Roberto L. Galski

Spacecraft thermal design with the Generalized Extremal Optimization Algorithm

This article describes an application of the Generalized Extremal Optimization (GEO) algorithm to the inverse design of a spacecraft thermal control system. GEO is a recently proposed global search meta-heuristic (Sousa, F.L. and Ramos, F.M., 2002, Function optimization using extremal dynamics. In: Proceedings of the 4th International Conference on Inverse Problems in Engineering (cd-rom), Rio de Janeiro, Brazil.; Sousa, F.L., Ramos, F.M., Paglione, P. and Girardi, R.M., 2003, New stochastic algorithm for design optimization. AIAA Journal, 41(9), 1808–1818.; Sousa, F.L., Ramos, F.M., Galski, R.L. and Muraoka, I., 2005, Chapter III. In: L.N. De Castro and F.J. Von Zuben (Eds) Generalized Extremal Optimization: A New Meta-heuristic Inspired by a Model of Natural Evolution, Accepted for publication in Recent Developments in Biologically Inspired Computing (Hershey, PA: Idea Group Inc.).) based on a model of natural evolution (Bak, P. and Sneppen, K., 1993, Punctuated equilibrium and criticality in a simple model of evolution. Physical Review Letters, 71(24), 4083–4086), and specially devised to be used in complex optimization problems (Sousa, F.L., Vlassov, V. and Ramos, F.M., 2002, Heat pipe design through generalized extremal optimization. In: Proceedings of the IX Brazilian Congress of Engineering and Thermal Sciences – ENCIT 2002, Caxambu, MG, Brazil.). GEO is easy to implement, has only one free parameter to adjust, does not make use of derivatives and can be applied to constrained or unconstrained problems, and to non-convex or even disjoint design spaces with any combination of continuous, discrete, or integer variables. The application reported here concerns the optimum design of a simplified configuration of the Brazilian Multi-mission Platform (in Portuguese, Plataforma Multi-missão, PMM) thermal control subsystem, comprising five radiators and one battery heater. The PMM is a multi-purpose space platform to be used in different types of missions such as Earth observation, scientific, or meteorological data collecting. The design procedure is tackled as a multiobjective optimization problem, considering two critical cases, operational hot case (HC) and cold case (CC). The results indicate the existence of non-intuitive, new and more efficient design solutions.

Application of a GEO + SA hybrid optimization algorithm to the solution of an inverse radiative transfer problem

In a former study (F.L. de Sousa, F.M. Ramos, F.J.C.P. Soeiro, and A.J. Silva Neto, Application of the generalized extremal optimization algorithm to an inverse radiative transfer problem, Inverse Probl. Sci. Eng. 15 (2007), pp. 699–714), a new evolutionary optimization metaheuristic–the generalized extremal optimization (GEO) algorithm (F.L. de Sousa, F.M. Ramos, P.Paglione, and R.M. Girardi, A new stochastic algorithm for design optimization, AIAA J. 41 (2003), pp. 1808–1818)–was applied to the solution of an inverse problem of radiative properties estimation. A comparison with two other stochastic methods; simulated annealing (SA) and genetic algorithms (GA), was also performed, demonstrating GEOs competitiveness for that problem. In the present article, a recently developed hybrid version of GEO and SA (R.L. Galski, Development of improved, hybrid, parallel, and multiobjective versions of the generalized extremal optimization method and its application to the design of spatial systems, D.Sc. Thesis, Instituto Nacional de Pequisas Espaciais, Brazil, 2006, p. 279. INPE-14795-TDI/1238 (in Portuguese)) is applied to the same radiative transfer problem and the results obtained are compared with those from the previous study. The present approach was already foreseen (e.g. in F.L. de Sousa, F.M. Ramos, F.J.C.P. Soeiro, and A.J. Silva Neto, Application of the generalized extremal optimization algorithm to an inverse radiative transfer problem, Inverse Probl. Sci. Eng. 15 (2007), pp. 699–714) as a technique that could significantly improve the performance of GEO for this problem. The idea is to make use of a scheduling for GEOs free parameter γ in a similar way to the cooling rate of SA. The main objective of this approach is to combine the good exploration properties of GEO during the early stages of the search with the good convergence properties of SA at the end of the search.

The q-gradient method for continuous global optimization

Here, we present an extension of the classical steepest descent method for solving global continuous optimization problems. To this end, we apply the concept of Jacksons derivative to compute the negative of the q-gradient of the objective function, used as the search direction. The use of Jacksons derivative has shown to be an effective mechanism for escaping from local minima. The q-gradient algorithm is complemented with strategies for selecting the parameter q and to compute the step length. These strategies are implemented in a way such that the search process gradually shifts from global in the beginning to local as the algorithm converges. For testing this new approach, we considered a set of multimodal test functions and compared our results with those obtained by Evolutionary Algorithms (EAs) widely used in optimizing multidimensional and multimodal functions. Overall, the q-gradient method performs well against the EAs arriving in forth position in a direct comparison with them, for the dimens...

The q-Gradient Vector for Unconstrained Continuous Optimization Problems

In the beginning of nineteenth century, Frank Hilton Jackson generalized the concepts of derivative in the q -calculus context and created the q -derivative, widely known as Jackson’s derivative. In the q -derivative, the independent variable is multiplied by a parameter q and in the limit, q → 1, the q -derivative is reduced to the classical derivative. In this work we make use of the first-order partial q -derivatives of a function of n variables to define here the q -gradient vector and take the negative direction as a new search direction for optimization methods. Therefore, we present a q -version of the classical steepest descent method called the q -steepest descent method, that is reduced to the classical version whenever the parameter q is equal to 1. We applied the classical steepest descent method and the q -steepest descent method to an unimodal and a multimodal test function. The results show the great performance of the q -steepest descent method, and for the multimodal function it was able to escape from many local minima and reach the global minimum.

Stochastic spacecraft thermal design optimization with low computational cost

This paper presents a strategy for a quick determination of the optimum configuration for radiators and solar absorbers in a spacecraft thermal design, to minimize heater power consumption and maximize temperature margins. It is particularly useful when applied to multimission platforms in which the thermal design is adapted for different orbits and operational modes. A two-step approach is adopted wherein a simplified thermal model is developed to search for the optimum radiator/solar absorber areas, and then the results are implemented in a detailed thermal model to verify the temperature distribution, thereby reducing computational time, a common drawback in complex engineering optimization problems. If necessary, small adjustments are then made in the radiator/solarabsorberconfiguration.Thesearchfortheoptimumdesignisaccomplishedusingarecentlyproposed global search metaheuristic, called generalized extremal optimization. Based on a model of natural evolution, it is easy to implement and has only one free parameter to adjust, making no use of derivatives. This paper presents the strategy as applied to the thermal design of the Brazilian Multimission Platform now under development. Nomenclature Ai = area of the radiator or solar absorber of node i, m 2 a = weighting factor for heater power consumption bl = weighting factor for temperature deviation for critical case l

The q-G method : A q-version of the Steepest Descent method for global optimization

AbstractIn this work, the q-Gradient (q-G) method, a q-version of the Steepest Descent method, is presented. The main idea behind the q-G method is the use of the negative of the q-gradient vector of the objective function as the search direction. The q-gradient vector, or simply the q-gradient, is a generalization of the classical gradient vector based on the concept of Jackson’s derivative from the q-calculus. Its use provides the algorithm an effective mechanism for escaping from local minima. The q-G method reduces to the Steepest Descent method when the parameter q tends to 1. The algorithm has three free parameters and it is implemented so that the search process gradually shifts from global exploration in the beginning to local exploitation in the end. We evaluated the q-G method on 34 test functions, and compared its performance with 34 optimization algorithms, including derivative-free algorithms and the Steepest Descent method. Our results show that the q-G method is competitive and has a great potential for solving multimodal optimization problems.

Método q-GC: uma generalização do método dos gradientes conjugados

Recentemente, baseado na derivada de Jackson, foi proposta uma generalizacao do metodo da maxima descida, denominada metodo do q-gradiente (q-G), para problemas de otimizacao global continua. Dentro desse contexto, este trabalho apresenta uma generalizacao do metodo dos gradientes conjugados (q-GC) com base no conceito do vetor q-gradiente. Para avaliar o desempenho do metodo q-GC foram considerados os resultados obtidos pelo metodo q-G e por tres Algoritmos Geneticos (AGs) para um conjunto de seis funcoes teste de 20 variaveis e mesmo criterio de parada. No geral, os resultados mostram que o q-GC ´e um metodo promissor para solucao de problemas de otimizacao multimodais.

GEO + ES Hybrid Optimization Algorithm Applied to the Parametric Thermal Model Estimation of a 200N Hydrazine Thruster

In the present paper, a hybrid version of the Generalized Extremal Optimization (GEO) and Evolution Strategies (ES) algorithms [1], developed in order to conjugate the convergence properties of GEO with the self-tuning characteristics present in the ES, is applied to the estimation of the temperature distribution of the film cooling near the internal wall of a thruster. The temperature profile is determined through an inverse problem approach using the hybrid. The profile was obtained for steady-state conditions, were the external wall temperature along the thruster is considered as a known input. The Boltzmann’s equation parameters [2], which define the cooling film temperature profile, are the design variables. Results using simulated data showed that this approach was efficient in recuperating those parameters. The approach showed here can be used on the design of thrusters with lower wall temperatures, which is a desirable feature of such devices.Copyright