Global optimization method for design problems

In structural design optimization method, numerical techniques are increasingly used. In typical structural optimization problems there may be many locally minimum configurations. For that reason, the application of a global method, which may escape from the locally minimum points, remains essential. In this paper, a new hybrid simulated annealing algorithm for global optimization with constraints is proposed. We have developed a new algorithm called Adaptive Simulated Annealing Penalty Simultaneous Perturbation Stochastic Approximation algorithm (ASAPSPSA) that uses Adaptive Simulated Annealing algorithm (ASA); ASA is a series of modifications done to the traditional simulated annealing algorithm that gives the global solution of an objective function. In addition, the stochastic method Simultaneous Perturbation Stochastic Approximation (SPSA) for solving unconstrained optimization problems is used to refine the solution. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems. The constraints are handled using exterior point penalty functions. The hybridization of both techniques ASA and PSPSA provides a powerful hybrid heuristic optimization method; the proposed method is applicable to any problem where the topology of the structure is not fixed; it is simple and capable of handling problems subject to any number of nonlinear constraints. Extensive tests on the ASAPSPSA as a global optimization method are presented; its performance as a viable optimization method is demonstrated by applying it first to a series of benchmark functions with 2 - 50 dimensions and then it is used in structural design to demonstrate its applicability and efficiency

Two-phase algorithm for global optimization

Orientador: Marcia A. Gomes RuggieroDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Neste trabalho estudamos a teoria de algumas heurísticas para otimização global, e também a generalização do algoritmo genético de Aarts, Eiben e van Hee. Propomos um algoritmo para otimização global de problemas canalizados e diferenciáveis utilizando simulated annealing e o solver local GENCAN. Experimentos numéricos com o problema OVO ( Order- Value Optimization) são apresentados, e também com 28 problemas clássicos da literatura. Para problemas de otimização com restrições, apontamos idéias de como utilizar solvers locais e heurísticas globais em busca de bons algoritmos para otimização global, e propomos um algoritmo baseado em simulated annealing com solver local ALGENCANAbstract: In this work we study the theory behind some classical heuristics for global optimization, and a generalization of genetic algorithms from Aarts, Eiben and van Hee. We propose an algorithm for global optimization of box-constrained differentiable problems, using simulated annealing and the local solver GENCAN. Numerical experiments are presented for the OVO problem (Order-Value Optimization) and 28 classical problems. For general nonlinear programming problems, we mention some ideas of how to use local solvers and global heuristics towards good algorithms for global optimization, we also propose an algorithm based on simulated annealing with local solver ALGENCANMestradoOtimizaçãoMestre em Matemática Aplicad

Design Optimization of High-Frequency Power Transformer by Genetic Algorithm and Simulated Annealing

This paper highlights the transformer design optimization problem. The objective of transformer design optimization problem requires minimizing the total mass (or cost) of the core and wire material by satisfying constraints imposed by international standards and transformer user specification. The constraints include appropriate limits on efficiency, voltage regulation, temperature rise, no-load current and winding fill factor. The design optimizations seek a constrained minimum mass (or cost) solution by optimally setting the transformer geometry parameters and require magnetic properties. This paper shows the above design problems can be formulated in genetic algorithm(GA) and simulated annealing (SA) format. The importance of the GA and SA format stems for two main features. First it provides efficient and reliable solution for the design optimization problem with several variables. Second, it guaranteed that the obtained solution is global optimum. This paper includes a demonstration of the application of the GP technique to transformer design.Key word—Optimization, Power Transformer, Genetic Algorithm (GA), Simulated Annealing Technique (SA)DOI:http://dx.doi.org/10.11591/ijece.v1i2.8

Simulated Annealing of Constrained Statistical Functions

In 1987, Corana et al. published a simulated annealing (SA) algorithm. Soon thereafter in 1993, Goffe et al. coded the algorithm in FORTRAN and showed that SA could uncover global optima missed by traditional optimization software when applied to statistical modeling and estimation in economics (econometrics). This chapter shows how and why SA can be used successfully to perform likelihood-based statistical inference on models where likelihood is constrained by often very complicated functions defined on a compact parameter space. These constraints arise because likelihood-based inference involves comparing the maxima of constrained versus unconstrained statistical optimization models. The chapter begins with a review of the relevant literature on SA and constrained optimization using penalty techniques. Next, a constrained optimization problem based in maximum likelihood stress-strength modeling is introduced, and its statistical and numerical properties are summarized. SA is then used to solve a sequence of penalty-constrained optimization problems, and the results are used to construct a confidence interval for the parameter of interest in the statistical model. The chapter concludes with a brief summary of the results and some ways we were able to enhance the performance of SA in this setting

Parallel Deterministic and Stochastic Global Minimization of Functions with Very Many Minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University