Network flow formulation of optimal perimeter sensory coverage problem

In this article, the perimeter detection optimization problem in field surveillance and target tracking are discussed. The detection range of sensors is assumed to be circular or elliptical. Sensors are also assumed to be associated with a cost factor reflecting their operational characteristics and power usage. We show that the problem of optimal sensor selection can be reduced to a network flow problem and can then be solved using any existing classical methodology. This significantly reduces the computational time of sensory selection problem which in many cases needs to be solved in almost real time basis, every time that the dynamics of the field changes. The field dynamics could change due to such events as wind direction change and sensor failures.     

Efficient sample sizes in stochastic nonlinear programming

We consider a class of stochastic nonlinear programs for which an approximation to a locally optimal solution is specified in terms of a fractional reduction of the initial cost error. We show that such an approximate solution can be found by approximately solving a sequence of sample average approximations. The key issue in this approach is the determination of the required sequence of sample average approximations as well as the number of iterations to be carried out on each sample average approximation in this sequence. We show that one can express this requirement as an idealized optimization problem whose cost function is the computing work required to obtain the required error reduction. The specification of this idealized optimization problem requires the exact knowledge of a few problems and algorithm parameters. Since the exact values of these parameters are not known, we use estimates, which can be updated as the computation progresses. We illustrate our approach using two numerical examples from structural engineering design.     

Impulsive optimal control model for the trajectory of horizontal wells

This paper presents an impulsive optimal control model for solving the optimal designing problem of the trajectory of horizontal wells. We take fully into account the effect of unknown disturbances in drilling. The optimal control problem can be converted into a nonlinear parametric optimization by integrating the state equation. We discuss here that the locally optimal solution depends in a continuous way on the parameters (disturbances) and utilize this property to propose a revised Hooke–Jeeves algorithm. The uniform design technique is incorporated into the revised Hooke–Jeeves algorithm to handle the multimodal objective function. The numerical simulation is in accordance with theoretical results. The numerical results illustrate the validity of the model and efficiency of the algorithm.     

Meta-control of an interacting-particle algorithm for global optimization

A common issue for stochastic global optimization algorithms is how to set the parameters of the sampling distribution (e.g. temperature, mutation/cross-over rates, selection rate, etc.) so that the samplings converge to the optimum effectively and efficiently. We consider an interacting-particle algorithm and develop a meta-control methodology which analytically guides the inverse temperature parameter of the algorithm to achieve desired performance characteristics (e.g. quality of the final outcome, algorithm running time, etc.). The main aspect of our meta-control methodology is to formulate an optimal control problem where the fractional change in the inverse temperature parameter is the control variable. The objectives of the optimal control problem are set according to the desired behavior of the interacting-particle algorithm. The control problem considers particles’ average behavior, rather than treating the behavior of individual particles. The solution to the control problem provides feedback on the inverse temperature parameter of the algorithm.     

Experimental design for distributed parameter vector systems

We formulate an optimal design problem for the selection of best states to observe and optimal sampling times and locations for parameter estimation or inverse problems involving complex nonlinear partial differential systems. An iterative algorithm for implementation of the resulting methodology is proposed.     

Portfolio selection under possibilistic mean–variance utility and a SMO algorithm

In this paper, we propose a new portfolio selection model with the maximum utility based on the interval-valued possibilistic mean and possibilistic variance, which is a two-parameter quadratic programming problem. We also present a sequential minimal optimization (SMO) algorithm to obtain the optimal portfolio. The remarkable feature of the algorithm is that it is extremely easy to implement, and it can be extended to any size of portfolio selection problems for finding an exact optimal solution.     

Self-Adaptive Genetic Algorithm for Clustering

Clustering is a hard combinatorial problem which has many applications in science and practice. Genetic algorithms (GAs) have turned out to be very effective in solving the clustering problem. However, GAs have many parameters, the optimal selection of which depends on the problem instance. We introduce a new self-adaptive GA that finds the parameter setup on-line during the execution of the algorithm. In this way, the algorithm is able to find the most suitable combination of the available components. The method is robust and achieves results comparable to or better than a carefully fine-tuned non-adaptive GA.     

A robust optimization approach to experimental design for model discrimination of dynamical systems

A high-ranking goal of interdisciplinary modeling approaches in science and engineering are quantitative prediction of system dynamics and model based optimization. Quantitative modeling has to be closely related to experimental investigations if the model is supposed to be used for mechanistic analysis and model predictions. Typically, before an appropriate model of an experimental system is found different hypothetical models might be reasonable and consistent with previous knowledge and available data. The parameters of the models up to an estimated confidence region are generally not known a priori. Therefore one has to incorporate possible parameter configurations of different models into a model discrimination algorithm which leads to the need for robustification. In this article we present a numerical algorithm which calculates a design of experiments allowing optimal discrimination of different hypothetic candidate models of a given dynamical system for the most inappropriate (worst case) parameter configurations within a parameter range. The design comprises initial values, system perturbations and the optimal placement of measurement time points, the number of measurements as well as the time points are subject to design. The statistical discrimination criterion is worked out rigorously for these settings, a derivation from the Kullback-Leibler divergence as optimization objective is presented for the case of discontinuous Heaviside-functions modeling the measurement decision which are replaced by continuous approximations during the optimization procedure. The resulting problem can be classified as a semi-infinite optimization problem which we solve in an outer approximations approach stabilized by a suggested homotopy strategy whose efficiency is demonstrated. We present the theoretical framework, algorithmic realization and numerical results.     

On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

An efficient algorithm for optimal design of area traffic control with network flows

An equilibrium network design (EQND) is a problem of finding the optimal design parameters while taking into account the route choice of users. This problem can be formulated as an optimization by taking the user equilibrium traffic assignment as a constraint. In this paper, the methods solving the EQND problem with signal settings are investigated via numerical calculations on two example road networks. An efficient algorithm is proposed in which improvement on a locally optimal search by combining the technique of parallel tangents with the gradient projection method is presented. As it shows, the method combines the locally optimal search and globally search heuristic achieved substantially better performance than did those other approaches.     

Optimal Noncollapsing Space-Filling Designs for Irregular Experimental Regions

Space-filling and noncollapsing are two important properties in designing computer experiments. We study how the noncollapsing, space-filling designs for irregular experimental regions can be generated efficiently by the proposed metaheuristic methods. We solve this optimal design problem using variants of the discrete particle swarm optimization (DPSO) approaches. Numerical results, including an application in data center thermal management, are used to illustrate the performances of the proposed algorithms. Based on these numerical results, we assert that the most efficient approach is to reformulate the target optimal design problem as a constrained optimization problem and then use a modified DPSO to solve the constrained optimization problem.     

基于可信性分布的投资组合问题的一种混合智能方法

研究了模糊环境下基于效用函数的有效资产投资组合的收益率模型,模型建立在可信性分布的基础上,而不是概率分布或可能性分布基础上.给出模糊环境下基于可信性分布的n种资产的最优投资组合问题的混合智能算法以寻找某种效用函数意义下的最优组合.并以实例仿真说明该方法的有效性.     

基于改进遗传算法的多机调度问题

遗传算法是解决多机调度组合优化问题最有效的方法之一,但由于其自身存在着一定的缺陷应用受到一定的限制.针对遗传算法的“早熟”和非均匀地在优化空间中搜索等缺陷,提出了一种自适应选择交叉概率、变异概率以及交叉位置非等概率选取的改进的遗传算法,并将其用于某钢管钢绳企业的多机调度问题,进行了仿真分析.     

Choosing Optimal Parameters in Iterative Processes

We consider the problem of choosing optimal parameters in certain iterative procedures. Specifically, we are interested in finite-step processes for which it is possible to estimate the computational cost and the error relaxation in terms of the process parameters. The problem of finding the optimal process that provides the required error relaxation with a minimal total computational cost is defined and studied. To solve the problem, it is generally necessary to solve a series of mathematical programming problems with rapidly increasing dimension. We suggest two ways to avoid that difficulty. The first is to find a process that is close to the optimal process, by solving only one mathematical programming problem. The second is to define optimal processes in some special cases when this problem can be simplified. We define conditions under which processes with geometrically decreasing error are optimal or asymptotically optimal. The methods of finding parameters of such processes are also provided. We illustrate our ideas with two examples: the bilevel gradient method for unconstrained function minimization and the iterative process for solving an optimal design problem.     

A new multi-objective discrete robust optimization algorithm for engineering design

This paper proposes a novel multi-objective discrete robust optimization (MODRO) algorithm for design of engineering structures involving uncertainties. In the present MODRO procedure, grey relational analysis (GRA), coupled with principal component analysis (PCA), was used as a multicriteria decision making model for converting multiple conflicting objectives into one unified cost function. The optimization process was iterated using the successive Taguchi approach to avoid the limitation that the conventional Taguchi method fails to deal with a large number of design variables and design levels. The proposed method was first verified by a mathematical benchmark example and a ten-bar truss design problem; and then it was applied to a more sophisticated design case of full scale vehicle structure for crashworthiness criteria. The results showed that the algorithm is able to achieve an optimal design in a fairly efficient manner attributable to its integration with the multicriteria decision making model. Note that the optimal design can be directly used in practical applications without further design selection. In addition, it was found that the optimum is close to the corresponding Pareto frontier generated from the other approaches, such as the non-dominated sorting genetic algorithm II (NSGA-II), but can be more robust as a result of introduction of the Taguchi method. Due to its independence on metamodeling techniques, the proposed algorithm could be fairly promising for engineering design problems of high dimensionality.     

The cutting stock problem for large sections in the iron and steel industries

The characteristics of a cutting stock problem for large sections in the iron and steel industries are as follows:(1) There is a variety of criterions such as maximizing yield and increasing effeciency of production lines. (2) A cutting stock problem is accompanied by an optimal stock selection problem. A two-phase algorithm is developed, using an heuristic method. This algorithm gives nearly optimal solutions in real time. It is applied to both batch-solving and on-line solving of one-dimensional cutting of large section. The new algorithm has played an important role in a large-section production system to increase the yield by approximately 2.5%.     

Bayesian source detection and parameter estimation of a plume model based on sensor network measurements

We consider a network of sensors that measure the intensities of a complex plume composed of multiple absorption–diffusion source components. We address the problem of estimating the plume parameters, including the spatial and temporal source origins and the parameters of the diffusion model for each source, based on a sequence of sensor measurements. The approach not only leads to multiple‐source detection, but also the characterization and prediction of the combined plume in space and time. The parameter estimation is formulated as a Bayesian inference problem, and the solution is obtained using a Markov chain Monte Carlo algorithm. The approach is applied to a simulation study, which shows that an accurate parameter estimation is achievable. Copyright © 2010 John Wiley & Sons, Ltd.     

Computing eigenvalues of Sturm-Liouville problems via optimal control theory

In this paper, we shall address three problems arising in the computation of eigenvalues of Sturm-Liouville boundary value problems. We first consider a well-posed Sturm-Liouville problem with discrete and distinct spectrum. For this problem, we shall show that the eigenvalues can be computed by solving for the zeros of the boundary condition at the terminal point as a function of the eigenvalue. In the second problem, we shall consider the case where some coefficients and parameters in the differential equation are continuously adjustable. For this, the eigenvalues can be optimized with respect to these adjustable coefficients and parameters by reformulating the problem as a combined optimal control and optimal parameter selection problem. Subsequently, these optimized eigenvalues can be computed by using an existing optimal control software, MISER. The last problem extends the first to nonstandard boundary conditions such as periodic or interrelated boundary conditions. To illustrate the efficiency and the versatility of the proposed methods, several non-trivial numerical examples are included.     

衰减信道下的决策融合问题

本文针对国际上近几年兴起的研究热点——无线传感器网络在信道衰减下的决策融合问题进行探讨。分析了已有传感器决策融合问题算法的结构,在已知信道传输错误概率的条件下,将信道无传输错误的分析方法推广到信道衰减的情况,对传输错误和融合律的关系进行了深入分析。对给定融合律的网络决策融合问题,获得了最优容错传感器观测量化器的必要条件并设计了迭代算法。在没有增加问题的计算复杂度的情况下,得到了最优观测量化器。与国际上现有结果不同,新结果不要求传感器决策条件独立,也不要求各传感器与融合中心之间的信道相互独立,具有更加广泛的使用范围。     

Monotonic optimization for sensor cover energy problem

We study the sensor cover energy problem (SCEP) in wireless communication—a difficult nonconvex problem with nonconvex constraints. A local approach based on DC programming called DCA was proposed by Astorino and Miglionico (Optim Lett 10(2):355–368, 2016) for solving this problem. In the present paper, we propose a global approach to (SCEP) based on the theory of monotonic optimization. By using an appropriate reformulation of (SCEP) we propose an algorithm for finding quickly a local optimal solution along with an efficient algorithm for computing a global optimal solution. Computational experiments are reported which demonstrate the practicability of the approach.