Modelação matemática da camada de plasma em microcanais

Neste estudo apresenta-se uma proposta de modelação matemática da camada de plasma observada em escoamentos sanguíneos. Numa fase inicial, a resolução do problema fez uso da otimização não linear para encontrar o modelo matemático que minimiza o erro quadrático não linear entre o modelo e os dados numéricos que caracterizam a camada de plasma. Para tal, foram testados os algoritmos Simulated Annealing, Pattern Search, Algoritmo Genético e Quasi-Newton. Neste estudo conclui-se que o método de otimização que obteve melhores resultados foi o Algoritmo Genético. Também foi possível concluir que o melhor modelo para aproximar os dados numéricos que caracterizam a camada de plasma presente em escoamentos sanguíneos é baseado na soma de funções trigonométricas.Os autores agradecem à FCT, COMPETE, QREN e União Europeia (FEDER) no âmbito dos projetos PTDC/SAU-ENB/116929/2010 e EXPL/EMS-SIS/2215/2013.info:eu-repo/semantics/publishedVersio

Solving constrained multilocal optimization problems with parallel stretched simulated annealing

Constrained multilocal programming optimization problems may be solved by solving a sequence of unconstrained problems. In turn, those unconstrained problems may be solved using techniques like the Stretched Simulated Annealing (SSA) method. In order to increase the solving performance and make possible the discovery of new optima, parallel approaches to SSA have been devised, like Parallel Stretched Simulated Annealing (PSSA). Recently, Constrained PSSA (coPSSA) was also proposed, coupling the penalty method with PSSA, in order to solve constrained problems. In this work, coPSSA is explored to solve four test problems using the l 1 penalty function. The effect of the variation of the reduction factor parameter of the l 1 penalty function is also studied.This work was been supported by FCT (Fundação para a Ciência e Tecnologia) in the scope of the project UID/CEC/00319/2013.info:eu-repo/semantics/publishedVersio

Solving multilocal optimization problems with a recursive parallel search of the feasible region

Stretched Simulated Annealing (SSA) combines simulated annealing with a stretching function technique, in order to solve multilocal programming problems. This work explores an approach to the parallelization of SSA, named PSSA-HeD, based on a recursive heterogeneous decomposition of the feasible region and the dynamic distribution of the resulting subdomains by the processors involved. Three PSSAHeD variants were implemented and evaluated, with distinct limits on the recursive search depth, offering different levels of numerical and computational efficiency. Numerical results are presented and discussed.This work was been supported by FCT (Fundação para a Ciência e Tecnologia) in the scope of the project PEst-OE/EEI/UI0319/2014

Caracterização da função de penalidade exponencial na resolução de problemas de programação semi-infinita

Os problemas de programação semi-infinita (PSI) são caracterizados por terem um conjunto finito de variáveis e um número infinito de restrições. A classe de métodos de redução é baseada na ideia que, sob certas condições, é possível substituir as infinitas restrições por um conjunto finito de restrições que, localmente, é suficiente para definir a região admissível do problema PSI. Neste trabalho é proposto um novo método de redução que combina o método simulated annealing para a optimização multilocal, e o método de penalidade para a optimização não linear com restrições

Experiences with reduction method to solve semi-infinite programming problems

In this talk, some variants of reduction-type method combined with a line search filter method to solve nonlinear semi-infinite programming problems are presented. We use the stretched simulated annealing method and the branch and bound technique to compute the maximizers of the constraint. The filter method is used as an alternative to merit functions to promote convergence from poor starting points

A study of simulated annealing variants

This work presents a study of some variants of simulated annealing method

A stretched simulated annealing algorithm for locating all global maximizers

Work partially supported by FCT grant POCTI/MAT/58957/2004.In this work we consider the problem of finding all the global maximizers of a given multimodal optimization problem. We propose a new algorithm that combines the simulated annealing (SA) method with a function stretching technique to generate a sequence of global maximization problems that are defined whenever a new maximizer is identified. Each global maximizer is located through a variant of the SA algorithm. Results of numerical experiments with a set of well-known test problems show that the proposed method is effective. We also compare the performance of our algorithm with other multi-global optimizers

Reduction method with simulated annealing for semi-infinite programming

Semi-infinite programming (SIP) problems are characterized by a finite number of variables and an infinite number of constraints. The class of the reduction methods is based on the idea that, under certain conditions, it is possible to replace the infinite constraints by a finite set of constraints, that are locally sufficient to define the feasible region of the SIP problem. We propose a new reduction method based on a simulated annealing algorithm for multi-local optimization and the penalty method for solving the finite problem

Modelação matemática da variação da temperatura do pé

Existem doenças que afetam diretamente a planta do pé, podendo ser um fator de elevada importância na qualidade de vida do indivíduo. Sabe-se que a presença de uma dada doença na planta do pé poderá afetar a normal distribuição da temperatura na planta do pé. Este estudo pretende identificar as principais características da distribuição da temperatura na planta de pés saudáveis. Com esse objetivo, foram testadas quatro modelações matemáticas para estimar a matriz de temperatura obtida através de diversas imagens termográficas da planta do pé saudável de diversos indivíduos. Os problemas a resolver pertencem à classe de problemas de otimização não linear com restrições

Comparative study of penalty simulated annealing methods for multiglobal programming

In a multiglobal optimization problem we aim to find all the global solutions of a constrained nonlinear programming problem where the objective function is multimodal. This class of global optimization problems is very important and frequently encountered in engineering applications, such as, process synthesis, design and control in chemical engineering. The most common method for solving this type of problems uses a local search method to refine a set of approximations, which are obtained by comparing objective function values at points of a predefined mesh. This type of method can be very expensive numerically. On the other hand, the success of local search methods depends on the starting point being at the neighbourhood of a solution. Stochastic methods are appropriate alternatives to find global solutions, in which convergence to a global solution can be guaranteed, with probability one. This is the case of the simulated annealing (SA) method. To compute the multiple solutions, a function stretching technique that transforms the objective function at each step is herein combined with SA to be able to force, step by step, convergence to each one of the required global solutions. The constraints of the problem are dealt with a penalty technique. This technique transforms the constrained problem into a sequence of unconstrained problems by penalizing the objective function when constraints are violated. Numerical experiments are shown with three penalty functions