Contingent epiderivatives and set-valued optimization

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.     

重力输水管道优化设计方法研究

针对重力输水管道设计中存在的问题，文章以管道造价最小为目标，应用动态规划，提出了一种新的重力输水管道优化设计方法，对输水管的当量管径、流量分配、连接管设置与可靠性校核计算等问题作了探讨。该方法可用于沿线有节点流量流出的并联输水管道优化设计，能明显节省投资，有良好的实用性     

New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.     

Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions

A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs.     

航线优化的随机动态规划模型

航空公司在给定的运力和机队配置条件下,如何适应航线需求的不断变化而合理地分配运力,使航空公司的经营效益最大化是我国航空经营管理的一个重大课题.根据航班效益分析,在一定的经营时间,航行班次的条件下,建立一个航线贡献最大化的含有随机变量的动态规划模型.求解方法是先用M ON TE C ARLO方法计算机仿真把模型转化为非线性的整数规划.再用动态规划中资源分配算法求出模型的最优解,编排最优各航线规划.     

Converging Marriage in Honey-Bees Optimization and Application to Stochastic Dynamic Programming

In this paper, we first refine a recently proposed metaheuristic called “Marriage in Honey-Bees Optimization” (MBO) for solving combinatorial optimization problems with some modifications to formally show that MBO converges to the global optimum value. We then adapt MBO into an algorithm called “Honey-Bees Policy Iteration” (HBPI) for solving infinite horizon-discounted cost stochastic dynamic programming problems and show that HBPI also converges to the optimal value.     

On the multi-attribute stopping problem with general value functions

We examine a sequential selection problem in which a single option must be selected. Each option's value is a function of its attributes, whose precise values can be ascertained at a given cost. We prove the optimality of a threshold stopping rule for a general class of objective functions.     

Solving multiple-objective problems in the objective space

Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.This work was partially sponsored by grants from CNP_q and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments.     

Sample-path optimization of convex stochastic performance functions

In this paper we propose a method for optimizing convex performance functions in stochastic systems. These functions can include expected performance in static systems and steady-state performance in discrete-event dynamic systems; they may be nonsmooth. The method is closely related to retrospective simulation optimization; it appears to overcome some limitations of stochastic approximation, which is often applied to such problems. We explain the method and give computational results for two classes of problems: tandem production lines with up to 50 machines, and stochastic PERT (Program Evaluation and Review Technique) problems with up to 70 nodes and 110 arcs. Sponsored by the National Science Foundation under grant number CCR-9109345, by the Air Force Systems Command, USAF, under grant numbers F49620-93-1-0068 and F49620-95-1-0222, by the U.S. Army Research Office under grant number DAAL03-92-G-0408, and by the U.S. Army Space and Strategic Defense Command under contract number DASG60-91-C-0144. The U.S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Sponsored by a Wisconsin/Hilldale Research Award, by the U.S. Army Space and Strategic Defense Command under contract number DASG60-91-C-0144, and the Air Force Systems Command, USAF, under grant number F49620-93-1-0068. Sponsored by the National Science Foundation under grant number DDM-9201813.     

Generating well-behaved utility functions for compromise programming

The purpose of this paper is to seek utility functions satisfying a weak condition which guarantees that the utility optimum always belongs to the compromise set. This set is a special subset of the attainable or feasible set, which is generated through the application of the well-known operational research approach called compromise programming. It is shown that there are large families of utility functions satisfying this condition, thus reinforcing the value of compromise programming as a good surrogate of the traditional utility optimum.Thanks are due to the reviewers for their helpful suggestions. The English editing by Ms. Christine Méndez is appreciated. The authors have been supported by the Comisión Interministerial de Ciencia y Tecnología (CICYT), Madrid, Spain.