A Comparative Study of Simulated Annealing with different Cooling Schedules for Geometric Optimization of a Heat Transfer Problem According to Constructal Design

In this paper it is proposed a comparison between two stochastic methods, Simulated Annealing and Luus-Jaakola algorithms, applied in association with Constructal Design to the geometric optimization of a heat transfer problem. The problem consists in a solid body with an internal uniform heat generation, which is cooled by an intruded cavity that is maintained at a minimal temperature. The other surfaces are kept as adiabatic. The objective is to minimize the maximum excess of temperature (θmax) in the solid domain through geometric optimization of the isothermal double-T shaped cavity. The problem geometry has five degrees of freedom, but in this study four degrees of freedom are evaluated, keeping fixed the ratio H/L (ratio between the height and length of the solid domain) as well as the cavity constraints. The search for the optimal geometry is performed by Simulated Annealing and the Luus-Jaakola algorithm with different configurations or set of main parameters. Each algorithm is executed twenty times and the results for θmax, and corresponding geometry ratios, are recorded. Results of two heuristics are compared in order to select the best method for future studies about the complete optimization of the cavity, as well as, the evaluation of constraints over the thermal performance of the problem. The method employed to compare and rank the different versions of the two algorithms is a statistical tool called multi-comparison of Kruskal-Wallis. With this statistical method it is possible to classify the algorithms in three main groups. Results showed that the Simulated Annealing with hybrid parameters of Cooling Schedule (BoltzExp and ConstExp2) and traditional ones (Exponential) led to the highest probability to find the global optimal shape, while the results obtained with the Luus-Jaakola algorithm reached to several local points of minimum far from the best shape for all versions of the algorithm studied here. However, the Luus-Jaakola algorithm led to the lowest magnitude of maximum excess of temperature, showing that the implementation of hybrid methods of optimization can be an interesting strategy for evaluation of this kind of problem.

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Evaluation of a Differential Evolution/Constructal Design Algorithm for Geometrical Optimization of Double T-Shaped Cavity Intruded into a Heat Generating Wall

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.396.145 ◽

2019 ◽

Vol 396 ◽

pp. 145-154

Author(s):

Gill Velleda Gonzales ◽

Liércio André Isoldi ◽

Luiz Alberto Oliveira Rocha ◽

Antônio José da Silva Neto ◽

Elizaldo Domingues dos Santos

Keyword(s):

Heat Transfer ◽

Differential Evolution ◽

Amplification Factor ◽

Transfer Problem ◽

Differential Evolution Algorithm ◽

Internal Heat ◽

Heat Transfer Problem ◽

Design Algorithm ◽

Constructal Design ◽

Geometrical Optimization

In the present work it is investigated the performance of an algorithm that associates Differential Evolution and Constructal Design for geometrical optimization of a heat transfer problem. It is considered the intrusion of a cooled Double T-shaped cavity into a rectangular conducting solid wall with internal heat generation. The main purpose here is to evaluate the algorithm capability to reproduce the effect of geometric ratios over the dimensionless maximum excess of temperature (performance indicator of the heat transfer problem), as well as, the influence of Differential Evolution (DE) parameters over the optimization analysis. The definition of search space for each degree of freedom and problem constraints is performed with Constructal Design, while the Differential Evolution algorithm is used in the optimization process. Here parameters as mutation operator (M), crossover constant (CR), differential amplification factor (F), Population Size (PS) and Generations number (G) are evaluated. A theoretical recommendation about the suitable parameters set for the optimization algorithm for this kind of heat transfer problem is proposed. Results indicated that the crossover constant (CR) and amplification factor (F) are important parameters for suitable prediction of the effect of degrees of freedom over thermal performance. Moreover, when CR = 0.7 and F = 1.5 results obtained with the algorithm are more robust for the achievement of the best shapes and requires lower number of iterations (IT = PS × G) for reproduction of effect of geometric variables over performance.

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