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.     

求解多目标社区发现问题的离散化随机漂移粒子群优化算法

针对求解复杂网络的多目标社区发现问题,提出了一种离散化随机漂移粒子群优化（DRDPSO）算法。首先,通过对社区进行随机化编码操作和针对随机漂移算法的离散化操作,来改善局部网络结构并逐渐增强全局模块度值;其次,根据核K均值（KKM）和比例割（RC）两个目标函数来控制网络中的社区规模、缓解模块度分辨率限制;最后,根据多目标求解策略逐步更新Pareto非劣解集,从Pareto非劣解集选取满足需求的目标社区结构。为了验证所提算法的有效性,将DRDPSO算法与其他社区发现算法在三种具有10个不同参数设置的生成网络及三种真实网络上进行对比实验,并采用两个最佳社区评价指标对各算法获得的社区发现结果进行对比分析。实验结果表明,使用DRDPSO算法求解复杂网络的多目标社区发现问题时,获得的社区发现评价指标（归一化互信息和模块度）最高的概率达到95%以上。可见DRDPSO算法在真实网络进行应用能进一步地提高网络社区划分的精确度和鲁棒性。     

基于自适应Memetic算法的多目标复杂网络社区检测

针对提高复杂网络社区检测准确度问题, 提出了一种自适应Memetic算法的多目标社区检测算法。在全局搜索中利用Logistic函数来设置与全局优化相应的交叉概率和变异概率,并将多目标优化问题转化成同时最小优化Kernel K-Means和Ratio Cut这两个目标函数;在局部搜索中利用权重将两个目标函数合并成一个局部优化目标,并采用爬山搜索来寻找个体最优。在虚拟和真实网络实验平台下,与五个基于遗传算法的方法以及Fast Modularity算法相比,结果表明算法能有效提高社区检测准确度,具有更好的寻优效果。     

A Posteriori Approach for Community Detection

Conventional community detection approaches in complex network are based on the optimization of a priori decision, i.e., a single quality function designed beforehand. This paper proposes a posteriori decision approach for community detection. The approach includes two phases: in the search phase, a special multi-objective evolutionary algorithm is designed to search for a set of tradeoff partitions that reveal the community structure at different scales in one run; in the decision phase, three model selection criteria and the Possibility Matrix method are proposed to aid decision makers to select the preferable solutions through differentiating the set of optimal solutions according to their qualities. The experiments in five synthetic and real social networks illustrate that, in one run, our method is able to obtain many candidate solutions, which effectively avoids the resolution limit existing in priori decision approaches. In addition, our method can discover more authentic and comprehensive community structures than those priori decision approaches.     

基于多目标优化的网络社区发现方法

社区发现是复杂网络挖掘中的重要任务之一,在恐怖组织识别、蛋白质功能预测、舆情分析等方面具有重要的理论和应用价值.但是,现有的社区质量评判指标具有数据依赖性与耦合关联性,而且基于单一评判指标优化的网络社区发现算法有很大的局限性.针对这些问题,将网络社区发现问题形式化为多目标优化问题,提出了一种基于多目标粒子群优化的网络社区发现算法MOCD-PSO,它选取模块度Q、最小最大割MinMaxCut 与轮廓(silhouette)这3 个指标进行综合寻优.实验结果表明,MOCD-PSO 算法具有较好的收敛性,能够发现分布均匀且分散度较高的Pareto 最优网络社区结构集,并且无论与单目标优化方法(GN 与GA-Net)相比较,还是与多目标优化算法(MOGANet与SCAH-MOHSA)相比较,MOCD-PSO 算法都能在无先验信息的条件下挖掘出更高质量的网络社区.     

网络社区发现的多目标分解粒子群优化算法

通过分析社会网络中社区发现问题的优化目标,构造了社区发现的多目标优化模型,提出一种网络社区发现的多目标分解粒子群优化算法。该算法采用切比雪夫法将多目标优化问题分解为多个单目标优化子问题,使用粒子群优化(PSO)算法对社区结构进行挖掘,并引入了一种新颖的基于局部搜索的变异策略以提高算法的搜索效率和收敛速度,该算法克服了单目标优化算法存在的解单一以及难以发现社区层次结构的缺陷。人工网络及真实网络上的实验结果表明,该算法能够快速准确地挖掘网络社区并揭示社区的层次结构。     

基于蚁群优化的多目标社区检测算法

蚁群优化算法作为单目标优化问题,由于只有一个目标函数,通常会将解限制到特定的范围内。当优化的目标不恰当时,算法可能失效,比如分辨率限制问题。我们将多目标优化的思想与传统的用于社区检测的蚁群优化算法相结合,增加了目标函数个数,即增加了解的评价指标数目。该算法引入多目标策略,提出多目标ACO算法,该算法在一次运行过程中会产生一组Pareto最优解。并在三个真实世界网络证明该算法的有效性和准确性。     

Multi-objective evolutionary algorithm using problem-specific genetic operators for community detection in networks

Automatic network clustering is an important method for mining the meaningful communities of complex networks. Uncovered communities help to understand the potential system structure and functionality. Many algorithms that use multiple optimization criteria and optimize a population of solutions are difficult to apply to real systems because they suffer a long optimization process. In this paper, in order to accelerate the optimization process and to uncover multiple significant community structures more effectively, a multi-objective evolutionary algorithm is proposed and evaluated using problem-specific genetic mutation and group crossover, and problem-specific initialization. Since crossover operators mainly contribute to performance of genetic algorithms, more problem-specific group crossover operators are introduced and evaluated for intelligent evolution of population. The experiments on both artificial and real-world networks demonstrate that the proposed evolutionary algorithm with problem-specific genetic operations has effective performance on discovering the community structure of networks.

     

一种优化模糊神经网络的多目标微粒群算法

模糊神经网络优化是一个多目标优化问题．通过对模糊神经网络和微粒群算法的深入分析,提出了一种多目标微粒群算法．在算法中将网络的精确性和复杂性分别作为目标进行优化,再用一种启发性分量加权均值法来选取个体极值和全局极值．算法能够引导粒子较快地向非劣最优解区域移动并最终获得多个非劣最优解,为模糊神经网络的精确性和复杂性的折中寻优问题提供了一种解决方法．茶味觉信号识别的仿真实验验证了该算法的有效性．     

基于多目标优化的多源组播网络编码的构造

在基于单目标优化构造网络编码的基础上,提出了基于多目标优化的网络编码的构造方法。把多源组播网络划分成多个单源组播网络,各单源组播网络的组播容量互相制约,为了使各单源组播网络的组播容量达到最大,采用粒子群优化算法进行子图划分,动态求解包含各子图组播容量的Pareto解集。用户可以优先考虑某个子图的组播容量,选择相应的解向量进行线性网络编码构造。仿真测试结果表明,本方法是可行的。     

Multi-level learning based memetic algorithm for community detection

Complex network has become an important way to analyze the massive disordered information of complex systems, and its community structure property is indispensable to discover the potential functionality of these systems. The research on uncovering the community structure of networks has attracted great attentions from various fields in recent years. Many community detection approaches have been proposed based on the modularity optimization. Among them, the algorithms which optimize one initial solution to a better one are easy to get into local optima. Moreover, the algorithms which are susceptible to the optimized order are easy to obtain unstable solutions. In addition, the algorithms which simultaneously optimize a population of solutions have high computational complexity, and thus they are difficult to apply to practical problems. To solve the above problems, in this study, we propose a fast memetic algorithm with multi-level learning strategies for community detection by optimizing modularity. The proposed algorithm adopts genetic algorithm to optimize a population of solutions and uses the proposed multi-level learning strategies to accelerate the optimization process. The multi-level learning strategies are devised based on the potential knowledge of the node, community and partition structures of networks, and they work on the network at nodes, communities and network partitions levels, respectively. Extensive experiments on both benchmarks and real-world networks demonstrate that compared with the state-of-the-art community detection algorithms, the proposed algorithm has effective performance on discovering the community structure of networks.     

A decision support system for optimal deployment of sonobuoy networks based on sea current forecasts and multi-objective evolutionary optimization

A decision support system for the optimal deployment of drifting acoustic sensor networks for cooperative track detection in underwater surveillance applications is proposed and tested on a simulated scenario. The system integrates sea water current forecasts, sensor range models and simple drifting buoy kinematic models to predict sensor positions and temporal network performance. A multi-objective genetic optimization algorithm is used for searching a set of Pareto optimal deployment solutions (i.e. the initial position of drifting sonobuoys of the network) by simultaneously optimizing two quality of service metrics: the temporal mean of the network area coverage and the tracking coverage. The solutions found after optimization, which represent different efficient tradeoffs between the two metrics, can be conveniently evaluated by the mission planner in order to choose the solution with the desired compromise between the two conflicting objectives. Sensitivity analysis through the Unscented Transform is also performed in order to test the robustness of the solutions with respect to network parameters and environmental uncertainty. Results on a simulated scenario making use of real probabilistic sea water current forecasts are provided showing the effectiveness of the proposed approach. Future work is envisioned to make the tool fully operational and ready to use in real scenarios.     

A novel multiobjective particle swarm optimization algorithm for signed network community detection

Signed graphs or networks are effective models for analyzing complex social systems. Community detection from signed networks has received enormous attention from diverse fields. In this paper, the signed network community detection problem is addressed from the viewpoint of evolutionary computation. A multiobjective optimization model based on link density is newly proposed for the community detection problem. A novel multiobjective particle swarm optimization algorithm is put forward to solve the proposed optimization model. Each single run of the proposed algorithm can produce a set of evenly distributed Pareto solutions each of which represents a network community structure. To check the performance of the proposed algorithm, extensive experiments on synthetic and real-world signed networks are carried out. Comparisons against several state-of-the-art approaches for signed network community detection are carried out. The experiments demonstrate that the proposed optimization model and the algorithm are promising for community detection from signed networks.     

Optimal flow control for utility-lifetime tradeoff in wireless sensor networks

In this paper, we study the utility-lifetime tradeoff in wireless sensor networks (WSNs) by optimal flow control. We consider the flow control in a more practical way by taking into account link congestion and energy efficiency in our network model, and formulate it as a constrained multi-objective optimization problem. Because of the variable coupling in the objective function, auxiliary variables are introduced to decouple it. We introduce the concept of inconsistent coordination price to balance the energy consumption of the sensor nodes. Based on the congestion price and inconsistent coordination prices, a distributed algorithm using gradient projection is proposed to solve the optimization problem. The convergence of the algorithm is also proved. Numerical results show the convergence of our algorithm, the tradeoff of utility and lifetime, as well as the necessity of considering link congestion in WSNs.     

Memetic algorithm with Preferential Local Search using adaptive weights for multi-objective optimization problems

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.     

Multi-objective evolutionary optimizations of a space-based reconfigurable sensor network under hard constraints

Wireless sensor networks have emerged as a promising way to develop high security systems. This paper presents the optimizations of a space-based reconfigurable sensor network under hard constraints by employing an efficient multi-objective evolutionary algorithm (MOEA). First, a system model is proposed for cluster-based space wireless sensor networks. Second, the statement of multi-objective optimization problems is mathematically formulated under hard constraints. Third, the MOEA is used to find multi-criteria solutions in the sense of Pareto optimality. Finally, simulation results are provided to illustrate the effectiveness of applying the MOEA to the multi-objective evolutionary optimizations of a space-based reconfigurable sensor network under hard constraints.     

Some convergence-based M-ary cardinal metrics for comparing performances of multi-objective optimizers

There is still a big question to the community of multi-objective optimization: how to compare effectively the performances of multi-objective stochastic optimizers? The existing metrics suffer from different drawbacks to address this question. In this article, three convergence-based M-ary cardinal metrics are proposed, based on different forms of dominance relations between two solutions, for comparing performances of two optimizers from their multiple runs. The metrics are first tested on some benchmark instances whose performances are already known, and then their outcomes for some other instances are compared with those of three existing metrics.     

Energy-efficient clustering in mobile ad-hoc networks using multi-objective particle swarm optimization

A mobile ad hoc network (MANET) is dynamic in nature and is composed of wirelessly connected nodes that perform hop-by-hop routing without the help of any fixed infrastructure. One of the important requirements of a MANET is the efficiency of energy, which increases the lifetime of the network. Several techniques have been proposed by researchers to achieve this goal and one of them is clustering in MANETs that can help in providing an energy-efficient solution. Clustering involves the selection of cluster-heads (CHs) for each cluster and fewer CHs result in greater energy efficiency as these nodes drain more power than noncluster-heads. In the literature, several techniques are available for clustering by using optimization and evolutionary techniques that provide a single solution at a time. In this paper, we propose a multi-objective solution by using multi-objective particle swarm optimization (MOPSO) algorithm to optimize the number of clusters in an ad hoc network as well as energy dissipation in nodes in order to provide an energy-efficient solution and reduce the network traffic. In the proposed solution, inter-cluster and intra-cluster traffic is managed by the cluster-heads. The proposed algorithm takes into consideration the degree of nodes, transmission power, and battery power consumption of the mobile nodes. The main advantage of this method is that it provides a set of solutions at a time. These solutions are achieved through optimal Pareto front. We compare the results of the proposed approach with two other well-known clustering techniques; WCA and CLPSO-based clustering by using different performance metrics. We perform extensive simulations to show that the proposed approach is an effective approach for clustering in mobile ad hoc networks environment and performs better than the other two approaches.     

Multi-objective community detection in complex networks

Community detection in social network analysis is usually considered as a single objective optimization problem, in which different heuristics or approximate algorithms are employed to optimize a objective function that capture the notion of community. Due to the inadequacy of those single-objective solutions, this paper first formulates a multi-objective framework for community detection and proposes a multi-objective evolutionary algorithm for finding efficient solutions under the framework. After analyzing and comparing a variety of objective functions that have been used or can potentially be used for community detection, this paper exploits the concept of correlation between objective which charcterizes the relationship between any two objective functions. Through extensive experiments on both artifical and real networks, this paper demonstrates that a combination of two negatively correlated objectives under the multi-objective framework usually leads to remarkably better performance compared with either of the orignal single objectives, including even many popular algorithms..     

Handling multiple objectives with biogeography-based optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method inspired by biogeography. In this paper, BBO is extended to a multi-objective optimization, and a biogeography-based multi-objective optimization (BBMO) is introduced, which uses the cluster attribute of islands to naturally decompose the problem. The proposed algorithm makes use of nondominated sorting approach to improve the convergence ability effciently. It also combines the crowding distance to guarantee the diversity of Pareto optimal solutions. We compare the BBMO with two representative state-of-the-art evolutionary multi-objective optimization methods, non-dominated sorting genetic algorithm-II (NSGA-II) and archive-based micro genetic algorithm (AMGA) in terms of three metrics. Simulation results indicate that in most cases, the proposed BBMO is able to find much better spread of solutions and converge faster to true Pareto optimal fronts than NSGA-II and AMGA do.