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Improved Fruit Fly Algorithm on Structural Optimization Li and Han Brain Inf. (2020) 7:1 https://doi.org/10.1186/s40708-020-0102-9 Brain Informatics RESEARCH Open Access Improved fruit fy algorithm on structural optimization Yancang Li1* and Muxuan Han2 Abstract To improve the efciency of the structural optimization design in truss calculation, an improved fruit fy optimiza- tion algorithm was proposed for truss structure optimization. The fruit fy optimization algorithm was a novel swarm intelligence algorithm. In the standard fruit fy optimization algorithm, it is difcult to solve the high-dimensional nonlinear optimization problem and easy to fall into the local optimum. To overcome the shortcomings of the basic fruit fy optimization algorithm, the immune algorithm self–non-self antigen recognition mechanism and the immune system learn–memory–forgetting knowledge processing mechanism were employed. The improved algorithm was introduced to the structural optimization. Optimization results and comparison with other algorithms show that the stability of improved fruit fy optimization algorithm is apparently improved and the efciency is obviously remark- able. This study provides a more efective solution to structural optimization problems. Keywords: Truss structure optimization, Fruit fy algorithm, Improvement, Immune response 1 Introduction an improved software package for stamping die struc- With the rapid development of computer technology, the ture that can greatly reduce the weight. Ide [3] designed efciency of structural optimization is greatly improved, the lightweight structure with the structural optimiza- and structural designers can have more time and energy tion method, and successfully realized the lightweight to consider how to get better structural design scheme. gear box design by using the design method of reduc- In 1974, Schimit and Farshi proposed to combine fnite ing contact constraint stress. Kaveh [4] proposed water element theory with mathematical induction theory to evaporation optimization algorithm (WEO), which is solve the optimal weight problem of engineering struc- a population-based intelligent optimization algorithm ture. Structural optimization has stepped into a new era inspired by physics and used for continuous structural [1]. After that, the intelligent optimization algorithm is optimization. In order to apply diferent optimization also widely applied to the structural optimization, and solvers to various fnite-based structural topology opti- the modern structural optimization method is gradually mization problems Rojas-Laband [5], developed a widely applied to the engineering practice. Now, after years of representative example library of mechanism design research and development, structural optimization has problems with minimum compliance, minimum volume changed from the original optimization of structure size and diferent sizes. Sivapuram [6] discussed various cal- to the present optimization of topology and further opti- culus methods and numerical methods commonly used mization of material distribution. From a single objective to solve structural topology optimization problems. optimization problem, multiple objectives are optimized Inspired by the foraging process of fruit fies, scholar simultaneously. Azamirad and Arezoo [2] proposed Pan [7] proposed a more efcient swarm intelligence optimization algorithm in 2012: fruit fy optimization algorithm (FOA). Te algorithm has the advantages of *Correspondence: [email protected] 1 College of Water Conservancy and Hydroelectric Power, Hebei clear principle, fewer parameters and simple opera- University of Engineering, Handan, Heibei Province, China tion. However, there are also some shortcomings, such Full list of author information is available at the end of the article as weak ability to solve complex, high-dimensional and © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Li and Han Brain Inf. (2020) 7:1 Page 2 of 13 nonlinear optimization problems and easy to fall into compared with other algorithms to verify the feasibility local extremum. In view of the above typical problems, of the improvements. many scholars have proposed many improvements. As for the generation of candidate solutions [8], added an escape parameter that can be negative to the taste con- 2 Basic fruit fy algorithm centration judgment value, so that the candidate solu- FOA (fruit fy optimization algorithm) is a new heuris- tion can take a negative value. A novel double strategy tic algorithm that simulates the foraging activities of evolutionary fruit fy optimization algorithm (DSE- fruit fies in nature to seek the optimal solution of the FOA) was proposed by Fang [9]. DSEFOA dynamically objective function. Te foraging iteration diagram of divided the fruit fy population into spermatogonium fruit fies is shown in Fig. 1. subgroups and ordinary subgroups, and adopted dif- Te basic steps are as follows [23–26]: ferent strategies to update the evolution of drosophila at diferent levels of evolution, which improved the Step 1: initialize parameters. Set Sizepop and Maxgen optimization ability of the whole population. In terms of the population size, and initialize the population of search radius, Sang et al. [10] introduced adaptive position: parameters to adjust the search radius of drosophila X , Y . so as to better balance the global search capability and _axis _axis (1) local search capability. Cao [11] proposed to replace Step 2: fruit fy searches in the olfactory system, the traditional search mechanism with sector search which can make the search direction and the search mechanism, and the new fruit fy algorithm was gen- step randomly. Random value (RV) is to be the erated to efectively improve the stability of the algo- search distance, and the position of the population is rithm. In terms of fight strategy [12–14], added the updated simultaneously: operation of group collaboration and random perturba- tion to solve the problem of premature development of X = X + RV i _axis . the algorithm. Sheng [15] proposed that the length of Yi = Y_axis + RV (2) fruit fy search for Uber should be dynamically changed according to the change rate of concentration difer- Step 3: since the exact location of the food is ence, which can efectively balance the global optimiza- unknown, it is necessary to calculate the distance tion ability and the local optimization ability. In terms ( Disti ) between the fruit fies and the origin of the of population diversity [16], divided the drosophila coordinate and then calculate the taste concentra- population into multiple subpopulations of the same tion parameter ( Si): size. Han [17] et al. proposed a dynamic twin group co- 2 2 evolutionary FOA to improve the search accuracy. Xin Disti = Xi + Yi (3) [18] used the gaussian sampling method to update the fruit fy. Tis method can increase the chance of jump- 1 ing out of the local extremum in the early stage of the Si = . Dist (4) algorithm and conduct more accurate search in the i later stage. Aiming at improving the performance of the standard fruit fy optimization algorithm, the hybrid algorithm was designed to combine with fusion immune response. Immune algorithm was fully utilized to improve the defciency of fruit fy algorithm that is prone to fall into local extreme value in the later stage. In other words, when the number of evolutionary stasis steps t is greater than the threshold value of evolutionary stasis steps T, immune operation is performed to overcome the defect of basic fruit fy algorithm. Te improved algorithm was proved to have better robustness and intelligence through standard functions and tests for solving 0–1 knapsack problems [19–21]. Finally, it was applied to the optimization of truss structure [22] and Fig. 1 FOA foraging schematic diagram Li and Han Brain Inf. (2020) 7:1 Page 3 of 13 Step 4: substitute the fruit fy favor concentration 3.1 Immune algorithm determination value (Si) into the taste concentration Immune algorithm (IA) is a kind of bionic optimiza- decision function, the ftness function, then we will tion algorithm. In 1990, Bersini [32] frst used immune obtain the individual taste concentration of the fruit algorithm to solve problems. By simulating biological fies Smelli. immune system identify antigen (objective function), simulation of the principle of the memory in the immune Smelli = Fitness(Si). (5) system, combination of antigen and antibody (optimiza- Step 5: identify the individual with the highest favor tion) solution, and diversity of imitation immune system, concentration in the drosophila population. IA algorithm can realize the antigen recognition, cell dif- ferentiation, and memory of the immune system and self- = min(Smell). [bestSmell, bestIndex] (6) regulating function [2, 33,
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