# Smart Topology Optimization Using Adaptive Neighborhood Simulated Annealing  
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] Smart Topology Optimization Using Adaptive Neighborhood Simulated Annealing. _Appl. Sci._**2021**, _11_, 5257. [[https://doi.org/10.3390/app1115257](https://doi.org/10.3390/app1115257)]([https://doi.org/10.3390/app1115257](https://doi.org/10.3390/app1115257))  
Footnote †: journal: Applied  
not be too fine that it increase the computational cost without improving the results. The variables are the material density inside each element. Using the intermediate density for elements can improve some common problems: The checkerboard and the discontinuity of the design. The Solid Isotropic Material with Penalization (SIMP) method is one of the most applicable approaches to solving TO problems with less complexity. SIMP models the density of each element with a continuous value between a non-zero minimum and one. This method models the properties of material through a power law approach to penalize unfavorable intermediate densities [4]. The TO algorithm includes generating new solutions and evaluates them based on defined criteria [5]. A variety of methods have been proposed to generate new solutions and evaluate them [2]. From an optimizer point of view, TO methods can be divided into two main types: Gradient-based and non-gradient-based. The gradient-based methods such as Optimal Criteria (OC) and the Method of Moving Asymptotes (MMA) use sensitivity information of the objective functions (that is, its first order derivatives). In order to obtain the sensitivity information, the derivation of the objective function is required. These methods have a fast convergence to the final results. The gradient-based methods are widely used for TO problems [6; 7; 8]. Aside from the good performance of these methods in TO, they are limited in the sensitivity information of the objective functions. However, finding the sensitivity of the objective function is not easy [9]. In such cases, where the objective function derivative is difficult to obtain, the non-gradient-based methods are more advantageous. Non-gradient based methods work only with the value of the objective functions [10; 11]. Genetic Algorithm (GA) and Simulated Annealing (SA) are two popular meta-heuristics that have been used in non-gradient-based TO. The main advantage of these non-gradient-based methods is that, unlike gradient-based methods, they do not need the sensitivity information of the objective function. GA uses the theory of natural selection for heuristic search [12]. Despite GA being used in TO and having represented good results [13], it has high computational costs even for simple problems. The determination of some parameters is also a challenge in GA-based TO which can notably change the results. These parameters are the probability of crossover, probability of mutation, fitness scaling coefficient, population size, selection algorithm, and crossover operator [12]. SA is the other meta-heuristic for non-gradient-based TO. SA uses the concept of metal annealing for the optimization process. The SA generates new candidates randomly and accepts the one which improves the objective function. Additionally, SA also accepts the worst candidates (which do not improve the objective function) under certain conditions [14; 15]. This fact allows SA to escape from local minima [16]. The Multi-Resolution Design Variable (MRDV) is used in the literature to enhance search performance [17]. Nevertheless, this approach still has high computational costs and the checkerboard pattern problem still remains. Combining SIMP with SA in structural TO is also used to obtain better results and less gray areas [18]. However, SIMP with SA is not efficient enough due to the high computational costs. Using SA in TO is almost new and needs more research to improve its convergence and computational cost which is the main objective of this work.