化时能够及时有效地做出响应.为了解决上述问题,提出一种基于决策变量关系的动态多目标优化算法.首先,通过决策变量对收敛性和多样性贡献大小的检测机制将决策变量分为收敛性相关决策变量(CV)和多样性相关决策变量(DV),对不同类型决策变量采用不同的优化策略;其次,提出一种局部搜索多样性维护机制,使个体在Pareto前沿分布更加均匀;最后,对两部分产生的组合个体进行非支配排序构成新环境下的种群.为了验证DVR的性能,将DVR与3种动态多目标优化算法在15个基准测试问题上进行比较,实验结果表明, DVR算法相较于其他3种算法表现出更优的收敛性和多样性.     

An objective reduction algorithm using representative Pareto solution search for many-objective optimization problems

In recent years, many-objective optimization problems (i.e. more than three objectives) have attracted the interests of many researchers. The main difficulties of many-objective optimization problems lie in high computational cost, stagnation in search process, etc. It is almost impossible to design an algorithm effective for all problems. However, for some problems, especially for problems with redundant objectives, it is possible to design effective algorithms by removing the redundant objectives and keeping the non-redundant objectives so that the original problem becomes the one with much fewer objectives. To do so, first, a multi-objective evolutionary algorithm-based decomposition is adopted to generate a smaller number of representative non-dominated solutions widely distributed on the Pareto front. Then the conflicting objective pairs are identified through these non-dominated solutions, and the redundant objectives are determined by these pairs and then removed. Based on these, a fast non-redundant objectives generation algorithm is proposed in this paper. Finally, the experiments are conducted on a set of benchmark test problems and the results indicate the effectiveness and efficiency of the proposed algorithm.     

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。     

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.     

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.     

考虑安全约束的连退生产过程多目标操作优化

针对连退生产过程中经常出现的薄料带钢跑偏问题,建立考虑安全约束的连退生产过程多目标操作优化模型,并针对问题特点提出一种基于分类和多种群竞争协调的多目标进化算法(MOEA-CMCC).在算法中引入具有不同进化策略的多个种群以增强搜索的多样性,并在多种群之间引入竞争机制和信息共享的协调机制以提高算法的鲁棒性;通过对外部档案集中的解进行分类并在类内进行局部搜索,以保证外部档案集的分散性和算法的收敛速度.基于Benchmark问题的实验结果表明,所提出的算法具有较好的收敛性和分散性;对连退操作优化问题的实验结果表明,所提出的算法能够有效求解该问题.     

一种基于个体密度估算的多目标优化演化算法

通过在目标空间中利用目标本身信息估算个体k最近邻距离之和,作为个体的密度信息,根据个体的密度信息对群体中过剩的非劣解进行逐个去除,以便更好地维护解的多样性,由此给出了一种基于个体密度估算的多目标优化演化算法IDEMOEA。用这个算法对几个典型的多目标优化函数进行测试。测试结果表明,算法IDEMOEA求解多目标优化问题是行之有效的。     

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) provides an excellent algorithmic framework for solving multi-objective optimization problems. It decomposes a target problem into a set of scalar sub-problems and optimizes them simultaneously. Due to its simplicity and outstanding performance, MOEA/D has been widely studied and applied. However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions. It is well-known that MO-VRPTW is a challenging problem and has very few Pareto optimal solutions. To address this problem, a novel selection operator is designed in this work to enhance the original MOEA/D for dealing with MO-VRPTW. Moreover, three local search methods are introduced into the enhanced algorithm. Experimental results indicate that the proposed algorithm can obtain highly competitive results on Solomon׳s benchmark problems. Especially for instances with long time windows, the proposed algorithm can obtain more diverse set of non-dominated solutions than the other algorithms. The effectiveness of the proposed selection operator is also demonstrated by further analysis.     

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.     

基于参考线的预测策略求解动态多目标优化问题

为了快速且准确地跟踪动态多目标优化问题变化的Pareto前沿与Pareto解集,在可以不依靠历史信息的前提下,提出一种基于参考线预测策略的求解动态多目标优化问题的算法(RLPS).该算法通过记录每个参考线关联的种群个体在环境变化初始时和个体自主进化一小段时间后个体位置的变化,预测最优个体所在方向,同时在该方向上均匀分布若干延伸个体,选出每个参考线关联的非支配个体作为当前环境下的引导个体,在选出的引导个体邻域内随机产生若干伴随个体增加种群多样性.通过5个标准动态测试函数对该算法测试,并与两个现有算法作对比分析,实验结果表明所提出的算法具有更快地响应环境变化的能力.     

A self-adaptive multi-objective harmony search algorithm based on harmony memory variance

Although harmony search (HS) algorithm has shown many advantages in solving global optimization problems, its parameters need to be set by users according to experience and problem characteristics. This causes great difficulties for novice users. In order to overcome this difficulty, a self-adaptive multi-objective harmony search (SAMOHS) algorithm based on harmony memory variance is proposed in this paper. In the SAMOHS algorithm, a modified self-adaptive bandwidth is employed, moreover, the self-adaptive parameter setting based on variation of harmony memory variance is proposed for harmony memory considering rate (HMCR) and pitch adjusting rate (PAR). To solve multi-objective optimization problems (MOPs), the proposed SAMOHS uses non-dominated sorting and truncating procedure to update harmony memory (HM). To demonstrate the effectiveness of the SAMOHS, it is tested with many benchmark problems and applied to solve a practical engineering optimization problem. The experimental results show that the SAMOHS is competitive in convergence performance and diversity performance, compared with other multi-objective evolutionary algorithms (MOEAs). In the experiment, the impact of harmony memory size (HMS) on the performance of SAMOHS is also analyzed.     

改进的约束优化多目标遗传算法及工程应用

利用多目标法处理约束条件,提出一种改进的基于多目标优化的遗传算法用于求解约束优化问题。该算法将约束优化问题转化为两个目标的多目标优化问题; 利用庄家法构造非劣个体,将种群分为支配子种群和非支配子种群,以一定概率分别从支配子种群和非支配子种群中选择个体进行算术交叉操作,引导个体逐步向极值点靠近,增强算法的局部搜索能力,对非支配子种群进行多样性变异操作。8个标准测试函数和3个工程应用的仿真实验结果表明了该算法的有效性。     

Learning the Search Range for Evolutionary Optimization in Dynamic Environments

Conventional evolutionary algorithms operate in a fixed search space with limiting parameter range, which is often predefined via a priori knowledge or trial and error in order to ‘guess’ a suitable region comprising the global optimal solution. This requirement is hard, if not impossible, to fulfil in many real-world optimization problems since there is often no clue of where the desired solutions are located in these problems. Thus, this paper proposes an inductive–deductive learning approach for single- and multi-objective evolutionary optimization. The method is capable of directing evolution towards more promising search regions even if these regions are outside the initial predefined space. For problems where the global optimum is included in the initial search space, it is capable of shrinking the search space dynamically for better resolution in genetic representation to facilitate the evolutionary search towards more accurate optimal solutions. Validation results based on benchmark optimization problems show that the proposed inductive–deductive learning is capable of handling different fitness landscapes as well as distributing nondominated solutions uniformly along the final trade-offs in multi-objective optimization, even if there exist many local optima in a high-dimensional search space or the global optimum is outside the predefined search region. Received 15 January 2001 / Revised 8 June 2001 / Accepted in revised form 24 July 2001     

Simple heuristics-based selection of guides for multi-objective PSO with an application to electrical distribution system planning

In multi-objective particle swarm optimization (MOPSO), a proper selection of local guides significantly influences detection of non-dominated solutions in the objective/solution space and, hence, the convergence characteristics towards the Pareto-optimal set. This paper presents an algorithm based on simple heuristics for selection of local guides in MOPSO, named as HSG-MOPSO (Heuristics-based-Selection-of-Guides in MOPSO). In the HSG-MOPSO, the set of potential guides (in a PSO iteration) consists of the non-dominated solutions (which are normally stored in an elite archive) and some specifically chosen dominated solutions. Thus, there are two types of local guides in the HSG-MOPSO, i.e., non-dominated and dominated guides; they are named so as to signify whether the chosen guide is a non-dominated or a dominated solution. In any iteration, a guide, from the set of available guides, is suitably selected for each population member. Some specified proportion of the current population members follow their respective nearest non-dominated guides and the rest follow their respective nearest dominated guides. The proposed HSG-MOPSO is firstly evaluated on a number of multi-objective benchmark problems along with investigations on the controlling parameters of the guide selection algorithm. The performance of the proposed method is compared with those of two well-known guide selection methods for evolutionary multi-objective optimization, namely the Sigma method and the Strength Pareto Evolutionary Algorithm-2 (SPEA2) implemented in PSO framework. Finally, the HSG-MOPSO is evaluated on a more involved real world problem, i.e., multi-objective planning of electrical distribution system. Simulation results are reported and analyzed to illustrate the viability of the proposed guide selection method for MOPSO.     

Vehicle power train optimization using multi-objective bird swarm algorithm

In this paper, a multi-objective bird swarm algorithm (MOBSA) is proposed to cope with multi-objective optimization problems. The algorithm is explored based on BSA which is an evolutionary algorithm suitable for single objective optimization. In this paper, non-dominated sorting approach is used to distinguish optimal solutions and parallel coordinates is applied to evaluate the distribution density of non-dominated solution and further update the external archive when it is full to overflowing, which ensure faster convergence and more widespread of Pareto front. Then, the MOBSA is adopted to optimize benchmark problems. The results demonstrate that MOBSA gets better performance compared with NSGA-II and MOPSO. Since a vehicle power train problem could be treated as a typical multi-objective optimization problem with constraints, with integration of constrained non-dominated solution, MOBSA is adopted to acquire optimal gear ratios and optimize vehicle power train. The results compared with other popular algorithm prove the proposed algorithm is more suitable for constrained multi-objective optimization problem in engineering field.

     

New mechanism for archive maintenance in PSO-based multi-objective feature selection

In classification problems, a large number of features are typically used to describe the problem’s instances. However, not all of these features are useful for classification. Feature selection is usually an important pre-processing step to overcome the problem of “curse of dimensionality”. Feature selection aims to choose a small number of features to achieve similar or better classification performance than using all features. This paper presents a particle swarm Optimization (PSO)-based multi-objective feature selection approach to evolving a set of non-dominated feature subsets which achieve high classification performance. The proposed algorithm uses local search techniques to improve a Pareto front and is compared with a pure multi-objective PSO algorithm, three well-known evolutionary multi-objective algorithms and a current state-of-the-art PSO-based multi-objective feature selection approach. Their performances are examined on 12 benchmark datasets. The experimental results show that in most cases, the proposed multi-objective algorithm generates better Pareto fronts than all other methods.