A neuro-gradient evolution method for simultaneous size and layout optimization of half-timbered structures in the combined variable area

Differential Evolution (DE) is a population -based algorithm that is rooted in genetic temps [1]. The proper performance of DE (including the convergence speed and variety of population) depends heavily on its control parameters, such as the population size (population size$N_P$), Rate of crossovers ($C_R$) and the mutation strategies [2]. Individuals that are gathered in the population of DE are seeds of evolution that can either collect or lose eligible evolutionary characteristics throughout the process. From a biological point of view, crossover refers to the transfer of genetic information between chromosomes, and mutation is a slight change in this information in the context of DE, a test vector (${\mathbf{\text{U}}}_{IPresentG}$) Results of CrossOvers and a mutated vector (((${\mathbf{\text{V}}}_{IPresentG}$) Derived from the characteristics of the population represents mutations. In order to improve the general suitability of the population, superior persons between the base, experiment and mutated vectors (i.e. parents and descendants) are selected for the next generation to imitate the survival of the strongest from the Darwinian Evolution theory [3]. The logic behind the search strategy of differential development is shown in Fig. 1. In this illustration, the mutated vector is based on a random walk [4]Indicates the extent of the stochastic search, while crossover develops a recombination scheme for generating a test vector. A few of three-dimensional bases and mutant vectors ($N=3$), have six possible test vectors (${\mathbf{\text{U}}}_{IPresentG}^1$Present ${\mathbf{\text{U}}}_{IPresentG}^2$Present $\dots$Present ${\mathbf{\text{U}}}_{IPresentG}^6$). If the dimensionality of decision -making variables increases, a unit is $N$-Dimensional sphere expresses the efficient omnidirectional search scheme. Still how $N$ approaches infinite ($N\to \mathrm{\infty }$) almost all corners of unity $N$-Cube is outside the device $N$-Sphere and thus most test vectors on the corner points of the unit $N$-Cube is just an inefficient expenses of calculation. One should take into account the fact that in the case of complex optimization problems, given the fact that the deterministic gradient path of the next optimal step is easily accessible, the above -mentioned wasteful calculations are excessively in vain.

In the real problems with restricted optimization problems (COPS), a number of equality, inequality and marginal restrictions have an effect on the solutions [5]. However, evolutionary salgorithms are naturally not limited search engines and require additional manipulations to manage restrictions [6]. An overview of the most important restrictions on the handling techniques (CHTS) is shown in Table 1. Variants of the queue function, namely static [7]dynamic [8]and adaptive [9]Present [10]are the most intuitive approaches to reduce the suitability of the non -realizable solutions. The methods based on the static queue function use a constant punitive coefficient [11]While in the case of dynamic and adaptive a predefined function [12]and the properties of the population [13] Set the values ​​of punitive coefficients. In the attempt to avoid the need for a fine -tuning of punitive coefficients, Runarsson and Yao [14] have proposed the stochastic ranking (SR) approach, so that an evenly generated random number ($U\in \mathcal{U}$(0.1)) decides whether the objective function or restriction is the measure of the ranking. In its original form, SR is only applicable to algorithms that include the order of the population. On the other hand, instead of eliminating non -realizable solutions, it is possible to repair and maintain non -repairable solutions. Repair methods use gradient base [15]probabilistically [16]adaptive [17]and other [18] Approaches to restore outside the bound variables into the realizable region. And last but not least, the core idea behind the separation of objective functions and restrictions is exactly that of breastfeeding functions. Methods in this category, such as B. a limited dominance principle (feasibility rules [19]) and Epsilon level control [20]Treat the restriction injury regardless of the target function.

It is worth noting that the practice of specialist optimization deals with all three aspects of CHS. Gl. (1) represents the typical weight minimization of shackles together with the limitations of the border, equality and inequality. The vector $\mathbf{F}$ Is a real value $N$-Dimensional solution contains both B form variables and $N–B$ Size variables.$\begin{array}{ll}\text{find}& \mathbf{F}\in {\mathbb{R}}^N;\mathbf{F}=[f_1,f_2,f_3,\dots ,f_b,f_{b+1},f_{b+2},f_{b+3},\dots ,f_n]\\ \text{minimize}& W((\mathbf{F})))=R\times \sum _{I=1}^M{A}_I\times L_I\\ \text{exposed to}& min((F_P)))\le F_P\le Max.((F_P)));P=1Present2Present3Present\dots PresentB\\ & min((|A((F_Q)))–A_{SET}|)))=0;Q=B+1PresentB+2PresentB+3Present\dots PresentN\\ & |A_I|–A_{AI}\le 0;I=1Present2Present3Present\dots PresentM\end{array}$wherein $R$ Is the material density $M$ Is the total number of members $A_I$Present $L_I$Present $A_I$And $A_{AI}$ are the cross -sectional area, the length, the existing voltage and the permissible voltage of the $I$The member and the surfaces of the available cross -sections are listed in the $A_{SET}$. In the present work, limit and equality restrictions of non-realizable solutions are treated by hybridization between the punishment and the gradient-based repair methods (section 2.1.2) in order to apply the inequality restrictions on voltage injury, the significant and feasible draft environment that must be treated on the separation of the objective functions from the objective functions processed solutions to the areas of solutions in the areas of solutions.

In the past decade, a variety of research and development of the size optimization of half -timbered structures was devoted to just a few, Truong et al. [22] Used K-NNC classification (K-NNC) K-Nearest Neighbor comparison (K-NNC) in connection with Rao-algorithms [23] To optimize non -linear and unelastic half -timbered structures. Tejani et al. [24]Present [25]Present [26]Present [27]Present [28]Present [29]Present [30] proposed various algorithms for the optimization of multi-lenses. Tang and Lee [31] developed a chaotically reinforced differential development that implemented adaptive mutations to accelerate solutions and prevent premature convergence of discreet variables. Kaveh et al. [32] have demonstrated the superior performance of the success -based differential development (shadow). [33] When looking for optimal designs of large dome binders. They reported that these promising results are due to the ability of the shadow algorithm to avoid premature convergence by using a number of best solutions to obtain the population variety. In addition, topology optimization is an extreme major problem in which no valuated variables are permitted [34]. An approach to finding the optimized topology is to remove additional elements from a floor structure [35]. Since the removal of the elements has a negative impact on the following steps of the optimization process and impair the detection of the global optima, an efficient strategy should be developed to reactivate some of the eliminated elements. So Martínez et al. [36] have proposed growth paths for the soil structure. Hagishita and Ohsaki [37] Use an expanding reducing soil structure to optimize the topology of specialist works. In the comprehensive case of simultaneous topology, shape and size (TSS) optimization, Rajan [38] Is the pioneer and dillen et al. [39] have expanded this to the generic steel structures through hybridization between the gradient base and the meta-theuristic approaches. Their method assigns the meta-theuristic module to optimize discreet variables, while continuous variables are optimized via a gradient-based routine.

As explained in Section 1.1, the main disadvantage of different development is the urgency for the thoughtful selection of the control parameters and mutation strategies. However, none of these restrictions affect the newem. This algorithm can work with a population like just one person, but in such a case the solution in local optima is very susceptible to catching. To prevent this, a method is created that was formulated as a “local Optima Evading process (LOEP)”. In contrast to a randomized population or a population that comes from the previous generation, the core concept of LOEP is to create a gradient -based population of modifications. It should be taken into account that the Negem's evolution only passes the basic solution to the next generation. The overlap of the population of modifications to the basic solution from the previous step creates test solutions of the current generation. These test solutions will then go through a non -dominated selection and ranking -based sorting to determine the basic solution for the next generation. The philosophy of the introduction of mutations is to restore the diversity of the population in DE. The above -mentioned approach of the generation of the population still preserves the diversity and therefore there is no need for mutations.

The rest of this paper is organized in the following way. First, in section 2.1, section 2.2 or section 2.3, each component of the negative is thoroughly explained. After a fixed theoretical reason for the proposed methodology has been laid, three numerical design examples are discussed in Section 3. Finally, the content of this paper is completed in Section 4.