Geometrical Design of Plate-Fin Heat Sinks Using Hybridization of MOEA and RSM

The work in this paper is aimed at demonstrating the practical multiobjective optimization of plate-fin heat sinks and the superiority of using a combined response surface method and multiobjective evolutionary optimizer over solely using the evolutionary optimizer. The design problem assigned is to minimize a heat sink junction temperature and fan pumping power. Design variables determine a heat sink geometry and inlet air velocity. Design constraints are given in such a way that the maximum and minimum fin heights are properly limited. Function evaluation is carried out by using finite volume analysis software. Two multiobjective evolutionary optimization strategies, real-code strength Pareto evolutionary algorithm with and without the use of a response surface technique, are implemented to explore the Pareto optimal front. The optimum results obtained from both design approaches are compared and discussed. It is illustrated that the multiobjective evolutionary technique is a powerful tool for the multiobjective design of electronic air-cooled heat sinks. With the same design conditions and an equal number of function evaluations, the multiobjective optimizer in association with the response surface technique totally outperforms the other. The design parameters affecting the diversity of the Pareto front include fin thickness, fin height distribution, and inlet air velocity while the plate base thickness and the total number of fins of the non-dominated solutions tend to approach certain values.     

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 optimization of diagnostic classifiers withimplications for generating receiver operating characteristiccurves

It is well understood that binary classifiers have two implicit objective functions (sensitivity and specificity) describing their performance. Traditional methods of classifier training attempt to combine these two objective functions (or two analogous class performance measures) into one so that conventional scalar optimization techniques can be utilized. This involves incorporating a priori information into the aggregation method so that the resulting performance of the classifier is satisfactory for the task at hand. We have investigated the use of a niched Pareto multiobjective genetic algorithm (GA) for classifier optimization. With niched Pareto GA's, an objective vector is optimized instead of a scalar function, eliminating the need to aggregate classification objective functions. The niched Pareto GA returns a set of optimal solutions that are equivalent in the absence of any information regarding the preferences of the objectives. The a priori knowledge that was used for aggregating the objective functions in conventional classifier training can instead be applied post-optimization to select from one of the series of solutions returned from the multiobjective genetic optimization. We have applied this technique to train a linear classifier and an artificial neural network (ANN), using simulated datasets. The performances of the solutions returned from the multiobjective genetic optimization represent a series of optimal (sensitivity, specificity) pairs, which can be thought of as operating points on a receiver operating characteristic (ROC) curve. All possible ROC curves for a given dataset and classifier are less than or equal to the ROC curve generated by the niched Pareto genetic optimization.     

Multiminima heuristic methods for antenna optimization

Two general approaches to multiminima optimization are considered. The first approach is based on repetition of a single minima method (e.g., the Nelder-Mead simplex applied to the best solution in a set of random trials). The second approach is based on a coarse estimation of local minima using initial set of points and local optimization starting from these local minima (e.g., random search as a generator of the initial set of points and Nelder-Mead simplex as a local optimizer). A comparison of various optimization algorithms has been done on one analytical problem and two well-known examples of antenna design. It is found that: a) the multiminima method based on coarse estimation enables finding more minima with smaller number of iterations than that based on repetition, b) the best multiminima methods are comparable with the best single minima methods in a number of iterations needed for finding the global minima, and c) the multiminima method based on coarse estimation restarted with different weighting coefficients of multiobjective cost function enables efficient Pareto optimization.     

Connectivity constrained wireless sensor deployment using multiobjective evolutionary algorithms and fuzzy decision making

Deployment of sensor nodes is an important issue in designing sensor networks. The sensor nodes communicate with each other to transmit their data to a high energy communication node which acts as an interface between data processing unit and sensor nodes. Optimization of sensor node locations is essential to provide communication for a longer duration. An energy efficient sensor deployment based on multiobjective particle swarm optimization algorithm is proposed here and compared with that of non-dominated sorting genetic algorithm. During the process of optimization, sensor nodes move to form a fully connected network. The two objectives i.e. coverage and lifetime are taken into consideration. The optimization process results in a set of network layouts. A comparative study of the performance of the two algorithms is carried out using three performance metrics. The sensitivity analysis of different parameters is also carried out which shows that the multiobjective particle swarm optimization algorithm is a better candidate for solving the multiobjective problem of deploying the sensors. A fuzzy logic based strategy is also used to select the best compromised solution on the Pareto front.     

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.     

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.     

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.     

基于Pareto支配的MPRM电路面积与可靠性优化

针对MPRM（Mixed-Polarity Reed-Muller）电路的面积与可靠性折中优化问题,在逻辑级建立面积估算模型以及电路SER（Soft Error Rate）解析评价模型,并采用Pareto支配概念对MPRM电路进行面积与可靠性多目标优化.通过对MPRM电路的XOR部分进行树形异或门分解,并考虑多个输出之间异或门的共享,建立面积估算模型.采用信号概率和故障传播方法,并考虑电路中的逻辑屏蔽因素以及信号相关性,建立电路SER解析评价模型.根据所提出的面积和SER评价模型,采用极性向量的格雷码序穷举搜索MPRM的极性空间得到MPRM电路面积与可靠性的Pareto最优解集,并使用效率因子技术指标选取最终解.MCNC基准电路的实验结果表明,与面积最小MPRM电路相比,所选取的MPRM电路可以在较小面积开销的前提下获得较高电路可靠性.     

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。     

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。     

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.     

Multiobjective gas turbine engine controller design using geneticalgorithms

This paper describes the use of multiobjective genetic algorithms (MOGAs) in the design of a multivariable control system for a gas turbine engine. The mechanisms employed to facilitate multiobjective search with the genetic algorithm are described with the aid of an example. It is shown that the MOGA confers a number of advantages over conventional multiobjective optimization methods by evolving a family of Pareto-optimal solutions rather than a single solution estimate. This allows the engineer to examine the trade-offs between the different design objectives and configurations during the course of an optimization. In addition, the paper demonstrates how the genetic algorithm can be used to search in both controller structure and parameter space thereby offering a potentially more general approach to optimization in controller design than traditional numerical methods. While the example in the paper deals with control system design, the approach described can be expected to be applicable to more general problems in the fields of computer aided design (CAD) and computer aided engineering (CAE)     

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     

Development of robust interconnect model based on design ofexperiments and multiobjective optimization

When designing an integrated circuit, it is important to take into consideration random variations arising from process variability. Traditional optimization studies on VLSI interconnect attempt to find the deterministic optimum of a cost function but do not take into account the effect of these random variations on the objective. We have developed an effective methodology based on TCAD simulation and design of experiments to optimize interconnect including the effects of process variations. The aim of the study is to search for optimum designs that both meet the performance specification and are robust with respect to process variations. A multiobjective optimization technique known as Normal Boundary Intersection is used to find evenly-spaced tradeoff points on the Pareto curve. Designers can then select designs from the curve without using arbitrary weighting parameters. The proposed methodology was applied to a 0.12 μm CMOS technology; optimization results are discussed and verified using Monte Carlo simulation     

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.     

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.     

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.     

Performance modeling and optimization of multiple‐objective cross‐layer design in multi‐flow ad‐hoc networks

In ad‐hoc wireless networks, to achieve good performance, multiple parameters need to be optimized jointly. However, existing literature lacks a design framework that investigates the synchronic impact of several parameters on overall system performance. Among several design parameters, energy conservation, end‐to‐end delay minimization, and improved throughput are considered most important for efficient operation of these networks. In this paper, we propose a novel scheme for multiple‐objective cross‐layer optimization capable of optimizing all these performance objectives simultaneously for reliable, energy‐efficient, and timely transmission of continuous media information across the network. The three global criteria considered for optimization are incorporated in a single programming problem via linear scalarization. Besides, we employ standard convex optimization method and Lagrangian technique to solve the proposed problem to seek optimality. Extensive simulation results are generated accounting for several topologies with multiple concurrent flows in the network. These results are used to validate the analytical results and demonstrate the efficiency of the proposed optimization model. Efficiency of the model is verified by finding the set of Pareto‐optimal solutions plotted in three‐dimensional objective space. These solution points constituting the Pareto front are used as the best possible balance points among maximum throughput, maximum residual energy, and least network delay. Finally, to emphasize the effectiveness and supremacy of our proposed multiple‐objective cross‐layer design scheme, we compare it with the conventional multiple‐objective genetic algorithm. Simulation results demonstrate that our method provides significant performance gain over the genetic algorithm approach in terms of the above specified three objectives.