Self-adaptive combination of global tabu search and local search for nonlinear equations

Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptive combination of a metaheuristic with a classical local search method is able to converge to some difficult problems that are not solved by Newton-type methods.

Classification of some penalty methods

Optimization problems arise in science, engineering, economy, etc. and we need to find the best solutions for each reality. The methods used to solve these problems depend on several factors, including the amount and type of accessible information, the available algorithms for solving them, and, obviously, the intrinsic characteristics of the problem. There are many kinds of optimization problems and, consequently, many kinds of methods to solve them. When the involved functions are nonlinear and their derivatives are not known or are very difficult to calculate, these methods are more rare. These kinds of functions are frequently called black box functions. To solve such problems without constraints (unconstrained optimization), we can use direct search methods. These methods do not require any derivatives or approximations of them. But when the problem has constraints (nonlinear programming problems) and, additionally, the constraint functions are black box functions, it is much more difficult to find the most appropriate method. Penalty methods can then be used. They transform the original problem into a sequence of other problems, derived from the initial, all without constraints. Then this sequence of problems (without constraints) can be solved using the methods available for unconstrained optimization. In this chapter, we present a classification of some of the existing penalty methods and describe some of their assumptions and limitations. These methods allow the solving of optimization problems with continuous, discrete, and mixing constraints, without requiring continuity, differentiability, or convexity. Thus, penalty methods can be used as the first step in the resolution of constrained problems, by means of methods that typically are used by unconstrained problems. We also discuss a new class of penalty methods for nonlinear optimization, which adjust the penalty parameter dynamically.

Adapted Control Methods for Cerebral Palsy Users of an Intelligent Wheelchair

The development of an intelligent wheelchair (IW) platform that may be easily adapted to any commercial electric powered wheelchair and aid any person with special mobility needs is the main objective of this project. To be able to achieve this main objective, three distinct control methods were implemented in the IW: manual, shared and automatic. Several algorithms were developed for each of these control methods. This paper presents three of the most significant of those algorithms with emphasis on the shared control method. Experiments were performed by users suffering from cerebral palsy, using a realistic simulator, in order to validate the approach. The experiments revealed the importance of using shared (aided) controls for users with severe disabilities. The patients still felt having complete control over the wheelchair movement when using a shared control at a 50% level and thus this control type was very well accepted. Thus it may be used in intelligent wheelchairs since it is able to correct the direction in case of involuntary movements of the user but still gives him a sense of complete control over the IW movement.

Modelação e previsão de vendas no setor do retalho de calçado

Dissertação apresentada ao Instituto Politécnico do Porto para obtenção do Grau de Mestre em Logística Orientada por: Professora Doutora Patrícia Alexandra Gregório Ramos