An improved multiobjective approach inspired by the flashing behaviour of fireflies for Traffic Grooming in optical WDM networks

Nowadays, the traffic demands in optical networks are low-speed traffic requests (low bandwidth requirement of a few Mbps) that employ the huge capacity of a fiber channel (Gbps), causing a waste of bandwidth as a result. Fortunately, by using electronic grooming nodes, we can multiplex (groom) several low-speed demands onto one channel in order to optimize the available resources in an optical network. The problem of grooming low-speed traffic requests is known in the literature as the Traffic Grooming problem and is considered an NP-hard optimization problem. In this work, we use both multiobjective optimization and evolutionary computation with the aim of facing this optical networking problem. The selected evolutionary algorithm is based in the behaviour of fireflies, the Firefly Algorithm (FA). In order to optimize more than one conflicting objective function of the Traffic Grooming problem simultaneously, we have modified the standard FA to the multiobjective domain (MO-FA). After carrying out different experiments with diverse real-world optical networks, comparing the results of the MO-FA with other multiobjective approaches and different standard heuristics for this problem, we can conclude saying that the new version of the MO-FA is an effective approach for dealing with this telecommunication problem.     

Design of multiobjective reconfigurable antenna array with discrete phase shifters using multiobjective differential evolution based on decomposition

The reconfigurable design problem is to find the element that will result in a sector pattern main beam with side lobes. The same excitation amplitudes applied to the array with zero phase should be in a high directivity, low‐side lobe pencil‐shaped main beam. This work presents a multiobjective approach to solve this problem. We consider two design objectives: the minimum value for the dual beam and the dynamic range ratio in qualify the entire array radiation pattern in order to achieve the optimal value between the antenna‐array elements. We use a recently developed and very competitive multiobjective evolutionary algorithm, called MOEA/D. This algorithm uses a decomposition approach to convert the problem of approximation of the Pareto Front into a number of single objective optimization problems. We illustrate that the best solutions obtained by the MOEA/D can outperform stat‐of‐art single objective algorithm: generalized generation‐gap model genetic algorithm (G3‐GA) and differential evolution algorithm (DE). In addition, we compare the results obtained by MOEA/D with those obtained by one of the most widely multiobjective algorithm called NSGA‐II and mutliobjective DE. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22: 675–681, 2012.     

A hybrid approach to parallelize a fast non‐dominated sorting genetic algorithm for phylogenetic inference

The field of computational biology encloses a wide range of optimization problems that show non‐deterministic polynomial‐time hard complexities. Nowadays, phylogeneticians are dealing with a growing amount of biological data that must be analyzed to explain the origins of modern species. Evolutionary relationships among organisms are often described by means of tree‐shaped structures known as phylogenetic trees. When inferring phylogenies, two main challenges must be addressed. First, the inference of reliable evolutionary trees on data sets where different optimality principles support conflicting evolutionary hypotheses. Second, the processing of enormous tree searches spaces where traditional sequential strategies cannot be applied. In this sense, phylogenetic inference can benefit from the combination of high performance computing and evolutionary computation to carry out the reconstruction of complex evolutionary histories in reduced execution times. In this paper, we introduce multiobjective phylogenetics, a hybrid OpenMP/MPI approach to parallelize a well‐known multiobjective metaheuristic, the fast non‐dominated sorting genetic algorithm (NSGA‐II). This algorithm has been designed to conduct phylogenetic analyses on multi‐core clusters in accordance with two principles: maximum parsimony and maximum likelihood. The main goal is to combine the benefits of shared‐memory and distributed‐memory programming paradigms to efficiently infer a set of high‐quality Pareto solutions. Experiments on six real nucleotide data sets and comparisons with other hybrid parallel approaches show that multiobjective phylogenetics is able to achieve significant performance in terms of parallel, multiobjective, and biological results. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiobjective evolutionary algorithms for electric power dispatch problem

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.     

Multiobjective model for solving resource‐leveling problem with discounted cash flows

Nowadays, executers are struggling to improve the economic and scheduling situation of projects. Construction scheduling techniques often produce schedules that cause undesirable resource fluctuations that are inefficient and costly to implement on site. The objective of the resource‐leveling problem is to reduce resource fluctuation related costs (hiring and firing costs) without violating the project deadline. In this article, minimizing the discounted costs of resource fluctuations and minimizing the project makespan are considered in a multiobjective model. The problem is formulated as an integer nonlinear programming model, and since the optimization problem is NP‐hard, we propose multiobjective evolutionary algorithms, namely nondominated sorting genetic algorithm‐II (NSGA‐II), strength Pareto evolutionary algorithm‐II (SPEA‐II), and multiobjective particle swarm optimization (MOPSO) to solve our suggested model. To evaluate the performance of the algorithms, experimental performance analysis on various instances is presented. Furthermore, in order to study the performance of these algorithms, three criteria are proposed and compared with each other to demonstrate the strengths of each applied algorithm. To validate the results obtained for the suggested model, we compared the results of the first objective function with a well‐tuned genetic algorithm and differential algorithm, and we also compared the makespan results with one of the popular algorithms for the resource constraints project scheduling problem. Finally, we can observe that the NSGA‐II algorithm presents better solutions than the other two algorithms on average.     

基于目标空间划分的自适应多目标进化算法

目前,多目标进化算法在众多领域具有极高的应用价值,是优化领域的研究热点之一.分析已有多目标进化算法在保持种群多样性方面的不足并提出一种基于解空间划分的自适应多目标进化算法（space division basedadaptive multiobjective evolutionary algorithm,简称SDA-MOEA）来解决多目标优化问题.该方法首先将多目标优化问题的解空间划分为大量子空间,在算法进化过程中,每个子空间都保留一个非支配解集,以保证种群的多样性.另外,该方法根据每个子空间推进种群前进的距离,自适应地为每个子空间分配进化机会,以提高种群的进化速度.最后,利用3组共14个多目标优化问题检验SDA-MOEA的性能,并将SDA-MOEA与其他5个已有多目标进化算法进行对比分析.实验结果表明：在10个问题上,算法SDA-MOEA显著优于其他对比算法.     

Effective Evolutionary Algorithms for Many-Specifications Attainment: Application to Air Traffic Control Tracking Filters

This paper addresses a real-world engineering design requiring the application of effective and global optimization techniques. The problem it deals with is the design of nonlinear tracking filters under up to several hundreds of performance specifications. The suitability of different evolutionary computation techniques for solving multiobjective problems is explored, contrasting the performance achieved with recent multiobjective evolutionary algorithm (MOEAs) proposals and different aggregation schemes. In particular, a new scheme is proposed to build a fitness function based on an operator that selects worst cases of multiple specifications in different situations. They have been evaluated in the design of an air traffic control (ATC) tracking filter that should accomplish a specific normative with 264 specifications. Results show their performance in terms of effectiveness and computational load, comparing their capability to scale the problem with respect to problem size.     

分层多目标最优化进化算法

文章用进化算法给出了求解二层字典分层多目标最优化的方法,该算法把求解问题转化为多目标最优化,并研究了这两个问题的解集之间的联系。对多目标最优化定义了一个新的选择算子和适应值函数,这样定义的选择算子和适应值函数结合均匀设计能有效地引导搜索,直接求出问题的解而不用逐层求解。数值模拟表明该方法十分有效。     

A hybrid evolutionary multiobjective optimization strategy for the dynamic power supply problem in magnesia grain manufacturing

The supply trajectory of electric power for submerged arc magnesia furnace determines the yields and grade of magnesia grain during the manufacture process. As the two production targets (i.e., the yields and the grade of magnesia grain) are conflicting and the process is subject to changing conditions, the supply of electric power needs to be dynamically optimized to track the moving Pareto optimal set with time. A hybrid evolutionary multiobjective optimization strategy is proposed to address the dynamic multiobjective optimization problem. The hybrid strategy is based on two techniques. The first one uses case-based reasoning to immediately generate good solutions to adjust the power supply once the environment changes, and then apply a multiobjective evolutionary algorithm to accurately solve the problem. The second one is to learn the case solutions to guide and promote the search of the evolutionary algorithm, and the best solutions found by the evolutionary algorithm can be used to update the case library to improve the accuracy of case-based reasoning in the following process. Due to the effectiveness of mutual promotion, the hybrid strategy can continuously adapt and search in dynamic environments. Two prominent multiobjective evolutionary algorithms are integrated into the hybrid strategy to solve the dynamic multiobjective power supply optimization problem. The results from a series of experiments show that the proposed hybrid algorithms perform better than their component multiobjective evolutionary algorithms for the tested problems.     

SAR image segmentation based on quantum-inspired multiobjective evolutionary clustering algorithm

The segmentation task in the feature space of an image can be formulated as an optimization problem. Recent researches have demonstrated that the clustering techniques, using only one objective may not obtain suitable solution because the single objective function just can provide satisfactory result to one kind of corresponding data set. In this letter, a novel multiobjective clustering approach, named a quantum-inspired multiobjective evolutionary clustering algorithm (QMEC), is proposed to deal with the problem of image segmentation, where two objectives are simultaneously optimized. Based on the concepts and principles of quantum computing, the multi-state quantum bits are used to represent individuals and quantum rotation gate strategy is used to update the probabilistic individuals. The proposed algorithm can take advantage of the multiobjective optimization mechanism and the superposition of quantum states, and therefore it has a good population diversity and search capabilities. Due to a set of nondominated solutions in multiobjective clustering problems, a simple heuristic method is adopted to select a preferred solution from the final Pareto front and the results show that a good image segmentation result is selected. Experiments on one simulated synthetic aperture radar (SAR) image and two real SAR images have shown the superiority of the QMEC over three other known algorithms.     

基于分解的演化多目标优化算法综述

基于分解的演化多目标优化算法(MOEA/D)的基本思想是将一个多目标优化问题转化成一系列子问题(单目标或者多目标)来进行优化求解.自2007年提出以来, MOEA/D受到了国内外学者的广泛关注,已经成为最具代表性的演化多目标优化算法之一.总结过去13年中关于MOEA/D的一些研究进展,具体内容包括:(1)关于MOEA/D的算法改进;(2) MOEA/D在超多目标优化问题及约束优化问题上的研究;(3) MOEA/D在一些实际问题上的应用.然后,实验对比几个具有代表性的MOEA/D改进算法.最后,指出一些MOEA/D未来的研究方向.     

MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.     

A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multiobjective Optimization

In addition to the need for satisfying several competing objectives, many real-world applications are also dynamic and require the optimization algorithm to track the changing optimum over time. This paper proposes a new coevolutionary paradigm that hybridizes competitive and cooperative mechanisms observed in nature to solve multiobjective optimization problems and to track the Pareto front in a dynamic environment. The main idea of competitive-cooperative coevolution is to allow the decomposition process of the optimization problem to adapt and emerge rather than being hand designed and fixed at the start of the evolutionary optimization process. In particular, each species subpopulation will compete to represent a particular subcomponent of the multiobjective problem, while the eventual winners will cooperate to evolve for better solutions. Through such an iterative process of competition and cooperation, the various subcomponents are optimized by different species subpopulations based on the optimization requirements of that particular time instant, enabling the coevolutionary algorithm to handle both the static and dynamic multiobjective problems. The effectiveness of the competitive-cooperation coevolutionary algorithm (COEA) in static environments is validated against various multiobjective evolutionary algorithms upon different benchmark problems characterized by various difficulties in local optimality, discontinuity, nonconvexity, and high-dimensionality. In addition, extensive studies are also conducted to examine the capability of dynamic COEA (dCOEA) in tracking the Pareto front as it changes with time in dynamic environments.      

混合个体选择机制的多目标进化算法

在多目标进化算法中,如何从后代候选集中选择最优解,显著地影响优化过程.当前,最优解的选择方式主要是基于实际目标值或者代理模型估计目标值.然而,这些选择方式往往是非常耗时或者存在精度差等问题,特别是对于一些实际的复杂优化问题.最近,一些研究人员开始利用有监督分类辅助后代选择,但是这些工作难以准备准确的正例和负例样本,或者存在耗时的参数调整等问题.为了解决这些问题,提出了一种新颖的融合分类与代理的混合个体选择机制,用于从后代候选集中选择最优解.在每一代优化中,首先利用分类器选择优良解;然后设计了一个轻量级的代理模型用于估计优良解的目标值;最后利用这些目标值对优良解进行排序,并选择最优解作为后代解.基于典型的多目标进化算法MOEA/D,利用混合个体选择机制设计了新的算法框架MOEA/D-CS.与当前流行的基于分解多目标进化算法比较,实验结果表明,所提出的算法取得了最好的性能.     

COMPARISON AND SELECTION OF OBJECTIVE FUNCTIONS IN MULTIOBJECTIVE COMMUNITY DETECTION

Detecting communities of complex networks has been an effective way to identify substructures that could correspond to important functions. Conventional approaches usually consider community detection as a single‐objective optimization problem, which may confine the solution to a particular community structure property. Recently, a new community detection paradigm is emerging: multiobjective optimization for community detection, which means simultaneously optimizing multiple criteria and obtaining a set of community partitions. The new paradigm has shown its advantages. However, an important issue is still open: what type of objectives should be optimized to improve the performance of multiobjective community detection? To exploit this issue, we first proposed a general multiobjective community detection solution (called NSGA‐Net) and then analyzed the structural characteristics of communities identified by a variety of objective functions that have been used or can potentially be used for community detection. After that, we exploited correlation relations (i.e., positively correlated, independent, or negatively correlated) between any two objective functions. Extensive experiments on both artificial and real networks demonstrate that NSGA‐Net optimizing over a pair of negatively correlated objectives usually leads to better performances compared with the single‐objective algorithm optimizing over either of the original objectives, or even to other well‐established community detection approaches.     

基于分解和多策略变异的多目标差分进化算法*

差分进化是一种有效的优化技术,已成功用于多目标优化问题。但也存在Pareto最优集合的收敛慢和多样性差等问题。针对上述不足,本文提出了一种基于分解和多策略变异的多目标差分进化算法(MODE/DMSM)。该算法利用基于分解的方法将多目标优化问题分解为多个单目标优化问题;通过高效的非支配排序方法选择具有良好收敛性和多样性的解来指导差分进化过程;采用了多策略变异方法来平衡进化过程中收敛性和多样性。在ZDT和DTLZ的10个测试函数上的仿真结果表明,本文算法在Parato最优集合的收敛性和多样性优于其他六种代表性多目标优化算法。     

改进NSGA-Ⅱ终止判断准则

在基于进化算法的多目标优化中,往往是通过设置最大进化代数来确定算法何时终止.但是,如果最大进化代数设置太大,会增加许多不必要的计算量,设置太小可能得不到理想的结果.为了解决上述问题,提出一种改进的终止判断准则,通过该终止判断准则,即使在最大进化代数设置得非常大的情况下,只要连续几次获得的相隔一定进化代数的Pareto优解集的种群距离均小于给定的阈值,算法即可终止,并得到理想的结果,算法不再继续计算直到进化到最大进化代数后才终止.从仿真结果可以看出,通过终止判断准则,不仅降低了进化代数,减少了计算量,证实了新终止判断准则可行.     

A Pareto-based hybrid multiobjective evolutionary approach for constrained multipath traffic engineering optimization in MPLS/GMPLS networks

This paper proposes a hybrid evolutionary algorithm for solving the constrained multipath traffic engineering problem in MPLS (Multi-Protocol Label Switching) network and its extended architecture GMPLS (Generalized MPLS). Multipath traffic engineering is gaining more importance in contemporary networks. It aims to satisfy the requirements of emerging network applications while optimizing the network performance and the utilization of the available resources within the network. A formulation of this problem as a multiobjective constrained mixed-integer program, which is known to be NP-hard, is first extended. Then, we develop a hybrid heuristic algorithm based on combining linear programming with a devised Pareto-based genetic algorithm for approximating the optimal Pareto curve. A numerical example is adopted from the literature to evaluate and compare the performance of six variations of the proposed heuristic. We study the statistical significance of the results using Kruskal–Wallis nonparametric test. We also compare the results of the heuristic approach with the lexicographic weighted Chebyshev method using a variety of performance metrics.     

A hybrid evolutionary algorithm for multiobjective variation tolerant logic mapping on nanoscale crossbar architectures

Nanoscale crossbar architectures have received steadily growing interests as a result of their great potential to be main building blocks in nanoelectronic circuits. However, due to the extremely small size of nanodevices and the bottom-up self-assembly nanofabrication process, considerable process variation will be an inherent vice for crossbar nanoarchitectures. In this paper, the variation tolerant logical mapping problem is treated as a bilevel multiobjective optimization problem. Since variation mapping is an NP-complete problem, a hybrid multiobjective evolutionary algorithm is designed to solve the problem adhering to a bilevel optimization framework. The lower level optimization problem, most frequently tackled, is modeled as the min–max-weight and min-weight-gap bipartite matching (MMBM) problem, and a Hungarian-based linear programming (HLP) method is proposed to solve MMBM in polynomial time. The upper level optimization problem is solved by evolutionary multiobjective optimization algorithms, where a greedy reassignment local search operator, capable of exploiting the domain knowledge and information from problem instances, is introduced to improve the efficiency of the algorithm. The numerical experiment results show the effectiveness and efficiency of proposed techniques for the variation tolerant logical mapping problem.