Convex Optimization Strategies for Coordinating Large-Scale Robot Formations

This paper investigates convex optimization strategies for coordinating a large-scale team of fully actuated mobile robots. Our primary motivation is both algorithm scalability as well as real-time performance. To accomplish this, we employ a formal definition from shape analysis for formation representation and repose the motion planning problem to one of changing (or maintaining) the shape of the formation. We then show that optimal solutions, minimizing either the total distance or minimax distance the nodes must travel, can be achieved through second-order cone programming techniques. We further prove a theoretical complexity for the shape problem of O(m^1.5) as well as O(m) complexity in practice, where m denotes the number of robots in the shape configuration. Solutions for large-scale teams (1000's of robots) can be calculated in real time on a standard desktop PC. Extensions integrating both workspace and vehicle motion constraints are also presented with similar complexity bounds. We expect these results can be generalized for additional motion planning tasks, and will prove useful for improving the performance and extending the mission lives of large-scale robot formations as well as mobile ad hoc networks.     

A Greedy Algorithm for Decomposing Convex Structuring Elements

This paper presents a greedy algorithm for decomposing convex structuring elements as sequence of Minkowski additions of subsets of the elementary square (i.e., the 3 × 3 square centered at the origin). The technique proposed is very simple and it is based on algebraic and geometric properties of Minkowski additions. Besides its simplicity, the advantage of this new technique over other known algorithms is that it generates a minimal sequence of not necessarily convex subsets of the elementary square. Thus, subsets with smaller cardinality are generated and a faster implementation of the corresponding dilations and erosions can be achieved. Experimental results, proof of correctness and analysis of computational time complexity of the algorithm are also given.     

求解TSP问题的伪贪婪离散粒子群优化算法

以旅行商问题为例,提出一种基于元胞结构的伪贪婪离散粒子群优化算法.为了体现粒子对环境的感知能力,设计了伪贪婪的粒子位置修改操作算子,为了反映粒子间不同学习能力,体现粒子的个体差异性,设计了3种学习算子来提高算法的局部求精能力,为了更好地保持粒子群的多样性,采用了元胞结构作为粒子群的种群拓扑和邻城结构,这些策略使算法在空...     

Quasi-Lagrangian Neural Network for Convex Quadratic Optimization

A new neural network for convex quadratic optimization is presented in this brief. The proposed network can handle both equality and inequality constraints, as well as bound constraints on the optimization variables. It is based on the Lagrangian approach, but exploits a partial dual method in order to keep the number of variables at minimum. The dynamic evolution is globally convergent and the steady-state solutions satisfy the necessary and sufficient conditions of optimality. The circuit implementation is simpler with respect to existing solutions for the same class of problems. The validity of the proposed approach is verified through some simulation examples.     

基于穴度的三维时空优化问题的贪心调度算法

研究了基于二维矩形Packing的三维时空优化问题,即对给定的一个任意宽、高的大矩形框和有限个有连续加工时间要求的任意宽、高的小矩形块,如何安排每个小矩形块的入框时刻及其出框前每一时刻的位置和方向,使得所有小矩形块的总加工时间即总调度长度makespan最短。与经典布局问题的不同之处在于,各矩形块在框内可随时间的绵延而改变其位置和方向,从而能更充分地利用矩形框的空间。基于实角与实占角动作的定义,设计了求解其子问题二维矩形Packing问题的增强穴度算法。然后,每步迭代优先考虑剩余加工时间长的矩形块,提出了求解此问题的贪心穴度调度算法(caving-degree based greedy scheduling algorithm,CGSA)。作为比较,同时设计了矩形块在框内不可随时间移动的将时间简单类比为空间的对应Packing问题的调度算法CGSA′。对于实验中提出的满足非闸断模式的4个小型算例,它们在原问题上的最优调度长度为2,但若将时间简单地类比为空间,即矩形块放入框内后不可随时间移动其方位,则其最优调度长度为3。实验表明,算法CGSA在这4个非闸断算例上均得到了最优调度。进一步地研究出满足闸断模式的21组共210个自动生成算例,通过实验验证了算法CGSA的最优解的数目明显多于CGSA′,且CGSA的平均调度长度明显短于CGSA′。     

Distributed Convex Optimization for Flocking of Nonlinear Multi-agent Systems

International Journal of Control, Automation and Systems - A distributed optimization problem with differentiable convex objective function is discussed for continuous-time multi-agent systems with...     

Convex Optimization Algorithms for Active Balancing of Humanoid Robots

We show that a large class of active balancing problems for legged robots can be framed as a second-order cone programming (SOCP) problem, a convex optimization problem for which efficient and numerically robust algorithms exist. We describe this general SOCP balancing framework, show that several existing optimization-based balancing strategies reduce to special cases of this more general formulation, and investigate the computational performance of our SOCP algorithms through simulation studies involving a humanoid model.     

Entropy Optimization Models with Convex Constraints

In this paper, we study the minimum cross-entropy optimization problem subject to a general class of convex constraints. Using a simple geometric inequality and the conjugate inequality we demonstrate how to directly construct a "partial" geometric dual program which allows us to apply the dual perturbation method to derive the strong duality theorem and a dual-to-primal conversion formula. This approach generalizes the previous results of linearly, quadratically, and entropically constrained cross-entropy optimization problems and provides a platform for using general purpose optimizers to generate ε-optimal solution pair to the problem.     

Optimal Strategies for Inventory Control Systems with a Convex Cost Function

Some controlled Markovian processes in discrete time in the context of optimization of inventory control systems are studied. Optimality of (s, S)-policies for the case of convex cost functions is proved using theorems on existence and uniqueness of a nonrandomized stationary optimal policy for Markovian processes with discrete time and a continuous control set for criteria characterizing mean costs per unit time and overestimated total costs and Bellman equations.     

基于凸规划方法的计算机辅助结构拓扑优化设计

基于SIMP密度-刚度插值模型和移动渐近线方法,推导并建立了线弹性连续体结构刚度拓扑优化设计的数学模型．对中间密度材料进行研究,得出了惩罚因子的合理取值范围,分析了棋盘格式和网格依赖性等数值计算中存在的问题,并结合一种敏度过滤技术改善了这些问题．给出文中方法的程序流程,开发出二维结构的拓扑优化系统,通过一些经典的算例,证明了文中方法的有效性．     

A Convex Optimization Approach to ARMA Modeling

We formulate a convex optimization problem for approximating any given spectral density with a rational one having a prescribed number of poles and zeros ($n$ poles and $m$ zeros inside the unit disc and their conjugates). The approximation utilizes the Kullback–Leibler divergence as a distance measure. The stationarity condition for optimality requires that the approximant matches $n+1$ covariance moments of the given power spectrum and $m$ cepstral moments of the corresponding logarithm, although the latter with possible slack. The solution coincides with one derived by Byrnes, Enqvist, and Lindquist who addressed directly the question of covariance and cepstral matching. Thus, the present paper provides an approximation theoretic justification of such a problem. Since the approximation requires only moments of spectral densities and of their logarithms, it can also be used for system identification.      

基于凸优化的宽带阵列方向图综合算法

针对宽带任意阵列天线的方向图综合问题,提出了基于凸优化及其求解软件的方向图综合方法.其中针对宽带最低旁瓣方向图综合问题的特殊性,利用了凸优化的优良数值求解特性,以及最新的凸优化求解软件cvx时任意阵列天线的宽带最低旁瓣方向图综合算法进行了有效的建模和求解,获得了满足给定要求的宽带综合方向图.并通过详细的仿真分析验证了所提方法的正确性和有效性,而且优于当前提出的迭代算法.     

多主体服务组合的优化策略

论文分析了目前多主体服务组合的研究现状和存在的问题,为了提高多主体服务组合的性能,研究了主体服务请求的分类方法。在服务请求分类的基础上,研究了多主体服务组合的优化策略,提出了等价优化策略、相似优化策略和互补优化策略等三种优化策略,从理论上分析这些优化策略的性能特点,并用仿真实验验证了这些优化策略的有效性。     

基于凸优化的小蜂窝网络最小功耗方法

在考虑所有用户服务质量和每根天线功率约束的前提下,为使整个下行多用户小蜂窝网络的功耗最小,提出一种网络功耗优化方法。用半正定松弛方法将初始功耗最小问题转化成凸问题,再用凸优化工具箱求出功耗的最优解。发现小蜂窝网络每个接入点工作的天线数和被服务的用户数之间存在1∶1的数量关系,可使功耗最小,因此利用该特点,在功耗优化之前先进行天线选择,从而进一步减少功耗。仿真结果表明,与只做功耗优化、不做任何功耗优化和天线选择的方法相比,该优化方法的网络功耗最小。     

海量数据凸壳快速优化算法研究

分析描述加速凸壳算法的基本思想.在分析传统的加速凸壳算法的基础上,根据加速算法剔除内点的时机将加速算法分成静态加速算法和动态加算法.同时阐述了动态加速算法的应用条件,并将动态加速算法应于金字塔凸壳算法之中.通过大量实验数据对比说明动态加速算法对提高平面海量散乱点集的生成速度非常有效。     

Simultaneous Optimization via Approximate Majorization for Concave Profits or Convex Costs

For multicriteria problems and problems with a poorly characterized objective, it is often desirable to approximate simultaneously the optimum solution for a large class of objective functions. We consider two such classes: (1) Maximizing all symmetric concave functions. (2) Minimizing all symmetric convex functions. The first class corresponds to maximizing profit for a resource allocation problem (such as allocation of bandwidths in a computer network). The concavity requirement corresponds to the law of diminishing returns in economics. The second class corresponds to minimizing cost or congestion in a load balancing problem, where the congestion/cost is some convex function of the loads. Informally, a simultaneous α-approximation for either class is a feasible solution that is within a factor α of the optimum for all functions in that class. Clearly, the structure of the feasible set has a significant impact on the best possible α and the computational complexity of finding a solution that achieves (or nearly achieves) this α. We develop a framework and a set of techniques to perform simultaneous optimization for a wide variety of problems. We first relate simultaneous α-approximation for both classes to α-approximate majorization. Then we prove that α-approximately majorized solutions exist for logarithmic values of α for the concave profits case. For both classes, we present a polynomial-time algorithm to find the best α if the set of constraints is a polynomial-sized linear program and discuss several non-trivial applications. These applications include finding a (log n)-majorized solution for multicommodity flow, and finding approximately best α for various forms of load balancing problems. Our techniques can also be applied to produce approximately fair versions of the facility location and bi-criteria network design problems. In addition, we demonstrate interesting connections between distributional load balancing (where the sizes of jobs are drawn from known probability distributions but the actual size is not known at the time of placement) and approximate majorization.