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Abstract
This paper represents how typical advanced engineering design can be structured using a set of parameters and objective functions corresponding to the nature of the problem. The set of parameters can be in different types, including integer, real, cyclic, combinatorial, interval, etc. Similarly, the objective function can be presented in various types including integer (discrete), float, and interval. The simulated annealing with crystallization heuristic can deal with all these combinations of parameters and objective functions when the crystallization heuristic presents a sensibility for real parameters. Herein, simulated annealing with the crystallization heuristic is enhanced by combining Bates and Gaussian distributions and by incorporating feedback strategies to emphasize exploration or refinement, or a combination of the two. The problems that are studied include solving an electrical impedance tomography problem with float parameters and a partially evaluated objective function represented by an interval requiring the solution of 32 sparse linear systems defined by the finite element method, as well as an airplane design problem with several parameters and constraints used to reduce the explored domain. The combination of the proposed feedback strategies and simulated annealing with the crystallization heuristic is compared with existing simulated annealing algorithms and their benchmark results are shown. The enhanced simulated annealing approach proposed herein showed better results for the majority of the studied cases.
Highlights
The solution of engineering problems often involves optimization
Simulated annealing (SA) with the crystallization heuristic was applied to some benchmark functions
The Zakharov function has a global optimum in place with a low gradient, making it difficult to determine with algorithms that use the gradient
Summary
The solution of engineering problems often involves optimization. There are several well-known optimization methods, mainly based on the cost function gradient property. The determination of the seed is an additional task which eventually cannot be determined To overcome problems such as the gradient property of the cost function and seed determination, a large set of metaheuristic methods have been proposed. The PSO was originally proposed to deal with real parameters, and modifications in the original approach allow its application to combinatorial problems [7]. This paper explains the motivations towards the enhancement of SA to manipulate real parameters and the proposed SA with the crystallization heuristic. This is an important property which can enhance the SA convergence.
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