Optimal Path Planning Based on Visibility

Various problems associated with optimal path planning for mobile observers such as mobile robots equipped with cameras to obtain maximum visual coverage of a surface in the three-dimensional Euclidean space are considered. The existence of solutions to these problems is discussed first. Then, optimality conditions are derived by considering local path perturbations. Numerical algorithms for solving the corresponding approximate problems are proposed. Detailed solutions to the optimal path planning problems for a few examples are given.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

Optimal stopping problems by two or more decision makers: a survey

A review of the optimal stopping problem with more than a single decision maker (DM) is presented in this paper. We classify the existing literature according to the arrival of the offers, the utility of the DMs, the length of the sequence of offers, the nature of the game and the number of offers to be selected. We enumerate various definitions for this problem and describe some dynamic approaches. Fouad Ben Abdelaziz is on leave from the Institut Superieur de Gestion, University of Tunis, Tunisia e-mail: foued.benabdelaz@isg.run.tn.     

Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.     

A floating-point genetic algorithm for solving the unit commitment problem

This paper proposes a floating-point genetic algorithm (FPGA) to solve the unit commitment problem (UCP). Based on the characteristics of typical load demand, a floating-point chromosome representation and an encoding–decoding scheme are designed to reduce the complexities in handling the minimum up/down time limits. Strategic parameters of the FPGA are characterized in detail, i.e., the evaluation function and its constraints, population size, operation styles of selection, crossover operation and probability, mutation operation and probability. A dynamic combination scheme of genetic operators is formulated to explore and exploit the FPGA in the non-convex solution space and multimodal objective function. Experiment results show that the FPGA is a more effective technique among the various styles of genetic algorithms, which can be applied to the practical scheduling tasks in utility power systems.     

Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems

A method for the numerical solution of state-constrained optimal control problems subject to higher-index differential-algebraic equation (DAE) systems is introduced. For a broad and important class of DAE systems (semiexplicit systems with algebraic variables of different index), a direct multiple shooting method is developed. The multiple shooting method is based on the discretization of the optimal control problem and its transformation into a finite-dimensional nonlinear programming problem (NLP). Special attention is turned to the mandatory calculation of consistent initial values at the multiple shooting nodes within the iterative solution process of (NLP). Two different methods are proposed. The projection method guarantees consistency within each iteration, whereas the relaxation method achieves consistency only at an optimal solution. An illustrative example completes this article.     

仓库容量有限条件下的一类存贮管理模型

建立了一类仓库容量有限条件下存贮管理决策模型 ,给出最优存贮策略 .     

Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian.     

解约束优化问题的QP-free可行域方法

本文利用一个新的分片线性NCP函数提出一个新的可行的QP-free方法解非线性不等式约束优化问题.不同于其他的QP-free方法,这个方法只考虑在工作集中的约束函数,工作集是积极集的一个估计,因此子问题的维数不是满秩的.这个方法可行的并且不需假定严格互补条件、聚点的孤立性得到算法的全局收敛性,并且积极约束函数的梯度不要求线性独立的,其中由拟牛顿法得到的子矩阵不需要求一致正定性.     

Semideterministic Global Optimization Method: Application to a Control Problem of the Burgers Equation

This paper has two objectives. We introduce a new global optimization algorithm reformulating optimization problems in terms of boundary-value problems. Then, we apply this algorithm to a pointwise control problem of the viscous Burgers equation, where the control weight coefficient is progressively decreased. The results are compared with those obtained with a genetic algorithm and an LM-BFGS algorithm in order to check the efficiency of our method and the necessity of using global optimization techniques.