基于项集归减的高维频繁高效用项集挖掘多目标优化方法

频繁高效用项集挖掘是数据挖掘的一项重要任务,挖掘到的项集由支持度和效用这2个指标衡量.在一系列用于解决这类问题的方法中,进化多目标方法能够提供1组高质量解以满足不同用户的需求,避免传统算法中支持度和效用的阈值难以确定的问题.但是已有多目标算法多采用0-1编码,使得决策空间的维度与数据集中项数成正比,因此,面对高维数据集会出现维度灾难问题.鉴于此,设计一种项集归减策略,通过在进化过程中不断对不重要项进行归减以减小搜索空间.基于此策略,进而提出一种基于项集归减的高维频繁高效用项集挖掘多目标优化算法(IR-MOEA),并针对可能存在的归减过度或未归减到位的个体提出基于学习的种群修复策略用以调整进化方向.此外还提出一种基于项集适应度的初始化策略,使得算法在进化初期生成利于后期进化的稀疏解.多个数据集上的实验结果表明,所提出算法优于现有的多目标优化算法,特别是在高维数据集上.     

Intelligent design of induction motors by multiobjective fuzzy genetic algorithm

In this paper an approach using multi-objective fuzzy genetic algorithm (MFGA) for optimum design of induction motors is presented. Single-objective genetic algorithm optimization is compared with the MFGA optimization. The efficiency of those algorithms is investigated on motor’s performance. The comparison results show that MFGA is able to find more compromise solutions and is promising for providing the optimum design. Besides, a design tool is developed to evaluate and analysis the steady-state characteristics of induction motors.     

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。     

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。     

Multi-objective reactive power market clearing in competitive electricity market using HFMOEA

This paper presents an application of a hybrid fuzzy multi-objective evolutionary algorithm (HFMOEA) for solving a highly constraint, mixed integer type, complex multi-objective reactive power market clearing (RPMC) problem for the competitive electricity market environment. In HFMOEA based multi-objective optimization approach, based on the output of a fuzzy logic controller crossover and mutation probabilities are varied dynamically. It enhances stochastic search capabilities of HFMOEA. In multi-objective RPMC optimization framework, two objective functions namely the total payment function (TPF) for reactive power support from generators and synchronous condensers and the total real transmission loss (TRTL) are minimized simultaneously for clearing the reactive power market. The proposed HFMOEA based multi-objective RPMC scheme is tested on a standard IEEE 24 bus reliability test system and its performance is compared with five other multi-objective evolutionary techniques such as MOPBIL, NSGA-II, UPS-EMOA and SPEA-2 and a new extended form of NSGA (ENSGA-II). Applying all these six evolutionary techniques, a detailed statistical analysis using T-test and boxplots is carried out on three performance metrics (spacing, spread and hypervolume) data for RPMC problem. The obtained simulation results confirm the overall superiority of HFMOEA to generate better Pareto-optimal solutions with higher convergence rate as compared to above mentioned algorithms. Further, TPF and TRTL values corresponding to the best compromise solutions are obtained using said multi-objective evolutionary techniques. These values are compared with one another to take better market clearing decisions in competitive electricity environment.     

进化高维多目标优化算法研究综述

首先针对常规多目标优化算法求解高维多目标优化时面临的选择压力衰减问题进行论述;然后针对该问题,按照选择机制的不同详细介绍基于Pareto支配、基于分解策略和基于性能评价指标的典型高维多目标优化算法,并分析各自的优缺点;接着立足于一种全新的性能评价指标-----R2指标,给出R2指标的具体定义,介绍基于R2指标的高维多目标优化算法,分析此类算法的本质,并按照R2指标的4个关键组成部分进行综述;最后,发掘其存在的潜在问题以及未来发展空间.     

基于多目标进化算法的多距离聚类研究

传统的聚类算法通常基于单一的距离度量而设计,如何将多种距离度量有机融合在一起是当前面临的一个挑战。提出了一种基于多目标进化算法的多距离度量聚类框架(multiobjective evolutionary multiple distance measure clustering,MOMDC),并使用欧氏距离和Path距离来设计实际框架。该框架首先将数据集分别用两种距离测度预聚类,而后将预聚类结果做合并,以降低问题的规模;其次分别计算子类间的两种距离关系;最后使用多目标进化算法在两种距离空间中并行聚类。在多目标进化算法设计中,使用实数-标签的编码方式来设计染色体,并且设计了基于两种距离测度的两个适应度函数对染色体进行评估。最终将MOMDC与其他几种经典算法在大量的数据集上进行实验对比。实验表明,该框架对不同分布的数据集均能取得良好的结果。     

Biologically inspired probabilistic coverage for mobile sensor networks

Coupling sensors in a sensor network with mobility mechanism can boost the performance of wireless sensor networks (WSNs). In this paper, we address the problem of self-deploying mobile sensors to reach high coverage. The problem is modeled as a multi-objective optimization that simultaneously minimizes two contradictory parameters; the total sensor moving distance and the total uncovered area. In order to resolve the aforementioned deployment problem, this study investigates the use of biologically inspired mechanisms, including evolutionary algorithms and swarm intelligence, with their state-of-the-art algorithms. Unlike most of the existing works, the coverage parameter is expressed as a probabilistic inference model due to uncertainty in sensor readings. To the best of our knowledge, probabilistic coverage of mobile sensor networks has not been addressed in the context of multi-objective bio-inspired algorithms. Performance evaluations on deployment quality and deployment cost are measured and analyzed through extensive simulations, showing the effectiveness of each algorithm under the developed objective functions. Simulations reveal that only one multi-objective evolutionary algorithm; the so-called multi-objective evolutionary algorithm with decomposition survives to effectively tackle the probabilistic coverage deployment problem. It gathers more than 78 % signals from all of the targets (and in some cases reaches 100 % certainty). On the other hand, non-dominated sorting genetic algorithm II, multi-objective particle swarm optimization, and non-dominated sorting particle swarm optimization show inferior performance down to 16–32 %, necessitating further modifications in their internal mechanisms.     

一种基于模拟退火的多目标Memetic算法

为了改善多目标进化算法的搜索效率，提出了基于模拟退火的多目标Memetic算法．此算法根据Pareto占优关系评价个体适应值，采用模拟退火进行局部搜索，并结合交叉算子和基于网格密度的选择机制改善算法的收敛速度和解的均衡分布．flowshop调度问题算例的仿真结果表明，基于模拟退火的多目标Memetic算法能够产生更接近Pareto前沿的近似集．     

An adaptive evolutionary multi-objective approach based on simulated annealing

A multi-objective optimization problem can be solved by decomposing it into one or more single objective subproblems in some multi-objective metaheuristic algorithms. Each subproblem corresponds to one weighted aggregation function. For example, MOEA/D is an evolutionary multi-objective optimization (EMO) algorithm that attempts to optimize multiple subproblems simultaneously by evolving a population of solutions. However, the performance of MOEA/D highly depends on the initial setting and diversity of the weight vectors. In this paper, we present an improved version of MOEA/D, called EMOSA, which incorporates an advanced local search technique (simulated annealing) and adapts the search directions (weight vectors) corresponding to various subproblems. In EMOSA, the weight vector of each subproblem is adaptively modified at the lowest temperature in order to diversify the search toward the unexplored parts of the Pareto-optimal front. Our computational results show that EMOSA outperforms six other well established multi-objective metaheuristic algorithms on both the (constrained) multi-objective knapsack problem and the (unconstrained) multi-objective traveling salesman problem. Moreover, the effects of the main algorithmic components and parameter sensitivities on the search performance of EMOSA are experimentally investigated.     

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems (LSMOPs) pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces. While evolutionary algorithms are good at solving small-scale multi-objective optimization problems, they are criticized for low efficiency in converging to the optimums of LSMOPs. By contrast, mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems, but they have difficulties in finding diverse solutions for LSMOPs. Currently, how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored. In this paper, a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method. On the one hand, conjugate gradients and differential evolution are used to update different decision variables of a set of solutions, where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front. On the other hand, objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions, and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent. In comparison with state-of-the-art evolutionary algorithms, mathematical programming methods, and hybrid algorithms, the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.      

A Novel Quantum - inspired Multi - Objective Evolutionary Algorithm Based on Cloud Theory

In the previous papers,Quantum-inspired multi-objective evolutionary algorithm(QMEA) was proved to be better than conventional genetic algorithms for multi-objective optimization problem.To improve the quality of the non-dominated set as well as the diversity of population in multi-objective problems,in this paper,a Novel Cloud -based quantum -inspired multi-objective evolutionary Algorithm(CQMEA) is proposed.CQMEA is proposed by employing the concept and principles of Cloud theory.The algorithm utilizes the random orientation and stability of the cloud model,uses a self-adaptive mechanism with cloud model of Quantum gates updating strategy to implement global search efficient.By using the self-adaptive mechanism and the better solution which is determined by the membership function uncertainly,Compared with several well-known algorithms such as NSGA-Ⅱ,QMEA.Experimental results show that(CQMEA) is more effective than QMEA and NSGA -Ⅱ.     

A multi-objective cellular grey wolf optimizer for hybrid flowshop scheduling problem considering noise pollution

The hybrid flowshop scheduling problem (HFSP) has been widely studied in the past decades. The most commonly used criterion is production efficiency. Green criteria, such as energy consumption and carbon emission, have attracted growing attention with the improvement of the environment protection awareness. Limited attention has been paid to noise pollution. However, noise pollution can lead to health and emotion disorder. Thus, this paper studies a multi-objective HFSP considering noise pollution in addition to production efficiency and energy consumption. First, we formulate a new mixed-integer programming model for this multi-objective HFSP. To realize the green scheduling, one energy conservation/noise reduction strategy is embedded into this model. Then, a novel multi-objective cellular grey wolf optimizer (MOCGWO) is proposed to address this problem. The proposed MOCGWO integrates the merits of cellular automata (CA) for diversification and variable neighborhood search (VNS) for intensification, which balances exploration and exploitation. Finally, to validate the efficiency and effectiveness of the proposed MOCGWO, we compare our proposal with other well-known multi-objective evolutionary algorithms by conducting comparison experiments. The experimental results show that the proposed MOCGWO is significantly better than its competitors on this problem.     

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.     

Fixed-Parameter Evolutionary Algorithms and the Vertex Cover Problem

In this paper, we consider multi-objective evolutionary algorithms for the Vertex Cover problem in the context of parameterized complexity. We consider two different measures for the problem. The first measure is a very natural multi-objective one for the use of evolutionary algorithms and takes into account the number of chosen vertices and the number of edges that remain uncovered. The second fitness function is based on a linear programming formulation and proves to give better results. We point out that both approaches lead to a kernelization for the Vertex Cover problem. Based on this, we show that evolutionary algorithms solve the vertex cover problem efficiently if the size of a minimum vertex cover is not too large, i.e., the expected runtime is bounded by O(f(OPT)?n ^c ), where c is a constant and f a function that only depends on OPT. This shows that evolutionary algorithms are randomized fixed-parameter tractable algorithms for the vertex cover problem.     

一种基于混合交叉策略的多目标演化算法

演化算法是求解多目标优化问题(MOP)重要而有效的方法,而应用演化策略、技巧是改善解性能的重要途径。论文叙述了多目标优化问题的有关概念,结合已有算法中的方法,设计了基于两种交叉操作相互结合的多目标演化算法(MOEAHC),该算法不仅具有较高的计算效率,而且能够保持解的多样性分布。测试结果表明该算法的良好性能。     

A polar-based guided multi-objective evolutionary algorithm to search for optimal solutions interested by decision-makers in a logistics network design problem

In practical multi-objective optimization problems, respective decision-makers might be interested in some optimal solutions that have objective values closer to their specified values. Guided multi-objective evolutionary algorithms (guided MOEAs) have been significantly used to guide their evolutionary search direction toward these optimal solutions using by decision makers. However, most guided MOEAs need to be iteratively and interactively evaluated and then guided by decision-makers through re-formulating or re-weighting objectives, and it might negatively affect the algorithms performance. In this paper, a novel guided MOEA that uses a dynamic polar-based region around a particular point in objective space is proposed. Based on the region, new selection operations are designed such that the algorithm can guide the evolutionary search toward optimal solutions that are close to the particular point in objective space without the iterative and interactive efforts. The proposed guided MOEA is tested on the multi-criteria decision-making problem of flexible logistics network design with different desired points. Experimental results show that the proposed guided MOEA outperforms two most effective guided and non-guided MOEAs, R-NSGA-II and NSGA-II.     

基于全局排序的高维多目标优化研究

目标数超过4的高维多目标优化是目前进化多目标优化领域求解难度最大的问题之一,现有的多目标进化算法求解该类问题时,存在收敛性和解集分布性上的缺陷,难以满足实际工程优化需求.提出一种基于全局排序的高维多目标进化算法GR-MODE,首先,采用一种新的全局排序策略增强选择压力,无需用户偏好及目标主次信息,且避免宽松Pareto支配在排序结果合理性与可信性上的损失;其次,采用Harmonic平均拥挤距离对个体进行全局密度估计,提高现有局部密度估计方法的精确性;最后,针对高维多目标复杂空间搜索需求,设计新的精英选择策略及适应度值评价函数.将该算法与国内外现有的5种高性能多目标进化算法在标准测试函数集DTLZ{1,2, 4,5}上进行对比实验,结果表明,该算法具有明显的性能优势,大幅提升了4~30维高维多目标优化的收敛性和分布性.     

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 soft-computing Pareto-based meta-heuristic algorithm for a multi-objective multi-server facility location problem

In this paper, a novel multi-objective location model within multi-server queuing framework is proposed, in which facilities behave as M/M/m queues. In the developed model of the problem, the constraints of selecting the nearest-facility along with the service level restriction are considered to bring the model closer to reality. Three objective functions are also considered including minimizing (I) sum of the aggregate travel and waiting times, (II) maximum idle time of all facilities, and (III) the budget required to cover the costs of establishing the selected facilities plus server staffing costs. Since the developed model of the problem is of an NP-hard type and inexact solutions are more probable to be obtained, soft computing techniques, specifically evolutionary computations, are generally used to cope with the lack of precision. From different terms of evolutionary computations, this paper proposes a Pareto-based meta-heuristic algorithm called multi-objective harmony search (MOHS) to solve the problem. To validate the results obtained, two popular algorithms including non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are utilized as well. In order to demonstrate the proposed methodology and to compare the performances in terms of Pareto-based solution measures, the Taguchi approach is first utilized to tune the parameters of the proposed algorithms, where a new response metric named multi-objective coefficient of variation (MOCV) is introduced. Then, the results of implementing the algorithms on some test problems show that the proposed MOHS outperforms the other two algorithms in terms of computational time.