Multiobjective optimization design of Yagi-Uda antenna

An optimization method, such as the steepest gradient methods, could not easily obtain globally optimum solutions for devising antenna design parameters that allow the antenna to simultaneously improve multiple performances such as gain, sidelobe level, and input impedance. The genetic algorithm (GA) is suitable for empirically solving optimization problems and is effective in designing an antenna. In particular, this method can solve the multiobjective optimization problem using various Pareto-optimal solutions in an extremely efficient manner. In this paper, the Pareto GA, by which various Pareto-optimal solutions for each objective function (performance) can be obtained in a single trial of a numerical simulation and which enables the selection of parameters in accordance with the design requirement, is applied to the multiobjective optimization design of the Yagi-Uda antenna. The effectiveness of the Pareto GA was demonstrated by comparing the performances obtained by the Pareto GA with those of the previously reported values, which were obtained by the conventional GA, and with the values of the design benchmark reference.     

Multiobjective genetic algorithm applied to aerodynamic design ofcascade airfoils

A multiobjective genetic algorithm (GA) based on Fonseca-Fleming's Pareto-based ranking and fitness-sharing techniques has been applied to aerodynamic shape optimization of cascade airfoil design. Airfoil performance is evaluated by a Navier-Stokes code. Evaluation of GA population is parallelized on the Numerical Wind Tunnel, a parallel vector machine. The present multiobjective design seeks high pressure rise, high flow turning angle, and low total pressure loss at a low Mach number. Pareto solutions that perform better than existing control diffusion airfoils were obtained     

Optimization and FROC analysis of rule-based detection schemes using a multiobjective approach

Computerized detection schemes have the potential of increasing diagnostic accuracy in medical imaging by alerting radiologists to lesions that they initially overlooked. These schemes typically employ multiple parameters such as threshold values or filter weights to arrive at a detection decision. In order for the system to have high performance, the values of these parameters need to be set optimally. Conventional optimization techniques are designed to optimize a scalar objective function. The task of optimizing the performance of a computerized detection scheme, however, is clearly a multiobjective problem: we wish to simultaneously improve the sensitivity and false-positive rate of the system. In this work we investigate a multiobjective approach to optimizing computerized rule-based detection schemes. In a multiobjective optimization, multiple objectives are simultaneously optimized, with the objective now being a vector-valued function. The multiobjective optimization problem admits a set of solutions, known as the Pareto-optimal set, which are equivalent in the absence of any information regarding the preferences of the objectives. The performances of the Pareto-optimal solutions can be interpreted as operating points on an optimal free-response receiver operating characteristic (FROC) curve, greater than or equal to the points on any possible FROC curve for a given dataset and detection scheme. It is demonstrated that generating FROC curves in this manner eliminates several known problems with conventional FROC curve generation techniques for rule-based detection schemes. We employ the multiobjective approach to optimize a rule-based scheme for clustered microcalcification detection that has been developed in our laboratory.     

多个体参与交叉的Pareto多目标遗传算法

Pareto多目标遗传算法是利用Pareto最优的概念发展出的一种求解多目标优化问题的向量优化方法,能够得到Pareto最优解集.由于采用常规的两个体参与交叉的遗传算法,使整个算法耗费在小生境(Niche)算子上的时间太多,导致算法的效率较低.本文发展出多个体参与交叉的Pareto多目标遗传算法,群体中的个体采用真实值表示,使该算法的速度大大提高,同时证明了相应的模式定理,并提出用方差和熵来分析该算法对解群多样性的影响.最后用算例说明了采用多个体参与交叉的Pareto多目标遗传算法与常规算法比较的结果,证明了本文提出算法的优越性.     

Multiobjective GA optimization using reduced models

In this paper, we propose a novel method for solving multiobjective optimization problems using reduced models. Our method, called objective exchange genetic algorithm for design optimization (OEGADO), is intended for solving real-world application problems. For such problems, the number of objective evaluations performed is a critical factor as a single objective evaluation can be quite expensive. The aim of our research is to reduce the number of objective evaluations needed to find a well-distributed sampling of the Pareto-optimal region by applying reduced models to steady-state multiobjective GAs. OEGADO runs several GAs concurrently with each GA optimizing one objective and forming a reduced model of its objective. At regular intervals, each GA exchanges its reduced model with the others. The GAs use these reduced models to bias their search toward compromise solutions. Empirical results in several engineering and benchmark domains comparing OEGADO with two state-of-the-art multiobjective evolutionary algorithms show that OEGADO outperformed them for difficult problems.     

A cross-layer framework for multiobjective performance evaluation of wireless ad hoc networks

In this paper we address the problem of finding the optimal performance region of a wireless ad hoc network when multiple performance metrics are considered. Our contribution is to propose a novel cross-layer framework for deriving the Pareto optimal performance bounds for the network. These Pareto bounds provide key information for understanding the network behavior and the performance trade-offs when multiple criteria are relevant. Our approach is to take a holistic view of the network that captures the cross-interactions among interference management techniques implemented at various layers of the protocol stack (e.g. routing and resource allocation) and determines the objective functions for the multiple criteria to be optimized. The resulting complex multiobjective optimization problem is then solved by multiobjective search techniques. The Pareto optimal sets for an example sensor network are presented and analyzed when delay, reliability and energy objectives are considered.     

Design of electrically small wire antennas using a pareto genetic algorithm

We report on the use of a genetic algorithm (GA) in the design optimization of electrically small wire antennas, taking into account of bandwidth, efficiency and antenna size. For the antenna configuration, we employ a multisegment wire structure. The Numerical Electromagnetics Code (NEC) is used to predict the performance of each wire structure. To efficiently map out this multiobjective problem, we implement a Pareto GA with the concept of divided range optimization. In our GA implementation, each wire shape is encoded into a binary chromosome. A two-point crossover scheme involving three chromosomes and a geometrical filter are implemented to achieve efficient optimization. An optimal set of designs, trading off bandwidth, efficiency, and antenna size, is generated. Several GA designs are built, measured and compared to the simulation. Physical interpretations of the GA-optimized structures are provided and the results are compared against the well-known fundamental limit for small antennas. Further improvements using other geometrical design freedoms are discussed.     

正交免疫克隆粒子群多目标优化算法

该文基于抗体克隆选择学说理论,提出了一种求解多目标优化问题的粒子群算法正交免疫克隆粒子群算法(Orthogonal Immune Clone Particle Swarm Optimization, OICPSO)。根据多目标的特点,提出了适合粒子群算法的克隆算子,免疫基因算子,克隆选择算子。免疫基因操作中采用了离散正交交叉算子来获得目标空间解的均匀采样,得到理想的Pareto解集,并引入拥挤距离来减少获得Pareto解集的大小,同时获得具有良好均匀性和宽广性的Pareto最优解集。实验中,与NSGA-II和MOPSO算法进行了比较,并对算法的性能指标进行了分析。结果表明,OICPSO不仅增加了种群解的多样性而且可以得到分布均匀的Pareto有效解集,对于多目标优化问题是有效地。     

Shape optimization of corrugated coatings under grazing incidence using a genetic algorithm

We report on the use of a genetic algorithm (GA) to design optimal shapes for a corrugated coating under near-grazing incidence. A full-wave electromagnetic solver based on the boundary integral formulation is employed to predict the performance of the coating shape. In our GA implementation, we encode each shape of the coating into a binary chromosome. A two-point crossover scheme involving three chromosomes and a geometrical filter are implemented to achieve efficient optimization. A standard magnetic radar absorbing material (MAGRAM) is used for the absorber coating. We present the optimized coating shapes depending on different polarizations. A physical interpretation for the optimized structure is discussed and the resulting shape is compared to conventional planar and triangular shaped designs. Next, we extend this problem from single to multiobjective optimization by using a Pareto GA. The optimization results with two different objectives, viz. height (or weight) of the coating versus absorbing performance, are presented.     

Multiobjective programming using uniform design and genetic algorithm

The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to the decision maker. We design a genetic algorithm for this purpose. We compose multiple fitness functions to guide the search, where each fitness function is equal to a weighted sum of the normalized objective functions and we apply an experimental design method called uniform design to select the weights. As a result, the search directions guided by these fitness functions are scattered uniformly toward the Pareto frontier in the objective space. With multiple fitness functions, we design a selection scheme to maintain a good and diverse population. In addition, we apply the uniform design to generate a good initial population and design a new crossover operator for searching the Pareto-optimal solutions. The numerical results demonstrate that the proposed algorithm can find the Pareto-optimal solutions scattered uniformly over the Pareto frontier.     

Pareto-Based Multiobjective Machine Learning: An Overview and Case Studies

Machine learning is inherently a multiobjective task. Traditionally, however, either only one of the objectives is adopted as the cost function or multiple objectives are aggregated to a scalar cost function. This can be mainly attributed to the fact that most conventional learning algorithms can only deal with a scalar cost function. Over the last decade, efforts on solving machine learning problems using the Pareto-based multiobjective optimization methodology have gained increasing impetus, particularly due to the great success of multiobjective optimization using evolutionary algorithms and other population-based stochastic search methods. It has been shown that Pareto-based multiobjective learning approaches are more powerful compared to learning algorithms with a scalar cost function in addressing various topics of machine learning, such as clustering, feature selection, improvement of generalization ability, knowledge extraction, and ensemble generation. One common benefit of the different multiobjective learning approaches is that a deeper insight into the learning problem can be gained by analyzing the Pareto front composed of multiple Pareto-optimal solutions. This paper provides an overview of the existing research on multiobjective machine learning, focusing on supervised learning. In addition, a number of case studies are provided to illustrate the major benefits of the Pareto-based approach to machine learning, e.g., how to identify interpretable models and models that can generalize on unseen data from the obtained Pareto-optimal solutions. Three approaches to Pareto-based multiobjective ensemble generation are compared and discussed in detail. Finally, potentially interesting topics in multiobjective machine learning are suggested.     

Virtual network function–forwarding graph embedding: A genetic algorithm approach

Network function virtualization (NFV) provides a simple and effective mean to deploy and manage network and telecommunications' services. A typical service can be expressed in the form of a virtual network function–forwarding graph (VNF‐FG). Allocating a VNF‐FG is equivalent to place VNFs and virtual links onto a given substrate network considering resources and quality‐of‐service (QoS) constraints. The deployment of VNF‐FGs in large‐scale networks, such that QoS measures and deployment cost are optimized, is an emerging challenge. Single‐objective VNF‐FGs allocation has been addressed in existing literature; however, there is still a lack of studies considering multiobjective VNF‐FGs allocation. In addition, it is not trivial to obtain optimal VNF‐FGs allocation due to its high computational complexity even in case of single‐objective VNF‐FGs allocation. Genetic algorithms (GAs) have been proved its ability in coping with multiobjective optimization problems; thus, we propose a GA‐based scheme to solve multiobjective VNF‐FGs allocation problem in this paper. The numerical results confirm that the proposed scheme can provide near Pareto‐optimal solutions within a short execution time.     

Cross‐layer optimization for full‐duplex cognitive radio network with cooperative spectrum sensing

In this paper, the cross‐layer optimal design of multihop ad hoc network employing full‐duplex cognitive radios (CRs) is investigated. Firstly, the analytical expressions of cooperative spectrum sensing performance for multihop CR networks over composite fading channels are derived. Then, the opportunistic throughput and transmit power of CRs are presented based on the derivation of false alarm and missed detection probability. Finally, a multiobjective optimization model is proposed to maximize the opportunistic throughputs and minimize the transmitting power. Simulation results indicate that Pareto optimal solution of sensing duration, decision threshold, and transmit power can be achieved by cross‐layer multiobjective optimization, it can balance the conflicts between different objective functions and reap the acceptable outcomes for multihop CR network.     

电力线通信系统中基于改进NSGA-II的自适应资源分配

 分析电力线通信系统在各种约束下,多用户多业务在多子载波上自适应资源分配的多层多目标模型。基于快速的非支配分类遗传算法II,提出改进的功率或速率自适应的资源分配多目标和单目标优化遗传算法。在使用多目标遗传算法获得实时用户资源分配的所有Pareto非劣解后,由每个Pareto解计算系统的剩余资源,再采用单目标遗传算法把剩余资源分给非实时用户,最后从所有的资源分配方案中寻找全局最优方案。在典型电力线信道环境下仿真结果表明,本文算法其性能更好且能更好地满足多用户资源分配的多目标要求。     

Multiobjective evolutionary algorithm for the optimization of noisy combustion processes

This work introduces a multiobjective evolutionary algorithm capable of handling noisy problems with a particular emphasis on robustness against unexpected measurements (outliers). The algorithm is based on the Strength Pareto evolutionary algorithm of Zitzler and Thiele and includes the new concepts of domination dependent lifetime, re-evaluation of solutions and modifications in the update of the archive population. Several tests on prototypical functions underline the improvements in convergence speed and robustness of the extended algorithm. The proposed algorithm is implemented to the Pareto optimization of the combustion process of a stationary gas turbine in an industrial setup. The Pareto front is constructed for the objectives of minimization of NO/sub x/ emissions and reduction of the pressure fluctuations (pulsation) of the flame. Both objectives are conflicting affecting the environment and the lifetime of the turbine, respectively. The optimization leads a Pareto front corresponding to reduced emissions and pulsation of the burner. The physical implications of the solutions are discussed and the algorithm is evaluated.     

Grid Implementation of a Parallel Multiobjective Genetic Algorithm for Optimized Allocation of Chlorination Stations in Drinking Water Distribution Systems: Chojnice Case Study

Solving multiobjective optimization problems requires suitable algorithms to find a satisfactory approximation of a globally optimal Pareto front. Furthermore, it is a computationally demanding task. In this paper, the grid implementation of a distributed multiobjective genetic algorithm is presented. The distributed version of the algorithm is based on the island algorithm with forgetting island elitism used instead of a genetic data exchange. The algorithm is applied to the allocation of booster stations in a drinking water distribution system. First, a multiobjective formulation of the allocation problem is further enhanced in order to handle multiple water demand scenarios and to integrate controller design into the allocation problem formulation. Next, the new grid-based algorithm is applied to a case study system. The results are compared with a nondistributed version of the algorithm.     

Wireless communication network design in IC factory

A wireless local area network (WLAN) is designed for an IC factory in Hong Kong using the hierarchical genetic algorithm (HGA). The HGA is capable of handling multiobjective functions and discrete constraints. Because of this uniqueness, together with the adoption of a Pareto ranking scheme, a solution can be reached even when skewed multiobjective functions and constraints confinements are being imposed. It has been found from this study that a precise number of base stations can be identified for the WLAN network, while it can satisfy a number of objectives and constraints. This added feature provides a further design tradeoff between cost and performance at no extra effort     

一种基于多样性信息和收敛度的多目标粒子群优化算法

为了提高多目标粒子群算法优化解的多样性和收敛性,提出了一种基于多样性信息和收敛度的多目标粒子群优化算法（Multiobjective Particle Swarm Optimization based on the Diversity Information and Convergence Degree,dicdMOPSO）.首先,利用非支配解多样性信息评估知识库中最优解的分布状态,设计出一种全局最优解选择机制,平衡了种群的进化过程,提高了非支配解的多样性和收敛性;其次,基于种群多样性信息设计出一种飞行参数调整机制,增强了粒子的全局探索能力和局部开发能力,获得了多样性和收敛性较好的种群.最后,将dicdMOPSO应用于标准测试函数测试,实验结果表明,dicdMOPSO与其他多目标算法相比不仅获得了多样性较高的可行解,而且能够较快的收敛到Pareto前沿.     

Designing resilient networks using multicriteria metaheuristics

The paper deals with the design of resilient networks that are fault tolerant against link failures. Usually, fault tolerance is achieved by providing backup paths, which are used in case of an edge failure on a primary path. We consider this task as a multiobjective optimization problem: to provide resilience in networks while minimizing the cost subject to capacity constraint. We propose a stochastic approach, which can generate multiple Pareto solutions in a single run. The feasibility of the proposed method is illustrated by considering several network design problems using a single weighted average of objectives and a direct multiobjective optimization approach using the Pareto dominance concept.