Statistical bound of genetic solutions to quadratic assignment problems

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Análise dos fundamentos do modelo value-based health care delivery à luz das teorias de estratégia

O setor de saúde, globalmente, apresenta problemas relacionados aos seus custos, qualidade e acesso. Porter e Teisberg (2004, 2006) propuseram modelo de gestão específico para a administração estratégica na área, o Value-Based Health Care Delivery (VBHCD). O modelo teve relativa repercussão e vem influenciando muitos atores no setor. Contudo, o modelo vem sendo aceito sem o devido questionamento de seus fundamentos e consistência com a teoria em estratégia. O presente trabalho busca, por meio de um ensaio teórico, analisar o modelo proposto à luz de paradigmas gerais da estratégia empresarial como, por exemplo, o modelo de Porter e a Visão Baseada em Recursos (RBV). Inicialmente, o artigo sintetiza as explicações teóricas do modelo porteriano clássico e da RBV. Em seguida, o VBHCD é examinado comparado a essas explicações, buscando-se relações e, eventualmente, contradições. Conclui-se que o modelo VBHCD não se alinha integralmente a nenhum corpo teórico isoladamente. Mesmo sendo proposto por Porter, parte de seus fundamentos advém, na verdade, de outras correntes teóricas. Esta abordagem integradora de teorias concorrentes, apesar de presente na literatura, ainda apresenta dificuldades e barreiras, um aspecto que não está explícito no modelo

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

Energy gain induced by boundary crisis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An alternative approach to solve convergence problems in the backpropagation algorithm

The multilayer perceptron network has become one of the most used in the solution of a wide variety of problems. The training process is based on the supervised method where the inputs are presented to the neural network and the output is compared with a desired value. However, the algorithm presents convergence problems when the desired output of the network has small slope in the discrete time samples or the output is a quasi-constant value. The proposal of this paper is presenting an alternative approach to solve this convergence problem with a pre-conditioning method of the desired output data set before the training process and a post-conditioning when the generalization results are obtained. Simulations results are presented in order to validate the proposed approach.

Studying properties of Lagrangian bounds for many-to-many assignment problems

Classical and modified Lagrangian bounds for the optimal value of optimization problems with a double decomposable structure are studied. For the class of many-to-many assignment problems, this property of constraints is used to design a subgradient algorithm for solving the modified dual problem. Numerical results are presented to compare the quality of classical and modified bounds, as well as the properties of the corresponding Lagrangian solutions.

Comparison of Lagrangian Bounds for One Class of Generalized Assignment Problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-linear analysis of reinforced concrete plates by the boundary element method and continuum damage mechanics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Necessary conditions for optimal impulsive control problems

A Maximum Principle is derived for a class of optimal control problems arising in midcourse guidance, in which certain controls are represented by measures and, the state trajectories are functions of bounded variation. The optimality conditions improves on previous optimality conditions by allowing nonsmooth data, measurable time dependence, and a possibly time varying constraint set for the conventional controls.

Quasilinear dirichlet problems in RN with critical growth

In this study, a given quasilinear problem is solved using variational methods. In particular, the existence of nontrivial solutions for GP is examined using minimax methods. The main theorem on the existence of a nontrivial solution for GP is detailed.

Structural change and productivity growth, 20 years later: old problems, new opportunities

Includes bibliography

The Mexican film industry and its participation in the global value chain

Includes bibliography

Structural change and productivity growth 20 years later: old problems, new opportunities. Summary

Includes bibliography