Experimental Comparisons of Derivative Free Optimization Algorithms

In this paper, the performances of the quasi-Newton BFGS algorithm, the NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm Optimizers (PSO) are compared experimentally on benchmark functions reflecting important challenges encountered in real-world optimization problems. Dependence of the performances in the conditioning of the problem and rotational invariance of the algorithms are in particular investigated.Comment: 8th International Symposium on Experimental Algorithms, Dortmund : Germany (2009

Generalized multiobjective evolutionary algorithm guided by descent directions

This paper proposes a generalized descent directions-guided multiobjective algorithm (DDMOA2). DDMOA2 uses the scalarizing fitness assignment in its parent and environmental selection procedures. The population consists of leader and non-leader individuals. Each individual in the population is represented by a tuple containing its genotype as well as the set of strategy parameters. The main novelty and the primary strength of our algorithm is its reproduction operator, which combines the traditional local search and stochastic search techniques. To improve efficiency, when the number of objective is increased, descent directions are found only for two randomly chosen objectives. Furthermore, in order to increase the search pressure in high-dimensional objective space, we impose an additional condition for the acceptance of descent directions found for leaders during local search. The performance of the proposed approach is compared with those produced by representative state-of-the-art multiobjective evolutionary algorithms on a set of problems with up to 8 objectives. The experimental results reveal that our algorithm is able to produce highly competitive results with well-established multiobjective optimizers on all tested problems.Moreover, due to its hybrid reproduction operator, DDMOA2 demonstrates superior performance on multimodal problems.This work has been supported by FCT Fundação para a Ciência e Tecnologia in the scope of the project: PEst-OE/EEI/UI0319/2014

Optimization and geophysical inverse problems

A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness or distance from a prior model. Various other constraints may also be imposed upon the process. Inverse problems are not restricted to geophysics, but can be found in a wide variety of disciplines where inferences must be made on the basis of indirect measurements. For instance, most imaging problems, whether in the field of medicine or non-destructive evaluation, require the solution of an inverse problem. In this report, however, the examples used for illustration are taken exclusively from the field of geophysics. The generalization of these examples to other disciplines should be straightforward, as all are based on standard second-order partial differential equations of physics. In fact, sometimes the non-geophysical inverse problems are significantly easier to treat (as in medical imaging) because the limitations on data collection, and in particular on multiple views, are not so severe as they generally are in geophysics. This report begins with an introduction to geophysical inverse problems by briefly describing four canonical problems that are typical of those commonly encountered in geophysics. Next the connection with optimization methods is made by presenting a general formulation of geophysical inverse problems. This leads into the main subject of this report, a discussion of methods for solving such problems with an emphasis upon newer approaches that have not yet become prominent in geophysics. A separate section is devoted to a subject that is not encountered in all optimization problems but is particularly important in geophysics, the need for a careful appraisal of the results in terms of their resolution and uncertainty. The impact on geophysical inverse problems of continuously improving computational resources is then discussed. The main results are then brought together in a final summary and conclusions section

Process Simulation and Control Optimization of a Blast Furnace Using Classical Thermodynamics Combined to a Direct Search Algorithm

Several numerical approaches have been proposed in the literature to simulate the behavior of modern blast furnaces: finite volume methods, data-mining models, heat and mass balance models, and classical thermodynamic simulations. Despite this, there is actually no efficient method for evaluating quickly optimal operating parameters of a blast furnace as a function of the iron ore composition, which takes into account all potential chemical reactions that could occur in the system. In the current study, we propose a global simulation strategy of a blast furnace, the 5-unit process simulation. It is based on classical thermodynamic calculations coupled to a direct search algorithm to optimize process parameters. These parameters include the minimum required metallurgical coke consumption as well as the optimal blast chemical composition and the total charge that simultaneously satisfy the overall heat and mass balances of the system. Moreover, a Gibbs free energy function for metallurgical coke is parameterized in the current study and used to fine-tune the simulation of the blast furnace. Optimal operating conditions and predicted output stream properties calculated by the proposed thermodynamic simulation strategy are compared with reference data found in the literature and have proven the validity and high precision of this simulation

Avaliação de critérios de heterogeneidade baseados em atributos morfológicos para segmentação de imagens por crescimento de regiões

Avalia-se neste trabalho o impacto de se considerar atributos morfológicos na formulação do critério que governa o crescimento de regiões na segmentação de imagens. Para tanto, uma extensão do algoritmo de segmentação multiresolução proposto por Baatz e Schäpe (2000) foi proposta e implementada, permitindo que se testassem critérios derivados de diferentes atributos morfológicos. O estudo valeu-se de um método supervisionado para medir numericamente a qualidade da segmentação. O resultado ideal da segmentação foi representado por um conjunto de segmentos de referência delineados manualmente para três recortes de imagens Quickbird-2. Para cada critério testado, os valores ótimos para os parâmetros do algoritmo de segmentação foram determinados por um processo estocástico que procurou minimizar a discrepância entre as referências e o resultado de cada segmentação. Uma análise tanto quantitativa quanto qualitativa dos resultados indicou inequivocamente que a inclusão de atributos morfológicos no critério de heterogeneidade, que decide a fusão entre segmentos adjacentes no processo de crescimento de regiões, pode resultar numa substancial melhoria da qualidade da segmentação. O artigo realça ainda a importância de se adotar atributos morfológicos apropriados para cada classe de objetos e tece considerações que orientam a escolha destes atributos