Visible to the public Biblio

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Dai, Z., Li, Z. Y..  2015.  Fuzzy Optimization of Automobile Supply Chain Network of Considering Risks. 2015 Seventh International Symposium on Parallel Architectures Algorithms and Programming (PAAP). :134–138.

In this paper, an optimization model of automobile supply chain network with risks under fuzzy price is put forward. The supply chain network is composed of component suppliers, plants, and distribution centers. The total costs of automobile supply chain consist of variable costs, fixed costs, and transportation costs. The objective of this study is to minimize the risks of total profits. In order to deal with this model, this paper puts forward an approximation method to transform a continuous fuzzy problem into discrete fuzzy problem. The model is solved using Cplex 12.6. The results show that Cplex 12.6 can perfectly solve this model, the expected value and lower semi-variance of total profits converge with the increasing number of discretization points, the structure of automobile supply chain network keeps unchanged with the increasing number of discretization points.

Luo, Z., Gilimyanov, R., Zhuang, H., Zhang, J..  2015.  Network-Wide Optimization of Uplink Fractional Power Control in LTE Networks. 2015 IEEE 82nd Vehicular Technology Conference (VTC2015-Fall). :1–5.

Next generation cellular networks will provide users better experiences by densely deploying smaller cells, which results in more complicated interferences environment. In order to coordinate interference, power control for uplink is particularly challenging due to random locations of uplink transmitter and dense deployment. In this paper, we address the uplink fractional power control (FPC) optimization problem from network optimization perspective. The relations between FPC parameters and network KPIs (Key Performance Indicators) are investigated. Rather than considering any single KPI in conventional approaches, multi-KPI optimization problem is formulated and solved. By relaxing the discrete optimization problem to a continuous one, the gradients of multiple KPIs with respect to FPC parameters are derived. The gradient enables efficiently searching for optimized FPC parameters which is particularly desirable for dense deployment of large number of cells. Simulation results show that the proposed scheme greatly outperforms the traditional one, in terms of network mean load, call drop & block ratio, and convergence speed.

Ahmad, A. A., Günlük, O..  2015.  Robust-to-dynamics linear programming. 2015 54th IEEE Conference on Decision and Control (CDC). :5915–5919.

We consider a class of robust optimization problems that we call “robust-to-dynamics optimization” (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP, etc.), and (ii) a dynamical system (e.g., a linear, nonlinear, discrete, or continuous dynamics). The objective is to maximize over the set of initial conditions that forever remain feasible under the dynamics. The focus of this paper is on the case where the optimization problem is a linear program and the dynamics are linear. We establish some structural properties of the feasible set and prove that if the linear system is asymptotically stable, then the RDO problem can be solved in polynomial time. We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs.

Prabhakar, A., Flaßkamp, K., Murphey, T. D..  2015.  Symplectic integration for optimal ergodic control. 2015 54th IEEE Conference on Decision and Control (CDC). :2594–2600.

Autonomous active exploration requires search algorithms that can effectively balance the need for workspace coverage with energetic costs. We present a strategy for planning optimal search trajectories with respect to the distribution of expected information over a workspace. We formulate an iterative optimal control algorithm for general nonlinear dynamics, where the metric for information gain is the difference between the spatial distribution and the statistical representation of the time-averaged trajectory, i.e. ergodicity. Previous work has designed a continuous-time trajectory optimization algorithm. In this paper, we derive two discrete-time iterative trajectory optimization approaches, one based on standard first-order discretization and the other using symplectic integration. The discrete-time methods based on first-order discretization techniques are both faster than the continuous-time method in the studied examples. Moreover, we show that even for a simple system, the choice of discretization has a dramatic impact on the resulting control and state trajectories. While the standard discretization method turns unstable, the symplectic method, which is structure-preserving, achieves lower values for the objective.

Poveda, J. I., Teel, A. R..  2015.  Event-triggered based on-line optimization for a class of nonlinear systems. 2015 54th IEEE Conference on Decision and Control (CDC). :5474–5479.

We consider the problem of robust on-line optimization of a class of continuous-time nonlinear systems by using a discrete-time controller/optimizer, interconnected with the plant in a sampled-data structure. In contrast to classic approaches where the controller is updated after a fixed sufficiently long waiting time has passed, we design an event-based mechanism that triggers the control action only when the rate of change of the output of the plant is sufficiently small. By using this event-based update rule, a significant improvement in the convergence rate of the closed-loop dynamics is achieved. Since the closed-loop system combines discrete-time and continuous-time dynamics, and in order to guarantee robustness and semi-continuous dependence of solutions on parameters and initial conditions, we use the framework of hybrid set-valued dynamical systems to analyze the stability properties of the system. Numerical simulations illustrate the results.

Tatarenko, T..  2015.  1-recall reinforcement learning leading to an optimal equilibrium in potential games with discrete and continuous actions. 2015 54th IEEE Conference on Decision and Control (CDC). :6749–6754.

Game theory serves as a powerful tool for distributed optimization in multiagent systems in different applications. In this paper we consider multiagent systems that can be modeled as a potential game whose potential function coincides with a global objective function to be maximized. This approach renders the agents the strategic decision makers and the corresponding optimization problem the problem of learning an optimal equilibruim point in the designed game. In distinction from the existing works on the topic of payoff-based learning, we deal here with the systems where agents have neither memory nor ability for communication, and they base their decision only on the currently played action and the experienced payoff. Because of these restrictions, we use the methods of reinforcement learning, stochastic approximation, and learning automata extensively reviewed and analyzed in [3], [9]. These methods allow us to set up the agent dynamics that moves the game out of inefficient Nash equilibria and leads it close to an optimal one in both cases of discrete and continuous action sets.

Wang, X., Teng, Y., Song, M., Wang, X., Yuan, H..  2015.  Joint Optimization of Coverage and Capacity Based on Power Density Distribution in Heterogeneous Cellular Networks. 2015 Fifth International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC). :251–255.

The paper presents a joint optimization algorithm for coverage and capacity in heterogeneous cellular networks. A joint optimization objective related to capacity loss considering both coverage hole and overlap area based on power density distribution is proposed. The optimization object is a NP problem due to that the adjusting parameters are mixed with discrete and continuous, so the bacterial foraging (BF) algorithm is improved based on network performance analysis result to find a more effective direction than randomly selected. The results of simulation show that the optimization object is feasible gains a better effect than traditional method.

Song, D., Liu, W., Ji, R., Meyer, D. A., Smith, J. R..  2015.  Top Rank Supervised Binary Coding for Visual Search. 2015 IEEE International Conference on Computer Vision (ICCV). :1922–1930.

In recent years, binary coding techniques are becoming increasingly popular because of their high efficiency in handling large-scale computer vision applications. It has been demonstrated that supervised binary coding techniques that leverage supervised information can significantly enhance the coding quality, and hence greatly benefit visual search tasks. Typically, a modern binary coding method seeks to learn a group of coding functions which compress data samples into binary codes. However, few methods pursued the coding functions such that the precision at the top of a ranking list according to Hamming distances of the generated binary codes is optimized. In this paper, we propose a novel supervised binary coding approach, namely Top Rank Supervised Binary Coding (Top-RSBC), which explicitly focuses on optimizing the precision of top positions in a Hamming-distance ranking list towards preserving the supervision information. The core idea is to train the disciplined coding functions, by which the mistakes at the top of a Hamming-distance ranking list are penalized more than those at the bottom. To solve such coding functions, we relax the original discrete optimization objective with a continuous surrogate, and derive a stochastic gradient descent to optimize the surrogate objective. To further reduce the training time cost, we also design an online learning algorithm to optimize the surrogate objective more efficiently. Empirical studies based upon three benchmark image datasets demonstrate that the proposed binary coding approach achieves superior image search accuracy over the state-of-the-arts.

Boykov, Y., Isack, H., Olsson, C., Ayed, I. B..  2015.  Volumetric Bias in Segmentation and Reconstruction: Secrets and Solutions. 2015 IEEE International Conference on Computer Vision (ICCV). :1769–1777.

Many standard optimization methods for segmentation and reconstruction compute ML model estimates for appearance or geometry of segments, e.g. Zhu-Yuille [23], Torr [20], Chan-Vese [6], GrabCut [18], Delong et al. [8]. We observe that the standard likelihood term in these formu-lations corresponds to a generalized probabilistic K-means energy. In learning it is well known that this energy has a strong bias to clusters of equal size [11], which we express as a penalty for KL divergence from a uniform distribution of cardinalities. However, this volumetric bias has been mostly ignored in computer vision. We demonstrate signif- icant artifacts in standard segmentation and reconstruction methods due to this bias. Moreover, we propose binary and multi-label optimization techniques that either (a) remove this bias or (b) replace it by a KL divergence term for any given target volume distribution. Our general ideas apply to continuous or discrete energy formulations in segmenta- tion, stereo, and other reconstruction problems.

Kerl, C., Stückler, J., Cremers, D..  2015.  Dense Continuous-Time Tracking and Mapping with Rolling Shutter RGB-D Cameras. 2015 IEEE International Conference on Computer Vision (ICCV). :2264–2272.

We propose a dense continuous-time tracking and mapping method for RGB-D cameras. We parametrize the camera trajectory using continuous B-splines and optimize the trajectory through dense, direct image alignment. Our method also directly models rolling shutter in both RGB and depth images within the optimization, which improves tracking and reconstruction quality for low-cost CMOS sensors. Using a continuous trajectory representation has a number of advantages over a discrete-time representation (e.g. camera poses at the frame interval). With splines, less variables need to be optimized than with a discrete representation, since the trajectory can be represented with fewer control points than frames. Splines also naturally include smoothness constraints on derivatives of the trajectory estimate. Finally, the continuous trajectory representation allows to compensate for rolling shutter effects, since a pose estimate is available at any exposure time of an image. Our approach demonstrates superior quality in tracking and reconstruction compared to approaches with discrete-time or global shutter assumptions.

Ding, C., Peng, J..  2015.  A hopping sensor deployment scheme based on virtual forces. 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO). :988–993.

Wireless sensor networks have been widely utilized in many applications such as environment monitoring and controlling. Appropriate sensor deployment scheme to achieve the maximal coverage is crucial for effectiveness of sensor network. In this paper, we study coverage optimization problem with hopping sensors. Although similar problem has been investigated when each mobile sensor has continuous dynamics, the problem is different for hopping sensor which has discrete and constraint dynamics. Based on the characteristics of hopping, we obtain dynamics equation of hopping sensors. Then we propose an enhanced virtual force algorithm as a deployment scheme to improve the coverage. A combination of attractive and repulsive forces generated by Voronoi neighbor sensors, obstacles and the centroid of local Voronoi cell is used to determine the motion paths for hopping sensors. Furthermore, a timer is designed to adjust the movement sequence of sensors, such that unnecessary movements can be reduced. Simulation results show that optimal coverage can be accomplished by hopping sensors in an energy efficient manner.

Reis, R..  2015.  Trends on EDA for low power. 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO). :1–4.

One of the main issues in the design of modern integrated circuits is power reduction. Mainly in digital circuits, the power consumption was defined by the dynamic power consumption, during decades. But in the new NanoCMOs technologies, the static power due to the leakage current is becoming the main issue in power consumption. As the leakage power is related to the amount of components, it is becoming mandatory to reduce the amount of transistors in any type of design, to reduce power consumption. So, it is important to obtain new EDA algorithms and tools to optimize the amount of components (transistors). It is also needed tools for the layout design automation that are able to design any network of components that is provided by an optimization tool that is able to reduce the size of the network of components. It is presented an example of a layout design automation tool that can do the layout of any network of transistors using transistors of any size. Another issue for power optimization is the use of tools and algorithms for gate sizing. The designer can manage the sizing of transistors to reduce power consumption, without compromising the clock frequency. There are two types of gate sizing, discrete gate sizing and continuous gate sizing. The discrete gate sizing tools are used when it is being used a cell library that has only few available sizes for each cell. The continuous gate sizing considers that the EDA tool can define any transistor sizing. In this case, the designer needs to have a layout design tool able to do the layout of transistors with any size. It will be presented the winner tools of the ISPD Contest 2012 and 2013. Also, it will be discussed the inclusion of our gate sizing algorithms in an industrial flow used to design state-of-the-art microprocessors. Another type of EDA tool that is becoming more and more useful is the visualization tools that provide an animated visual output of the running of EDA tools. This kind of tools is very usef- l to show to the tool developers how the tool is running. So, the EDA developers can use this information to improve the algorithms used in an EDA Tool.

Farayev, B., Sadi, Y., Ergen, S. C..  2015.  Optimal Power Control and Rate Adaptation for Ultra-Reliable M2M Control Applications. 2015 IEEE Globecom Workshops (GC Wkshps). :1–6.

The main challenge of ultra-reliable machine-to-machine (M2M) control applications is to meet the stringent timing and reliability requirements of control systems, despite the adverse properties of wireless communication for delay and packet errors, and limited battery resources of the sensor nodes. Since the transmission delay and energy consumption of a sensor node are determined by the transmission power and rate of that sensor node and the concurrently transmitting nodes, the transmission schedule should be optimized jointly with the transmission power and rate of the sensor nodes. Previously, it has been shown that the optimization of power control and rate adaptation for each node subset can be separately formulated, solved and then used in the scheduling algorithm in the optimal solution of the joint optimization of power control, rate adaptation and scheduling problem. However, the power control and rate adaptation problem has been only formulated and solved for continuous rate transmission model, in which Shannon's capacity formulation for an Additive White Gaussian Noise (AWGN) wireless channel is used in the calculation of the maximum achievable rate as a function of Signal-to-Interference-plus-Noise Ratio (SINR). In this paper, we formulate the power control and rate adaptation problem with the objective of minimizing the time required for the concurrent transmission of a set of sensor nodes while satisfying their transmission delay, reliability and energy consumption requirements based on the more realistic discrete rate transmission model, in which only a finite set of transmit rates are supported. We propose a polynomial time algorithm to solve this problem and prove the optimality of the proposed algorithm. We then combine it with the previously proposed scheduling algorithms and demonstrate its close to optimal performance via extensive simulations.

Ji, Y., Wang, J., Yan, S., Gao, W., Li, H..  2015.  Optimal microgrid energy management integrating intermittent renewable energy and stochastic load. 2015 IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC). :334–338.

In this paper, we focus on energy management of distributed generators (DGs) and energy storage system (ESS) in microgrids (MG) considering uncertainties in renewable energy and load demand. The MG energy management problem is formulated as a two-stage stochastic programming model based on optimization principle. Then, the optimization model is decomposed into a mixed integer quadratic programming problem by using discrete stochastic scenarios to approximate the continuous random variables. A Scenarios generation approach based on time-homogeneous Markov chain model is proposed to generate simulated time-series of renewable energy generation and load demand. Finally, the proposed stochastic programming model is tested in a typical LV network and solved by Matlab optimization toolbox. The simulation results show that the proposed stochastic programming model has a better performance to obtain robust scheduling solutions and lower the operating cost compared to the deterministic optimization modeling methods.

Wang, J., Zhou, Y..  2015.  Multi-objective dynamic unit commitment optimization for energy-saving and emission reduction with wind power. 2015 5th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT). :2074–2078.

As a clean energy, wind power is massively utilized in net recent years, which significantly reduced the pollution emission created from unit. This article referred to the concept of energy-saving and emission reducing; built a multiple objective function with represent of the emission of CO2& SO2, the coal-fired from units and the lowest unit fees of commitment; Proposed a algorithm to improving NSGA-D (Non-dominated Sorting Genetic Algorithm-II) for the dynamic characteristics, consider of some constraint conditions such as the shortest operation and fault time and climbing etc.; Optimized and commitment discrete magnitude and Load distribution continuous quantity with the double-optimization strategy; Introduced the fuzzy satisfaction-maximizing method to reaching a decision for Pareto solution and also nested into each dynamic solution; Through simulation for 10 units of wind power, the result show that this method is an effective way to optimize the Multi-objective unit commitment modeling in wind power integrated system with Mixed-integer variable.

Fan, H., Ji, X. y, Chen, S..  2015.  A hybrid algorithm for reactive power optimization based on bi-level programming. International Conference on Renewable Power Generation (RPG 2015). :1–4.

This paper established a bi-level programming model for reactive power optimization, considering the feature of the grid voltage-reactive power control. The targets of upper-level and lower-level are minimization of grid loss and voltage deviation, respectively. According to the differences of two level, such as different variables, different solution space, primal-dual interior point algorithm is suggested to be used in upper-level, which takes continuous variables in account such as active power source and reactive power source. Upper-level model guaranteed the sufficient of the reactive power in power system. And then in lower-level the discrete variables such as taps are optimized by random forests algorithm (RFA), which regulate the voltage in a feasible range. Finally, a case study illustrated the speediness and robustness of this method.

Santra, N., Biswas, S., Acharyya, S..  2015.  Neural modeling of Gene Regulatory Network using Firefly algorithm. 2015 IEEE UP Section Conference on Electrical Computer and Electronics (UPCON). :1–6.

Genes, proteins and other metabolites present in cellular environment exhibit a virtual network that represents the regulatory relationship among its constituents. This network is called Gene Regulatory Network (GRN). Computational reconstruction of GRN reveals the normal metabolic pathway as well as disease motifs. Availability of microarray gene expression data from normal and diseased tissues makes the job easier for computational biologists. Reconstruction of GRN is based on neural modeling. Here we have used discrete and continuous versions of a meta-heuristic algorithm named Firefly algorithm for structure and parameter learning of GRNs respectively. The discrete version for this problem is proposed by us and it has been applied to explore the discrete search space of GRN structure. To evaluate performance of the algorithm, we have used a widely used synthetic GRN data set. The algorithm shows an accuracy rate above 50% in finding GRN. The accuracy level of the performance of Firefly algorithm in structure and parameter optimization of GRN is promising.

Riffi, M. E., Bouzidi, M..  2015.  Discrete cuttlefish optimization algorithm to solve the travelling salesman problem. 2015 Third World Conference on Complex Systems (WCCS). :1–6.

The cuttlefish optimization algorithm is a new combinatorial optimization algorithm in the family of metaheuristics, applied in the continuous domain, and which provides mechanisms for local and global research. This paper presents a new adaptation of this algorithm in the discrete case, solving the famous travelling salesman problem, which is one of the discrete combinatorial optimization problems. This new adaptation proposes a reformulation of the equations to generate solutions depending a different algorithm cases. The experimental results of the proposed algorithm on instances of TSPLib library are compared with the other methods, show the efficiency and quality of this adaptation.

Li, Xiao-Ke, Gu, Chun-Hua, Yang, Ze-Ping, Chang, Yao-Hui.  2015.  Virtual machine placement strategy based on discrete firefly algorithm in cloud environments. 2015 12th International Computer Conference on Wavelet Active Media Technology and Information Processing (ICCWAMTIP). :61–66.

Because of poor performance of heuristic algorithms on virtual machine placement problem in cloud environments, a multi-objective constraint optimization model of virtual machine placement is presented, which taking energy consumption and resource wastage as the objective. We solve the model based on the proposed discrete firefly algorithm. It takes firefly's location as the placement result, brightness as the objective value. Its movement strategy makes darker fireflies move to brighter fireflies in solution space. The continuous position after movement is discretized by the proposed discrete strategy. In order to speed up the search for solution, the local search mechanism for the optimal solution is introduced. The experimental results in OpenStack cloud platform show that the proposed algorithm makes less energy consumption and resource wastage compared with other algorithms.

Torabi, A., Shishegar, A. A..  2015.  Combination of characteristic Green's function technique and rational function fitting method for computation of modal reflectivity at the optical waveguide end-facet. 2015 International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS). 2:14–21.

A novel method for computation of modal reflectivity at optical waveguide end-facet is presented. The method is based on the characteristic Green's function (CGF) technique. Using separability assumption of the structure and rational function fitting method (RFFM), a closed-form field expression is derived for optical planar waveguide. The uniform derived expression consists of discrete and continuous spectrum contributions which denotes guided and radiation modes effects respectively. An optimization problem is then defined to calculate the exact reflection coefficients at the end-facet for all extracted poles obtained from rational function fitting step. The proposed CGF-RFFM-optimization offers superior exactness in comparison with the previous reported CGF-complex images (CI) technique due to contribution of all components of field in the optimization problem. The main advantage of the proposed method lies in its simple implementation as well as precision for any refractive index contrast. Excellent numerical agreements with rigorous methods are shown in several examples.

Shen, M., Liu, F..  2015.  Query of Uncertain QoS of Web Service. 2015 IEEE 12th Intl Conf on Ubiquitous Intelligence and Computing and 2015 IEEE 12th Intl Conf on Autonomic and Trusted Computing and 2015 IEEE 15th Intl Conf on Scalable Computing and Communications and Its Associate. :1780–1785.

Quality of service (QoS) has been considered as a significant criterion for querying among functionally similar web services. Most researches focus on the search of QoS under certain data which may not cover some practical scenarios. Recent approaches for uncertain QoS of web service deal with discrete data domain. In this paper, we try to build the search of QoS under continuous probability distribution. We offer the definition of two kinds of queries under uncertain QoS and form the optimization approaches for specific distributions. Based on that, the search is extended to general cases. With experiments, we show the feasibility of the proposed methods.

Lian, Y..  2015.  Challenges in the design of self-powered wearable wireless sensors for healthcare Internet-of-Things. 2015 IEEE 11th International Conference on ASIC (ASICON). :1–4.

The design of low power chip for IoT applications is very challenge, especially for self-powered wireless sensors. Achieving ultra low power requires both system level optimization and circuit level innovation. This paper presents a continuous-in-time and discrete-in-amplitude (CTDA) system architecture that facilitates adaptive data rate sampling and clockless implementation for a wireless sensor SoC.

Jalili, A., Ahmadi, V., Keshtgari, M., Kazemi, M..  2015.  Controller placement in software-defined WAN using multi objective genetic algorithm. 2015 2nd International Conference on Knowledge-Based Engineering and Innovation (KBEI). :656–662.

SDN is a promising architecture that can overcome the challenges facing traditional networks. SDN enables administrator/operator to build a simpler, customizable, programmable, and manageable network. In software-defined WAN deployments, multiple controllers are often needed, and the location of these controllers affect various metrics. Since these metrics conflict each other, this problem can be regarded as a multi-objective combinatorial optimization problem (MOCO). A particular efficient method to solve a typical MOCO, which is used in the relevant literature, is to find the actual Pareto frontier first and give it to the decision maker to select the most appropriate solution(s). In small and medium sized combinatorial problems, evaluating the whole search space and find the exact Pareto frontier may be possible in a reasonable time. However, for large scale problems whose search spaces involves thousands of millions of solutions, the exhaustive evaluation needs a considerable amount of computational efforts and memory used. An effective alternative mechanism is to estimate the original Pareto frontier within a relatively small algorithm's runtime and memory consumption. Heuristic methods, which have been studied well in the literature, proved to be very effective methods in this regards. The second version of the Non-dominated Sorting Genetic Algorithm, called NSGA-II has been carried out quite well on different discrete and continuous optimization problems. In this paper, we adapt this efficient mechanism for a new presented multi-objective model of the control placement problem [7]. The results of implementing the adapted algorithm carried out on the Internet2 OS3E network run on MATLAB 2013b confirmed its effectiveness.

Finn, J., Nuzzo, P., Sangiovanni-Vincentelli, A..  2015.  A mixed discrete-continuous optimization scheme for Cyber-Physical System architecture exploration. 2015 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). :216–223.

We propose a methodology for architecture exploration for Cyber-Physical Systems (CPS) based on an iterative, optimization-based approach, where a discrete architecture selection engine is placed in a loop with a continuous sizing engine. The discrete optimization routine proposes a candidate architecture to the sizing engine. The sizing routine optimizes over the continuous parameters using simulation to evaluate the physical models and to monitor the requirements. To decrease the number of simulations, we show how balance equations and conservation laws can be leveraged to prune the discrete space, thus achieving significant reduction in the overall runtime. We demonstrate the effectiveness of our methodology on an industrial case study, namely an aircraft environmental control system, showing more than one order of magnitude reduction in optimization time.

Hu, N. G., Xiang, B. B..  2015.  Discrete variable optimization of reflector antenna with continuous method. Fifth Asia International Symposium on Mechatronics (AISM 2015). :1–4.

In practical reflector antenna structures, components of the back-up structure (BUS) are selected form a standard steel library which is normally manufactured. In this case, the design problem of the antenna structure is a discrete optimization problem. In most cases, discrete design is solved by heuristic-based algorithm which will be computing-expensive when the number of deign variable increases. In this paper, a continuous method is used to transfer the discrete optimization problem to a continuous one and gradient-based technique is utilized to solve this problem. The method proposed can achieve a well antenna surface accuracy with all components selected from a standard cross-section list, which is shown by a 9m diameter antenna optimization problem.