基于改进MOEA/D算法的WSN覆盖优化方法*

为了优化无线传感器网络（WSN）的覆盖方法,针对MOEA/D中缺少对本代优质个体的保存和最优解集中的个体极少的两个问题,提出了粒子群优化的基于分解的多目标进化算法（MOEA/D-PSO）。通过保留种群本代优质个体,改进本地优化解集在进化过程中的搜索方向和搜索进度,弥补了MOEA/D不足。仿真实验证明,相对于MOEA/D和非支配排序遗传算法（NSGA-II）,MOEA/D-PSO所得非支配解更接近Pareto最优曲面,解集分布的均匀性和多样性表现更佳,WSN的覆盖范围更广,能量消耗更少。     

Multi-objective clustered-based routing with coverage control in wireless sensor networks

A wireless sensor network (WSN) generally consists of a large number of inexpensive power constrained sensors that are small in size and communicate over short distances to perform a predefined task. Realizing the full potential of WSN poses many design problems, especially those which involve tradeoffs between multiple conflicting optimization objectives such as coverage preservation and energy conservation. While both energy conservation routing protocols in a cluster-based WSNs and coverage-maintenance problems have been extensively studied in the literature, these two problems have not been integrated in a multi-objective optimization (MOO) manner. This paper employs a recently developed MOO algorithm, the so-called multi-objective evolutionary algorithm based on decomposition (MOEA/D) to solve simultaneously the energy conservation and coverage preservation design problems in cluster-based WSNs. The performance of the proposed approach, in terms of network lifetime and coverage is compared with the heuristic LEACH and SEP clustering protocols and with another prominent MOEA, the so-called non-dominated sorting genetic algorithm II (NSGA II). Simulation results reveal that MOEA/D provides a more efficient and reliable behavior over other approaches.     

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。     

Decomposition-based multi-objective evolutionary algorithm for vehicle routing problem with stochastic demands

Vehicle routing problem with stochastic demands (VRPSD) is a famous and challenging optimization problem which is similar to many real world problems. To resemble the real world scenario, total traveling distance, total driver remuneration, the number of vehicles used and the difference between driver remuneration are considered and formulated in the multi-objective optimization perspective. This paper aims to solve multi-objective VRPSD under the constraints of available time window and vehicle capacity using decomposition-based multi-objective evolutionary algorithm (MOEA/D) with diversity-loss-based selection method incorporates with local search and multi-mode mutation heuristics. We have also compared the optimization performance of the decomposition-based approach with the domination-based approach to study the difference between these two well-known evolutionary multi-objective algorithm frameworks. The simulation results have showed that the decomposition-based approach with diversity-loss-based selection method is able to maintain diverse output solutions.     

Multi-objective node deployment in WSNs: In search of an optimal trade-off among coverage,lifetime, energy consumption,and connectivity

The increased demand of Wireless Sensor Networks (WSNs) in different areas of application have intensified studies dedicated to the deployment of sensor nodes in recent past. For deployment of sensor nodes some of the key objectives that need to be satisfied are coverage of the area to be monitored, net energy consumed by the WSN, lifetime of the network, and connectivity and number of deployed sensors. In this article the sensor node deployment task has been formulated as a constrained multi-objective optimization (MO) problem where the aim is to find a deployed sensor node arrangement to maximize the area of coverage, minimize the net energy consumption, maximize the network lifetime, and minimize the number of deployed sensor nodes while maintaining connectivity between each sensor node and the sink node for proper data transmission. We assume a tree structure between the deployed nodes and the sink node for data transmission. Our method employs a recently developed and very competitive multi-objective evolutionary algorithm (MOEA) known as MOEA/D-DE that uses a decomposition approach for converting the problem of approximation of the Pareto fronts (PF) into a number of single-objective optimization problems. This algorithm employs differential evolution (DE), one of the most powerful real parameter optimizers in current use, as its search method. The original MOEA/D has been modified by introducing a new fuzzy dominance based decomposition technique. The algorithm introduces a fuzzy Pareto dominance concept to compare two solutions and uses the scalar decomposition method only when one of the solutions fails to dominate the other in terms of a fuzzy dominance level. We have compared the performance of the resulting algorithm, called MOEA/DFD, with the original MOEA/D-DE and another very popular MOEA called Non-dominated Sorting Genetic Algorithm (NSGA-II). The best trade-off solutions from MOEA/DFD based node deployment scheme have also been compared with a few single-objective node deployment schemes based on the original DE, an adaptive DE-variant (JADE), original particle swarm optimization (PSO), and a state-of-the art variant of PSO (Comprehensive Learning PSO). In all the test instances, MOEA/DFD performs better than all other algorithms. Also the proposed multi-objective formulation of the problem adds more flexibility to the decision maker for choosing the necessary threshold of the objectives to be satisfied.     

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.     

基于在线感知Pareto前沿划分目标空间的多目标进化优化

多目标进化优化是求解多目标优化问题的可行方法.但是, 由于没有准确感知并充分利用问题的Pareto前沿, 已有方法难以高效求解复杂的多目标优化问题.本文提出一种基于在线感知Pareto前沿划分目标空间的多目标进化优化方法, 以利用感知的结果, 采用有针对性的进化优化方法求解多目标优化问题.首先, 根据个体之间的拥挤距离与给定阈值的关系感知优化问题的Pareto前沿上的间断点, 并基于此将目标空间划分为若干子空间; 然后, 在每一子空间中采用MOEA/D (Multi-objective evolutionary algorithm based on decomposition)得到一个外部保存集; 最后, 基于所有外部保存集生成问题的Pareto解集.将提出的方法应用于15个基准数值函数优化问题, 并与NSGA-Ⅱ、RPEA、MOEA/D、MOEA/DPBI、MOEA/D-STM和MOEA/D-ACD等比较.结果表明, 提出的方法能够产生收敛和分布性更优的Pareto解集, 是一种非常有竞争力的方法.     

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.     

Risk minimization in biometric sensor networks: an evolutionary multi-objective optimization approach

Biometric systems aim at identifying humans by their characteristics or traits. This article addresses the problem of designing a biometric sensor management unit by optimizing the risk, which is modeled as a multi-objective optimization (MO) problem with global false acceptance rate and global false rejection rate as the two objectives. In practice, when multiple biometric sensors are used, the decision is taken locally at each sensor and the data are passed to the sensor manager. At the sensor manager, the data are fused using a fusion rule and the final decision is taken. The optimization process involves designing the data fusion rule and setting of the sensor thresholds. In this work, we employ a fuzzy dominance and decomposition-based multi-objective evolutionary algorithm (MOEA) called MOEA/DFD and compare its performance with two state-of-the-art MO algorithms: MOEA/D and NSGA-II in context to the risk minimization task. The algorithm introduces a fuzzy Pareto dominance concept to compare two solutions and uses the scalar decomposition method only when one of the solutions fails to dominate the other in terms of a fuzzy dominance level. The MO algorithms are simulated on different number of sensor setups consisting of three, six, and eight sensors. The a priori probability of imposter is also varied from 0.1 to 0.9 to verify the performance of the system with varying degrees of threat. One of the most significant advantages of using the MO framework is that with a single run, just by changing the decision-making logic applied to the obtained Pareto front, one can find the required threshold and decision strategies for varying threats of imposter. However, with single-objective optimization, one needs to run the algorithms each time with change in the threat of imposter. Thus, multi-objective formulation of the problem appears to be more useful and better than the single-objective one. In all the test instances, MOEA/DFD performs better than all the other algorithms.     

基于分解的多目标花朵授粉算法

在过去几十年里，许多多目标进化算法被广泛应用于解决多目标优化问题，其中一种比较流行的多目标进化算法是基于分解的多目标进化算法(MOEA/D)。花朵授粉算法是一种启发式优化算法，但迄今为止，花朵授粉算法在基于分解的多目标进化算法领域的研究还非常少。本文在基于分解的多目标进化算法的框架下，将花朵授粉算法拓展至多目标优化领域，提出一种基于分解的多目标花朵授粉算法(MOFPA/D)。此外，为了保证非支配解的多样性，本文提出一种基于网格的目标空间分割法，该方法从找到的Pareto最优解集中筛选出一定数量且分布均匀的Pareto最优解。实验结果表明，基于分解的多目标花朵授粉算法在收敛性与多样性方面均优于基于分解的多目标进化算法。     

Identification of multi-resolution network structures with multi-objective immune algorithm

Community structure is one of the most important properties in complex networks, and the field of community detection has received an enormous amount of attention in the past several years. Many quality metrics and methods have been proposed for revealing community structures at multiple resolution levels, while most existing methods need a tunable parameter in their quality metrics to determine the resolution level in advance. In this study, a multi-objective evolutionary algorithm (MOEA) for revealing multi-resolution community structures is proposed. The proposed MOEA-based community detection algorithm aims to find a set of tradeoff solutions which represent network partitions at different resolution levels in a single run. It adopts an efficient multi-objective immune algorithm to simultaneously optimize two contradictory objective functions, Modified Ratio Association and Ratio Cut. The optimization of Modified Ratio Association tends to divide a network into small communities, while the optimization of Ratio Cut tends to divide a network into large communities. The simultaneous optimization of these two contradictory objectives returns a set of tradeoff solutions between the two objectives. Each of these solutions corresponds to a network partition at one resolution level. Experiments on artificial and real-world networks show that the proposed method has the ability to reveal community structures of networks at different resolution levels in a single run.     

一种基于最小生成树的多目标进化算法

怎样保证朝Pareto最优解的方向搜索和如何获得均匀分布且范围广泛的非支配解是多目标进化算法(MOEA)设计时的两个关键问题,它们很大程度上取决于适应度赋值和外部种群维护这两个重要部分.提出了一种基于最小生成树的多目标进化算法(MST_MOEA).在考虑了个体间支配关系的基础上,利用个体与非支配集的距离和不同等级个体的树聚集密度来对适应度赋值;在外部种群的非支配解个数超过规定的种群规模时,用树的度数和树聚集密度对其进行修剪.将其应用于不同维数下9个测试函数,并与NSGA-II,SPEA2进行对比,结果证实了算法良好的收敛性和分布性.     

基于幂变换的多目标进化算法MOEA?D权重设计方法

在多目标最优化问题中,如何求解一组均匀散布在前沿界面上的有效解具有重要意义.MOEA?D是最近出现的一种杰出的多目标进化算法,当前沿界面的形状是某种已知的类型时,MOEA?D使用高级分解的方法容易求出均匀散布在前沿界面上的有效解.然而,多目标优化问题的前沿界面的形状通常是未知的.为了使MOEA?D能求出一般多目标优化问题的均匀散布的有效解,利用幂函数对目标进行数学变换,使变换后的多目标优化问题的前沿界面在算法的进化过程中逐渐接近希望得到的形状,提出了一种求解一般的多目标优化问题的MOEA?D算法的权重设计方法,并且讨论了经过数学变换后前沿界面的保距性问题.采用建议的权重设计方法,MOEA?D更容易求出一般的多目标优化问题均匀散布的有效解.数值结果验证了算法的有效性.     

无线传感器网络中覆盖控制技术综述

覆盖控制是无线传感器网络应用的一个基本问题,反映了网络所能提供的"感知"服务质量,可以使无线传感器网络的空间资源得到优化分配,进而更好地完成环境感知、信息获取和有效传输的任务;立足于无线传感器网络的覆盖控制问题,分析了网络覆盖技术在国内外研究的现状与发展,指出了传感器网络覆盖算法中需要解决的问题,并提出了将多目标进化算法与智能计算技术用于动态覆盖控制技术研究设想。     

多目标进化算法及其在控制领域中的应用综述

多目标进化算法在求解多目标优化问题方面具有独特的优势.对此,介绍了多目标进化算法的基本原理,讨论了多目标进化算法的一系列改进方法;论述了近年来多目标进化算法在自动控制领域中的最新研究成果,并对其未来的发展方向进行了展望.     

A modified MOEA/D approach to the solution of multi-objective optimal power flow problem

This study presents a modified multi-objective evolutionary algorithm based decomposition (MOEA/D) approach to solve the optimal power flow (OPF) problem with multiple and competing objectives. The multi-objective OPF considers the total fuel cost, the emissions, the power losses and the voltage magnitude deviations as the objective functions. In the proposed MOEA/D, a modified Tchebycheff decomposition method is introduced as the decomposition approach in order to obtain uniformly distributed Pareto-Optimal solutions on each objective space. In addition, an efficiency mixed constraint handling mechanism is introduced to enhance the feasibility of the final Pareto solutions obtained. The mechanism employs both repair strategy and penalty function to handle the various complex constraints of the MOOPF problem. Furthermore, a fuzzy membership approach to select the best compromise solution from the obtained Pareto-Optimal solutions is also integrated. The standard IEEE 30-bus test system with seven different cases is considered to verify the performance of the proposed approach. The obtained results are compared with those in the literatures and the comparisons confirm the effectiveness and the performance of the proposed algorithm.     

基于动态多策略差分进化模型的MOEA/D算法*

在基于分解技术的多目标进化算法的框架中,引入一种动态多策略差分进化模型。该模型在分析不同差分进化策略的特点基础上,选择了三种差分进化策略,并对每种策略分配一子种群。在进化过程中,依据每种策略对邻域更新的贡献度,动态的调整其子种群的大小。对比分析采用不同差分进化算法的性能,结果表明运用多个策略之间相互协同进化,有利于提高算法性能。将新算法同NSG-II和MOEA/D算法在LZ09系列基准函数上进行性能对比,实验结果显示该算法的收敛性和多样性均优于对比算法。将新应用于I型梁多目标优化设计问题中,获得的Pareto前沿均匀,且解集域较宽广,对比分析表明算法的工程实用性。     

Adaptive design optimization of wireless sensor networks using genetic algorithms

We present a multi-objective optimization methodology for self-organizing, adaptive wireless sensor network design and energy management, taking into consideration application-specific requirements, communication constraints and energy-conservation characteristics. A precision agriculture application of sensor networks is used as an example. We use genetic algorithms as the optimization tool of the developed system and an appropriate fitness function is developed to incorporate many aspects of network performance. The design characteristics optimized by the genetic algorithm system include the status of sensor nodes (whether they are active or inactive), network clustering with the choice of appropriate clusterheads and finally the choice between two signal ranges for the simple sensor nodes. We show that optimal sensor network designs constructed by the genetic algorithm system satisfy all application-specific requirements, fulfill the existent connectivity constraints and incorporate energy-conservation characteristics. Energy management is optimized to guarantee maximum life span of the network without lack of the network characteristics that are required by the specific application.     

An effective model of multiple multi-objective evolutionary algorithms with the assistance of regional multi-objective evolutionary algorithms: VIPMOEAs

Division of the evolutionary search among multiple multi-objective evolutionary algorithms (MOEAs) is a recent advantage in MOEAs design, particularly in effective parallel and distributed MOEAs. However, most these algorithms rely on such a central (re) division that affects the algorithms’ efficiency. This paper first proposes a local MOEA that searches on a particular region of objective space with its novel evolutionary selections. It effectively searches for Pareto Fronts (PFs) inside the given polar-based region, while nearby the region is also explored, intelligently. The algorithm is deliberately designed to adjust its search direction to outside the region – but nearby – in the case of a region with no Pareto Front. With this contribution, a novel island model is proposed to run multiple forms of the local MOEA to improve a conventional MOEA (e.g. NSGA-II or MOEA/D) running along – in another island. To dividing the search, a new division technique is designed to give particular regions of objective space to the local MOEAs, frequently and effectively. Meanwhile, the islands benefit from a sophisticated immigration strategy without any central (re) collection, (re) division and (re) distribution acts. Results of three experiments have confirmed that the proposed island model mostly outperforms to the clustering MOEAs with similar division technique and similar island models on DTLZs. The model is also used and evaluated on a real-world combinational problem, flexible logistic network design problem. The model definitely outperforms to a similar island model with conventional MOEA (NSGA-II) used in each island.     

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.