Versatility of Simulated Annealing with Crystallization Heuristic: Its Application to a Great Assortment of Problems

Abstract

This chapter is related to several aspects of optimization problems in engineering. Engineers usually mathematically model a problem and create a function that must be minimized, like cost, required time, wasted material, etc. Eventually, the function must be maximized. This function has different names in the literature: objective function, cost function, etc. We will refer to it in the chapter as objective function. There is a wide range of possibilities for the problems and they can be classified in different ways. At first, the values of the parameters can be continuous, discrete (integers), cyclic (angles), intervals, and combinatorial. The result of the objective function can be continuous, discrete (integers) or intervals. One very difficult class of problems have continuous parameters and discrete objective function, this type of objective function has very weak sensibility. This chapter shows the versatility of the simulated annealing showing that it can have different possibilities of parameters and objective functions.

Optimizing the Ultrashort Laser Pulses for In Situ Nanostructure Generation Technique for High-Performance Supercapacitor Electrodes Using Artificial Neural Networks and Simulated Annealing Algorithms

“…The process involves several iterations to search for the optimal solution, and the temperature is gradually reduced at an extremely slow rate to ensure the precision of the solution. At the end of each iteration, annealing takes place, and the annealing temperature is reduced using eq , T K + 1 = T K × K where K represents the annealing rate. This is because slower annealing tends to provide better precision.…”

Using Feedback Strategies in Simulated Annealing with Crystallization Heuristic and Applications

“…The crystallization heuristic does not interfere with combinatorial or integer parameters. SA with the crystallization heuristic uses feedback to control the parameter named the crystallization factor, which represents the parameter sensibility [9]. SA with the crystallization heuristic was successfully applied to problems with discrete cost functions [10][11][12].…”

Design of surface micro-machined inertial MEMS sensor with meta-heuristic topology optimization.

“…The number of iterations is dependent on the physics of the optimization problem, domain, constraints, objective of optimization, and method of generating new solutions [93]. A practical rule of thumb to select a high enough number of iterations is to generate 20N new solutions in each temperature, where N is the number of discrete elements in the design domain [80]. In the case of TO, evaluation of the objective functions usually needs FEA which is usually expensive in the term of computations.…”

“…where the exponent β is a number in the range of 1 − 4 and can be selected based on the optimization problem and experience [80]. To make the annealing schedule more efficient, more advanced adaptive methods are developed based on laws of thermodynamics to adopt temperature by energy difference of two states [81].…”

“…It shows that the optimum solution is an optimum point in the neighborhood and it is not near a singular point. As a rule of thumb in optimization with SA, if the number of accepted solutions is more than half of the number of iterations, it is possible to decrease the temperature without changing the performance of optimization [80]. This is applied in this study to decrease computational costs if in case the initial temperature is selected higher than necessary or the number of accepted solutions is decreasing slowly.…”