关于最短路问题的一个双目标优化问题

本文研究了一个双目标最短路问题的变形问题,在该变形问题中,一个目标函数还是路的长度,另一个目标函数则是路的容量,在Pareto-optimal最优解的意义下,本文给出了一个时间复杂性为O（n^3 )的算法,在字典序最优解的意义下,本文给出了一个时间复杂性为O(n^3)的算法。     

Feedback Competitive Advertising Strategies with a General Objective Function

We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a two-parameter family of max–min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and show when these strategies are Nash equilibrium strategies. In an empirical application involving duopolistic competition in the cola market, we find evidence of a punitive motivation for the advertising strategies.     

Two theorems on multilevel programming problems with dominated objective functions

In this paper, we present two theorems on the structure of a type of multilevel programming problems. The theorems explore relations among a multilevel programming problem, a dynamical programming, and a nonlinear programming problem.     

Local search and suffix tree for car-sequencing problem with colors

This paper describes an approximation solution method for the car sequencing problem with colors. Firstly, we study the optimality of problems with a single ratio constraint. This study also introduces a data structure for efficient calculation of the penalties related to ratio constraints. We describe the constructive greedy algorithm and variable neighborhood search adjusted for the problem with colors. Tabu metaheuristic is used to improve the results obtained by VNS. We then represent the cars with their constraints as letters over an alphabet and apply the algorithm to spell the motifs in order to improve the number of batch colors without decreasing the costs associated to the set of ratio constraints. The algorithm achieves 19 out of the 64 best results for instance sets A and B. These instances are the reference instances for Challenge ROADEF.     

Scheduling at coal handling facilities using Simulated Annealing

The main thrust of this study is the operational scheduling of the continuous coal handling and blending processes when considering multiple, and sometimes conflicting, objectives. A widely applicable generic goal programming model is proposed. Furthermore, assumptions regarding the certainty of demand during different periods are challenged, endeavoring to provide more robust schedules in a largely stochastic environment. As the study aims to provide scheduling solutions to any coal handling facility, the Simulated Annealing metaheuristic is proposed to ensure that acceptably good solutions for large instances of the generic model can be found in reasonable computational time. The generic approach and its suggested application will be valuable not only in the coal handling environment, but also in the continuous product manufacturing/blending or continuous material handling environment.     

Effect of crystalline lens surfaces and refractive index on image quality by model simulation analysis

The surfaces and refractive index of crystalline lens play an important role in the optical performance of human eye.On the basis of two eye models,which are widely applied at present,the effect of lens surfaces and its refractive index distribution on optical imaging is analyzed with the optical design software ZEMAX (Zemax Development Co.,San Diego,USA).The result shows that good image quality can be provided by the aspheric lens surfaces or (and) the gradient-index (GRIN) distribution.It has great potential in the design of intraocular lens (IOL).The eye models with an intraocular implantation are presented.     

Weakly and properly nonessential objectives in multiobjective optimization problems

In this work we characterize objective functions which do not change the set of efficient solutions (weakly efficient solutions, properly efficient solutions). Necessary and sufficient conditions for an objective function to be weakly nonessential (properly nonessential) are presented. We establish relations between weakly nonessential, properly nonessential and nonessential functions.     

Unequal probability sampling from a finite population: A multicriteria approach

In this note we address the problem of determining selection probabilities for multipurpose surveys, when the aim is the simultaneous minimization of variances for each variable under study. A characterization of the set of Pareto-optimal designs is given for designs with replacement and also for a class of designs without replacement, namely, Poisson designs.     

Box-constrained multi-objective optimization: A gradient-like method without “a priori” scalarization

The aim of this paper is the development of an algorithm to find the critical points of a box-constrained multi-objective optimization problem. The proposed algorithm is an interior point method based on suitable directions that play the role of gradient-like directions for the vector objective function. The method does not rely on an “a priori” scalarization and is based on a dynamic system defined by a vector field of descent directions in the considered box. The key tool to define the mentioned vector field is the notion of vector pseudogradient. We prove that the limit points of the solutions of the system satisfy the Karush–Kuhn–Tucker (KKT) first order necessary condition for the box-constrained multi-objective optimization problem. These results allow us to develop an algorithm to solve box-constrained multi-objective optimization problems. Finally, we consider some test problems where we apply the proposed computational method. The numerical experience shows that the algorithm generates an approximation of the local optimal Pareto front representative of all parts of optimal front.     

Focal shift for off-axial partially coherent flat topped beams passing a thin lens

Focal shift is evaluated for partially coherent off-axis flat topped beams propagated through a thin lens. We have shown that the focal shift decreases as the off-axis parameter (x₀) increases and, for fully coherent flat topped beams, focal shift is enhanced as the order of flat topped beam decreases, but the partially coherent one does not show this behavior. Also we have shown that there is a critical point for partially coherent flat topped beams. We investigated the dependency of focal shift in thin lens on correlation length and focal length.