Predictive and comprehensible rule discovery using a multi-objective genetic algorithm

We present a multi-objective genetic algorithm for mining highly predictive and comprehensible classification rules from large databases. We emphasize predictive accuracy and comprehensibility of the rules. However, accuracy and comprehensibility of the rules often conflict with each other. This makes it an optimization problem that is very difficult to solve efficiently. We have proposed a multi-objective evolutionary algorithm called improved niched Pareto genetic algorithm (INPGA) for this purpose. We have compared the rule generation by INPGA with that by simple genetic algorithm (SGA) and basic niched Pareto genetic algorithm (NPGA). The experimental result confirms that our rule generation has a clear edge over SGA and NPGA.     

Classification rule mining using ant programming guided by grammar with multiple Pareto fronts

This paper proposes a multi-objective ant programming algorithm for mining classification rules, MOGBAP, which focuses on optimizing sensitivity, specificity, and comprehensibility. It defines a context-free grammar that restricts the search space and ensures the creation of valid individuals, and its heuristic function presents two complementary components. Moreover, the algorithm addresses the classification problem from a new multi-objective perspective specifically suited for this task, which finds an independent Pareto front of individuals per class, so that it avoids the overlapping problem that appears when measuring the fitness of individuals from different classes. A comparative analysis of MOGBAP using two and three objectives is performed, and then its performance is experimentally evaluated throughout 15 varied benchmark data sets and compared to those obtained using another eight relevant rule extraction algorithms. The results prove that MOGBAP outperforms the other algorithms in predictive accuracy, also achieving a good trade-off between accuracy and comprehensibility.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

基于粒子群算法求解多目标优化问题

粒子群优化算法自提出以来,由于其容易理解、易于实现,所以发展很快,在很多领域得到了应用．通过对粒子群算法全局极值和个体极值选取方式的改进,提出了一种用于求解多目标优化问题的算法,实现了对多目标优化问题的非劣最优解集的搜索,实验结果证明了算法的有效性．     

MODENAR: Multi-objective differential evolution algorithm for mining numeric association rules

In this paper, a Pareto-based multi-objective differential evolution (DE) algorithm is proposed as a search strategy for mining accurate and comprehensible numeric association rules (ARs) which are optimal in the wider sense that no other rules are superior to them when all objectives are simultaneously considered. The proposed DE guided the search of ARs toward the global Pareto-optimal set while maintaining adequate population diversity to capture as many high-quality ARs as possible. ARs mining problem is formulated as a four-objective optimization problem. Support, confidence value and the comprehensibility of the rule are maximization objectives while the amplitude of the intervals which conforms the itemset and rule is minimization objective. It has been designed to simultaneously search for intervals of numeric attributes and the discovery of ARs which these intervals conform in only single run of DE. Contrary to the methods used as usual, ARs are directly mined without generating frequent itemsets. The proposed DE performs a database-independent approach which does not rely upon the minimum support and the minimum confidence thresholds which are hard to determine for each database. The efficiency of the proposed DE is validated upon synthetic and real databases.     

Hybrid particle swarm optimization for rule discovery in the diagnosis of coronary artery disease

Coronary artery disease (CAD) is one of the major causes of mortality worldwide. Knowledge about risk factors that increase the probability of developing CAD can help to understand the disease better and assist in its treatment. Recently, modern computer‐aided approaches have been used for the prediction and diagnosis of diseases. Swarm intelligence algorithms like particle swarm optimization (PSO) have demonstrated great performance in solving different optimization problems. As rule discovery can be modelled as an optimization problem, it can be mapped to an optimization problem and solved by means of an evolutionary algorithm like PSO. An approach for discovering classification rules of CAD is proposed. The work is based on the real‐world CAD data set and aims at the detection of this disease by producing the accurate and effective rules. The proposed algorithm is a hybrid binary‐real PSO, which includes the combination of categorical and numerical encoding of a particle and a different approach for calculating the velocity of particles. The rules were developed from randomly generated particles, which take random values in the range of each attribute in the rule. Two different feature selection methods based on multi‐objective evolutionary search and PSO were applied on the data set, and the most relevant features were selected by the algorithms. The accuracy of two different rule sets were evaluated. The rule set with 11 features obtained more accurate results than the rule set with 13 features. Our results show that the proposed approach has the ability to produce effective rules with highest accuracy for the detection of CAD.     

一种均衡各速度项系数的多目标粒子群优化算法

粒子群优化算法已成为求解多目标优化问题的有效方法之一,而速度更新公式中的惯性、局部和全局3个速度项的系数的动态合理设置是算法优化效率的关键问题。为解决现有算法仅单独设置各速度项系数导致优化效率不高的问题,提出了一种均衡各速度项系数的多目标粒子群优化算法。该方法旨在通过粒子的局部最优和全局最优的信息来引导种群的进化方向,动态调整每一个粒子速度项系数来均衡惯性、局部和全局3个速度项在搜索中的作用,从而更为准确地刻画算法的搜索能力和搜索精度,更好地平衡算法的探究和探索能力,进一步提高粒子群优化算法解决复杂多目标优化问题的效率。在7个标准测试函数上进行实验,并与5种经典的进化算法进行对比,结果表明新算法在综合指标IGD以及多样性评估指标Δ评分上具有更好的收敛速度和分布性,验证了新算法的有效性。     

基于混合微粒群优化的多目标柔性Job-shop调度

应用传统方法求解多目标柔性Job-shop调度问题是十分困难的,微粒群优化采用基于种群的搜索方式,融合了局部搜索和全局搜索,具有很高的搜索效率.模拟退火算法使用概率来避免陷入局部最优,整个搜索过程可由冷却表来控制.通过对这两种算法的合理组合,建立了一种快速且易于实现的新的混合优化算法.实例计算以及与其他算法的比较说明,该算法是求解多目标柔性Job-shop调度问题的可行且高效的方法.     

A multi-objective GRASP for partial classification

Metaheuristic algorithms have been used successfully in a number of data mining contexts and specifically in the production of classification rules. Classification rules describe a class of interest or a subset of this class, and as such may also be used as an aid in prediction. The production and selection of classification rules for a particular class of the database is often referred to as partial classification. Since partial classification rules are often evaluated according to a number of conflicting objectives, the generation of such rules is a task that is well suited to a multi-objective (MO) metaheuristic approach. In this paper we discuss how to adapt well known MO algorithms for the task of partial classification. Additionally, we introduce a new MO algorithm for this task based on a greedy randomized adaptive search procedure (GRASP). GRASP has been applied to a number of problems in combinatorial optimization, but it has very seldom been used in a MO setting, and generally only through repeated optimization of single objective problems, using either linear combinations of the objectives or additional constraints. The approach presented takes advantage of some specific characteristics of the data mining problem being solved, allowing for the very effective construction of a set of solutions that form the starting point for the local search phase of the GRASP. The resulting algorithm is guided solely by the concepts of dominance and Pareto-optimality. We present experimental results for our partial classification GRASP and other MO metaheuristics. These show that such algorithms are generally very well suited to this data mining task and furthermore, the GRASP brings additional efficiency to the search for partial classification rules.     

A hybrid multi-objective PSO–EDA algorithm for reservoir flood control operation

Reservoir flood control operation (RFCO) is a complex multi-objective optimization problem (MOP) with interdependent decision variables. Traditionally, RFCO is modeled as a single optimization problem by using a certain scalar method. Few works have been done for solving multi-objective RFCO (MO-RFCO) problems. In this paper, a hybrid multi-objective optimization approach named MO-PSO–EDA which combines the particle swarm optimization (PSO) algorithm and the estimation of distribution algorithm (EDA) is developed for solving the MO-RFCO problem. MO-PSO–EDA divides the particle population into several sub-populations and builds probability models for each of them. Based on the probability model, each sub-population reproduces new offspring by using PSO based and EDA methods. In the PSO based method, a novel global best position selection method is designed. With the help of the EDA based reproduction, the algorithm can lean linkage between decision variables and hence have a good capability of solving complex multi-objective optimization problems, such as the MO-RFCO problem. Experimental studies on six benchmark problems and two typical multi-objective flood control operation problems of Ankang reservoir have indicated that the proposed MO-PSO–EDA performs as well as or superior to the other three competitive multi-objective optimization algorithms. MO-PSO–EDA is suitable for solving MO-RFCO problems.     

Attributed multi-objective comprehensive learning particle swarm optimization for optimal security of networks

In particle swarm optimization (PSO) each particle uses its personal and global or local best positions by linear summation. However, it is very time consuming to find the global or local best positions in case of complex problems. To overcome this problem, we propose a new multi-objective variant of PSO called attributed multi-objective comprehensive learning particle swarm optimizer (A-MOCLPSO). In this technique, we do not use global or local best positions to modify the velocity of a particle; instead, we use the best position of a randomly selected particle from the whole population to update the velocity of each dimension. This method not only increases the speed of the algorithm but also searches in more promising areas of the search space. We perform an extensive experimentation on well-known benchmark problems such as Schaffer (SCH), Kursawa (KUR), and Zitzler–Deb–Thiele (ZDT) functions. The experiments show very convincing results when the proposed technique is compared with existing versions of PSO known as multi-objective comprehensive learning particle swarm optimizer (MOCLPSO) and multi-objective particle swarm optimization (MOPSO), as well as non-dominated sorting genetic algorithm II (NSGA-II). As a case study, we apply our proposed A-MOCLPSO algorithm on an attack tree model for the security hardening problem of a networked system in order to optimize the total security cost and the residual damage, and provide diverse solutions for the problem. The results of our experiments show that the proposed algorithm outperforms the previous solutions obtained for the security hardening problem using NSGA-II, as well as MOCLPSO for the same problem. Hence, the proposed algorithm can be considered as a strong alternative to solve multi-objective optimization problems.     

一种用于多目标优化的混合粒子群优化算法

将粒子群算法与局部优化方法相结合,提出了一种混合粒子群多目标优化算法（HMOPSO）。该算法针对粒子群局部优化性能较差的缺点,引入多目标线搜索与粒子群算法相结合的策略,以增强粒子群算法的局部搜索能力。HMOPSO首先运行PSO算法,得到近似的Pareto最优解;然后启动多目标线搜索,发挥传统数值优化算法的优势,对其进行进一步的优化。数值实验表明,HMOPSO具有良好的全局优化性能和较强的局部搜索能力,同时HMOPSO所得的非劣解集在分散性、错误率和逼近程度等量化指标上优于MOPSO。     

基于量子行为的粒子群优化算法分类规则获取*

介绍了基本的粒子群算法,并针对基本的粒子群算法在收敛性能上的缺陷,提出将具有量子行为的粒子群优化算法应用于数据挖掘学科中的分类规则获取。对加州大学厄文分校的若干数据集模式分类规则进行提取,与其他规则提取方法相比,证明该算法提高了分类规则的正确率以及全局寻优能力。     

基于多目标粒子群优化的虚拟网络映射算法

在虚拟网络映射中,多数研究只考虑一个映射目标,不能体现多方的利益。为此,将多目标算法和粒子群算法结合,提出了一种基于多目标粒子群优化（PSO）的虚拟网络映射算法（VNE-MOPSO）。首先,在基本的粒子群算法中引入交叉算子,扩大了种群优化的搜索空间;其次,在多目标优化算法中引入非支配排序、拥挤距离排序,从而加快种群的收敛;最后,以同时最小化成本和节点负载均衡度为虚拟网络映射目标函数,采用多目标粒子群优化算法求解虚拟网络映射问题（VNMP）。实验结果表明,采用该算法求解虚拟网络映射问题,在网络请求接受率、平均成本、平均节点负载均衡度、基础设施提供商的收益等方面具有优势。     

基于PSO的矿山企业动态配矿优化研究

采用粒子群优化(PSO)算法求解矿山企业动态配矿问题。依据开采条件圈定出可开采的矿块,用粒子的一位代表矿块,并用0或者1代表选择该矿块来开采,重新定义在约束条件下PSO粒子的运算与“飞行”规则,实现动态配矿优化的粒子群算法。该PSO算法实施简单,优化效果明显,通过2009年实际生产情况与优化结果的对比表明,该算法在生产成本几乎不变的情况下,明显提高了企业效率。     

Exploring comprehensible classification rules from trained neural networks integrated with a time-varying binary particle swarm optimizer

Purpose

Extracting comprehensible classification rules is the most emphasized concept in data mining researches. In order to obtain accurate and comprehensible classification rules from databases, a new approach is proposed by combining advantages of artificial neural networks (ANN) and swarm intelligence.

Method

Artificial neural networks (ANNs) are a group of very powerful tools applied to prediction, classification and clustering in different domains. The main disadvantage of this general purpose tool is the difficulties in its interpretability and comprehensibility. In order to eliminate these disadvantages, a novel approach is developed to uncover and decode the information hidden in the black-box structure of ANNs. Therefore, in this paper a study on knowledge extraction from trained ANNs for classification problems is carried out. The proposed approach makes use of particle swarm optimization (PSO) algorithm to transform the behaviors of trained ANNs into accurate and comprehensible classification rules. Particle swarm optimization with time varying inertia weight and acceleration coefficients is designed to explore the best attribute-value combination via optimizing ANN output function.

Results

The weights hidden in trained ANNs turned into comprehensible classification rule set with higher testing accuracy rates compared to traditional rule based classifiers.     

基于混合的GA-PSO神经网络算法

粒子群优化(PSO)算法是一类随机全局优化的技术,它通过粒子间的相互作用发现复杂搜索空间中的最优区域。提出了一种基于GA和PSO混合的算法(GA-PSO)用于神经网络训练。算法在产生下一代时,结合了交叉、变异算子和粒子群算法中的速度—位移公式,充分利用了遗传算法的全局寻优和粒子群算法收敛速度快的优点。经GA-PSO训练的神经网络应用于三元奇偶问题和IRIS模式分类问题,与BP、GA和PSO算法相比,该算法在提高训练误差精度的同时加快收敛速度,并能有效避免早熟收敛。仿真结果表明,GA-PSO算法是有效的神经网络训练算法。     

基于多目标蝗虫优化算法的移动机器人路径规划

在静态多障碍物环境下的移动机器人路径规划问题中，粒子群算法存在容易产生早熟收敛和局部寻优能力较差等缺点，导致机器人路径规划精度低。为此，提出一种多目标蝗虫优化算法（MOGOA）来解决这一问题。根据移动机器人路径规划要求将路径长度、平滑度和安全性作为路径优化的目标，建立相应的多目标优化问题的数学模型。在种群的搜索过程中，引入曲线自适应策略以提高算法收敛速度，并使用Pareto最优准则来解决三个目标之间的共存问题。实验结果表明：所提出的算法在解决上述问题中寻找到的路径更短，表现出更好的收敛性。该算法与多目标粒子群（MOPSO）算法相比路径长度减少了约2.01%，搜索到最小路径的迭代次数减少了约19.34%。     

Community detection in complex networks: Multi-objective discrete backtracking search optimization algorithm with decomposition

Community detection is believed to be a very important tool for understanding both the structure and function of complex networks, and has been intensively investigated in recent years. Community detection can be considered as a multi-objective optimization problem and the nature-inspired optimization techniques have shown promising results in dealing with this problem. In this study, we present a novel multi-objective discrete backtracking search optimization algorithm with decomposition for community detection in complex networks. First, we present a discrete variant of the backtracking search optimization algorithm (DBSA) where the updating rules of individuals are redesigned based on the network topology. Then, a novel multi-objective discrete method (MODBSA/D) based on the proposed discrete variant DBSA is first proposed to minimize two objective functions in terms of Negative Ratio Association (NRA) and Ratio Cut (RC) of community detection problems. Finally, the proposed algorithm is tested on some real-world networks to evaluate its performance. The results clearly show that MODBSA/D has effective and promising performance for dealing with community detection in complex networks.     

A fuzzy particle swarm optimization algorithm for computer communication network topology design

Particle swarm optimization (PSO) is a powerful optimization technique that has been applied to solve a number of complex optimization problems. One such optimization problem is topology design of distributed local area networks (DLANs). The problem is defined as a multi-objective optimization problem requiring simultaneous optimization of monetary cost, average network delay, hop count between communicating nodes, and reliability under a set of constraints. This paper presents a multi-objective particle swarm optimization algorithm to efficiently solve the DLAN topology design problem. Fuzzy logic is incorporated in the PSO algorithm to handle the multi-objective nature of the problem. Specifically, a recently proposed fuzzy aggregation operator, namely the unified And-Or operator (Khan and Engelbrecht in Inf. Sci. 177: 2692–2711, 2007), is used to aggregate the objectives. The proposed fuzzy PSO (FPSO) algorithm is empirically evaluated through a preliminary sensitivity analysis of the PSO parameters. FPSO is also compared with fuzzy simulated annealing and fuzzy ant colony optimization algorithms. Results suggest that the fuzzy PSO is a suitable algorithm for solving the DLAN topology design problem.