Multiple Frequency Constraints Research Articles

SABO algorithm for optimum design of truss structures with multiple frequency constraints

In this study, a very recently developed intelligent algorithm called the self-adaptive bonomo optimizer (SABO) algorithm is implemented for the size and shape optimizations of the truss structures with the multiple frequency constraints. The bonomo optimizer (BO) algorithm is a recently developed metaheuristic optimization algorithm that imitates the social behavior and reproductive schemes of the bonobos and this algorithm is successfully applied to solve some challenging and highly nonlinear optimization problems. On the other hand, the BO algorithm suffers from the poor exploration and prematurely converges to the non-optimal solutions, especially when dealing with the multi-dimensional optimization problems. In order to overcome these shortcomings, an improved version of this algorithm, the so-called self-adaptive bonomo optimizer (SABO) algorithm, is utilized to optimize the truss structures subjected to the design constraints. The objective of this study is to minimize the weight of the truss structures with the multiple frequency constraints. Five well-known benchmark problems are considered to verify the robustness and reliability of the SABO algorithm. The design results obtained by the SABO algorithm are compared with those previously reported in the literature.

Optimal Design of Large-scale Dome Truss Structures with Multiple Frequency Constraints Using Success-history Based Adaptive Differential Evolution Algorithm

The success-history based adaptive differential evolution (SHADE) algorithm is an efficient modified version of the differential evolution (DE) algorithm, and it has been successfully applied to solve some real-world optimization problems. However, to the best of our knowledge, it has been rarely applied in the field of structural optimization. The optimal design of structures with frequency constraints is well known as a highly nonlinear and non-convex optimization problem with many local optima. In this paper, the SHADE algorithm is examined in the context of size optimization of large-scale truss structures with multiple frequency constraints. In SHADE, a historical memory of successful control parameter settings is used to guide the generation of new control parameters. In order to demonstrate the effectiveness and efficiency of SHADE, three truss optimization problems with multiple frequency constraints are presented. The three examples considered in this paper include a 600-bar single-layer dome-shaped truss, a 1180-bar single-layer dome-shaped truss, and a 1410-bar double-layer dome-shaped truss. The results obtained by the SHADE algorithm are presented and compared with the best-known results reported in the literature. Numerical results indicate the effectiveness and superior performance of SHADE over other algorithms in terms of solution accuracy and robustness. It is worth mentioning that in all the three cases considered, the optimal designs obtained by SHADE are the best ones reported in the literature so far. However, SHADE often requires fewer structural analyses than those required by the other algorithms.

Optimal design of dome structures with recently developed algorithm: Rao series

The modal parameters such as natural frequencies and mode shapes of structures are vital parameters that must be within the certain limits to ensure the desired structural behavior. Optimization of any type of structures regarding natural frequencies as constraints is considered as highly nonlinear and reaching the global solutions is very difficult. Furthermore, optimum design of small, medium and large-scale domes is known as a complicated optimization problem. In this study, the size optimization of the small, medium and large-scale truss dome structures subjected to multiple dynamic frequency constraints by using newly developed meta-heuristic algorithms named Rao algorithms (Rao-1, Rao-2 and Rao-3) is presented. The cross-sectional areas for the truss bar members of dome structures and first five natural frequencies are considered as the design variables and multiple dynamic constraints, respectively. To perform the optimization process of dome structures, a visual computer program is created in Matlab–GUI (Graphical User Interface). This program has combined the Rao algorithms and the finite element analysis using Eigen values of the stiffness matrix. Three different sizes such as small, medium and large-scale dome are examined to show the performance of the Rao algorithms. The examples for the small, medium and large-scale domes contain 120 bar, 600 bar, 1180 bar and1410 bar dome structures. The obtained near-optimal results are compared with the available results found in the literature to indicate the performance of the Rao algorithms. At the end of the study, it is concluded that the Rao algorithms performed similar to other methods and even better in some cases for designing the dome structures. Furthermore, Rao-2 algorithm has achieved the best results in the least number of generations compared to the Rao-1 algorithm.

Optimum design of truss structures with frequency constraints by an enhanced particle swarm optimization method with gradient directions based on emigration philosophy

In this article, the combined method of particle swarm optimization (PSO) with gradient directions (PSOG) is further extended to increase the capabilities of exploration and exploitation. Four different enhancements are added to the PSOG, based on emigration ideas. To investigate the power of the presented methods, 29 complicated functions are optimized with several local optima. Then, the suggested approaches are used in structural design problems with multiple frequency constraints containing sizing and shape design variables for two- and three-dimensional truss structures. The results are compared with some of the methods in the literature and the superiority of the suggested techniques is demonstrated.

Suppression in any configuration : A versatile coupling improved multi-objective manipulation framework for modular active vibration isolation system

Modular actuation units’ development dramatically expands the compatibility and expandability of the modular active vibration isolation system (MAVIS) in space missions. However, due to the current shortness of a unified framework, manipulating such a redundantly actuated multi-input-multi-output (MIMO) nonlinear system assembled by modular units often involves painstaking challenges and repetitive trial. We proposed a unified coordinated manipulation and multi-objective vibration control framework with the ultimate goal of effectively vibration isolation for such systems. This framework, built on a general model and inherently coupling analysis, incorporates optimized manipulation with inversion system improved multi-objective control. Compared with the traditional multivariable feedback control, this framework effectively reduces the controller’s order while ensuring the system’s multiple objectives and frequency constraints. Experiments and simulations demonstrate the effectiveness of the proposed framework in achieving coordinated manipulation and vibration attenuation on a physical system and indicate the potential role of its application for a family of modular active vibration isolation systems.

A novel hybrid differential evolution and symbiotic organisms search algorithm for size and shape optimization of truss structures under multiple frequency constraints

Although a large number of metaheuristic algorithms and their variants have been proposed for many engineering optimization problems, no paradigms hybridized by differential evolution (DE) and symbiotic organisms search (SOS) to concurrently improve the optimal solution quality and the convergence speed have been published thus far, especially for size and shape optimization of truss structures with multiple frequency constraints. Therefore, this article aims to propose a novel optimization algorithm as a cross-breed of the DE and the SOS, named HDS, for such problems. This algorithm can simultaneously and effectively enhance both global and local searching abilities by utilizing newly developed operators hybridized from the DE and SOS. An automatically adapted parameter is suggested for a better trade-off between those two capabilities. Furthermore, an elitist scheme is used in the selection phase to extract the best solutions for the next generation. As a consequence, the proposed methodology results in high-quality optimal solutions with a lower computational effort in comparison with two original methods, even many other optimization paradigms available in the literature. 26 benchmark mathematical functions are examined first. 5 numerical examples of shape and size optimization of truss structures are then investigated to validate the feasibility of the current paradigm.

An enhanced symbiotic organisms search algorithm for design optimization of trusses with frequency constraints

An enhanced symbiotic organisms search (ESOS) algorithm is developed and presented. Modifications to the basic symbiotic organisms search algorithm are carried out in all three phases of the algorithm with the aim of balancing the exploitation and exploration capabilities of the algorithm. To verify validity and capability of the ESOS algorithm in solving general optimization problems, the CEC2014 set of 22 benchmark functions is first optimized and the results are compared with other metaheuristic algorithms. The ESOS algorithm is then used to optimize the sizing and shape of five benchmark trusses with multiple frequency constraints. The best (minimum) mass, mean mass, standard deviation of the mass, total number of function evaluations, and the values of frequency constraints are then compared with those of a number of other metaheuristic solutions available in the literature. It is shown that the proposed ESOS algorithm is generally more efficient in optimizing the shape and sizing of trusses with dynamic frequency constraints compared to other reported metaheuristic algorithms, including the basic symbiotic organisms search and its other recently proposed improved variants such as the improved symbiotic organisms search algorithm (ISOS) and modified symbiotic organisms search algorithm (MSOS).

Frequency-constrained optimization of large-scale dome-shaped trusses using chaotic water strider algorithm

The frequency constrained design of large-scale structures is a complex optimization problem with many local optima. In order to tackle this problem, in this paper, a chaotic version of a newly-established metaheuristic algorithm, the so-called Water Strider Algorithm (WSA), is introduced. This version repetitively diversifies solutions and then focuses on promising areas during the course of iterations. The chaotic algorithm involves two types of succession states, namely explorative and exploitative states, and it probabilistically switches between them using the Circle map with a quasi-cyclic behavior. To examine the effectiveness of this algorithm, it is applied to structural optimization of large-scale structures with multiple frequency constraints such as 600-, 1180- and 1410-bar dome trusses. The results show that the new version outperforms its basic version as well as some other well-established algorithms in the literature. The statistical measures reveal that it is reasonably capable of providing a satisfactory performance in terms of both obtaining lighter designs and convergence speed.

Weighted superposition attraction-repulsion (WSAR) algorithm for truss optimization with multiple frequency constraints

Structural optimization of truss structures under multiple frequency constraints is a highly nonlinear and complex optimization problem with non-convex solution space. The optimization method used to solve mentioned problem is expected to provide a very good balance between solution accuracy and computational cost. In this work, the Weighted Superposition Attraction-Repulsion (WSAR) algorithm, which is a recent swarm intelligence based metaheuristic algorithm, is proposed for effective solution of truss optimization problems with multiple natural frequency constraints. The effectiveness and robustness of the WSAR algorithm is studied by solving several planar/space truss structures optimization problems. The optimization results reveal that the successfulness and effectiveness of WSAR in solving truss optimization problems under multiple frequency constraints where WSAR is able to generate the best results in terms of optimized weight and standard deviation compared to the other state-of-the-art metaheuristic algorithms.

Enhanced versions of the shuffled shepherd optimization algorithm for the optimal design of skeletal structures

This paper consists of two main parts. The first part is devoted to developing a parameter-free variant of the shuffled shepherd optimization algorithm (SSOA), named as a parameter-free shuffled shepherd optimization algorithm (PF-SSOA). Next, a set-theoretical multi-phase framework is proposed for the population-based metaheuristic algorithms. The proposed framework's main idea is based on dividing the population of candidate solutions into some number of well-arranged sub-populations. The number of sub-populations gradually changes during the optimization process. The framework is applied to the PF-SSOA, leading to a set-theoretical multi-phase variant of PF-SSOA named STMP-SSOA. The STMP-SSOA stands for a set-theoretical multi-phase shuffled shepherd optimization algorithm. Some skeletal structures are optimized to verify the validity and efficiency of the proposed algorithms. The optimization problems include two truss size optimization problems with multiple frequency constraints and two planar frame structures with strength and displacement constraints. The results indicate that the developed algorithms perform better than the standard version of the SSOA, especially in terms of robustness and convergence characteristics.

Set theoretical variants of the teaching–learning-based optimization algorithm for optimal design of truss structures with multiple frequency constraints

In this paper, a set theoretical framework is proposed for the population-based metaheuristic algorithms. Using the proposed framework, two new set theoretical variants of the teaching–learning-based optimization (TLBO) algorithm are developed. These algorithms are named as OST-TLBO and STMP-TLBO, which are acronyms for the “ordered set theoretical teaching–learning-based optimization” and “set theoretical multi-phase teaching–learning-based optimization”, respectively. The present framework can be applied to other population-based metaheuristic algorithms. In order to verify the stability and robustness of the presented algorithms, some optimization problems are examined. These problems include four truss optimization problems with multiple natural frequency constraints. Comparing the results obtained from the proposed algorithms with those of the standard version of the TLBO algorithm shows that the proposed set theoretical framework improves the performance of the standard TLBO in terms of robustness and convergence characteristics.

Meta-heuristic design optimization of steel moment resisting frames subjected to natural frequency constraints

Natural frequencies of a structure play a key role for finding underlying structural properties. Therefore, structural design considering natural frequencies is a very important issue for engineers. While there are many studies on optimization of truss structures under multiple frequency constraints, just a few studies have been published on steel frames for which only gradient based methods were applied. In this paper, meta-heuristic algorithms are applied for the first time ever to optimal design of steel frame structures with frequency constraints. Several benchmark design examples are solved with five algorithms including particle swarm optimization (PSO), charged system search (CSS), teaching-learning based optimization (TLBO), grey wolf optimizer (GWO) and a recently developed improved grey wolf optimizer (IGWO). Optimization results of these algorithms are compared in terms of statistical indices, convergence and optimum solutions. Various types of planar and space steel frames ranging from small to large scale cases are considered for illustrating merits and applicability of meta-heuristic algorithms to these sizing optimization problems wherein the large scale cases are studied in both continuous and discrete forms.

Chaos-based firefly algorithms for optimization of cyclically large-size braced steel domes with multiple frequency constraints

The success of the search in the firefly algorithm is highly dependent on a good balance between exploration and exploitation. Although, the basic firefly algorithm is relatively efficient; two chaotic firefly algorithms based on Logistic map (CLFA) and Gaussian map (CGFA) have been presented to improve basic FA. As numerical examples, some large-scale domes are designed for multiple frequency constraints optimization. Despite the fact that these problems are highly nonlinear, results illustrate a desirable performance of the algorithms in both obtaining lower weight and having a higher convergence rate.

Enhanced Artificial Coronary Circulation System Algorithm for Truss Optimization with Multiple Natural Frequency Constraints

In this paper, an enhanced artificial coronary circulation system (EACCS) algorithm is applied to structural optimization with continuous design variables and frequency constraints. The standard algorithm, artificial coronary circulation system (ACCS), is inspired biologically as a non-gradient algorithm and mimics the growth of coronary tree of heart circulation system. Designs generated by the EACCS algorithm are compared with other popular evolutionary optimization methods, the objective function being the total weight of the structures.Truss optimization with frequency constraints has attracted substantial attention to improve the dynamic performance of structures. This kind of problems is believed to represent nonlinear and non-convex search spaces with several local optima. These problems are also suitable for examining the capabilities of the new algorithms. Here, ACCS is enhanced (EACCS) and employed for size and shape optimization of truss structures and six truss design problems are utilized for evaluating and validating of the EACCS. This algorithm uses a fitness-based weighted mean in the bifurcation phase and runner phase of the optimization process. The numerical results demonstrate successful performance, efficiency and robustness of the new method and its competitive performance to some other well-known meta-heuristics in structural optimization.

Hypotrochoid spiral optimization approach for sizing and layout optimization of truss structures with multiple frequency constraints

The primary aim of this article is to present a new improved version of the spiral optimization algorithm (SPO) for shape and size optimization of truss structures under multiple frequency constraints. In the proposed method, which is named as hypotrochoid spiral optimization algorithm (HSPO), the movement operation of search points is redesigned, and mechanisms are utilized to boost the potency of the method in escaping from local optima and improving the accuracy of the results. Furthermore, a meta-optimization approach is developed by hybridizing the particle swarm optimization and the proposed technique for finding optimal parameter settings of the presented method. Thereafter, exploration and exploitation abilities of HSPO and SPO are compared by solving five benchmark design problems. Numerical results indicate that the convergence speed is enhanced, especially in the exploitation phase of the HSPO. The optimum designs found by the improved version are highly competitive with the best solutions reported in the literature.

Modified symbiotic organisms search for structural optimization

The structural dynamic response predominantly depends upon natural frequencies which fabricate these as a controlling parameter for dynamic response of the truss. However, truss optimization problems subjected to multiple fundamental frequency constraints with shape and size variables are more arduous due to its characteristics like non-convexity, non-linearity, and implicit with respect to design variables. In addition, mass minimization with frequency constraints are conflicting in nature which intricate optimization problem. Using meta-heuristic for such kind of problem requires harmony between exploration and exploitation to regulate the performance of the algorithm. This paper proposes a modification of a nature inspired Symbiotic Organisms Search (SOS) algorithm called a Modified SOS (MSOS) algorithm to enhance its efficacy of accuracy in search (exploitation) together with exploration by introducing an adaptive benefit factor and modified parasitism vector. These modifications improved search efficiency of the algorithm with a good balance between exploration and exploitation, which has been partially investigated so far. The feasibility and effectiveness of proposed algorithm is studied with six truss design problems. The results of benchmark planar/space trusses are compared with other meta-heuristics. Complementarily the feasibility and effectiveness of the proposed algorithms are investigated by three unimodal functions, thirteen multimodal functions, and six hybrid functions of the CEC2014 test suit. The experimental results show that MSOS is more reliable and efficient as compared to the basis SOS algorithm and other state-of-the-art algorithms. Moreover, the MSOS algorithm provides competitive results compared to the existing meta-heuristics in the literature.

Combining Migration and Differential Evolution Strategies for Optimum Design of Truss Structures with Dynamic Constraints

The structural optimization problem with frequency constraints is one of the most challenging problems in the field of structural optimization as it typically involves a high degree of nonlinearity which makes the challenge of finding optimum solutions hard. In this study, a combined migration and differential evolution strategies (MS–DE) algorithm is presented for optimum design of truss structures with multiple frequency constraints. In the proposed method, the migration strategy (MS) is helpful to provide an accurate exploitation in the search space by sharing information between the individuals, while the differential evolution (DE) strategy is beneficial for increasing diversity of the population and performing efficient search within the global range. Numerical results and comparisons to some existing optimization techniques based on six benchmark truss design examples with multiple frequency constraints demonstrate the effectiveness of the proposed MS–DE method.

An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints

A novel adaptive hybrid evolutionary firefly algorithm (AHEFA) for shape and size optimization of truss structures under multiple frequency constraints is proposed.This algorithm is a hybridization...

An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints

This paper presents a novel adaptive hybrid evolutionary firefly algorithm (AHEFA) for shape and size optimization of truss structures under multiple frequency constraints. This algorithm is a hybridization of the differential evolution (DE) algorithm and the firefly algorithm (FA). An automatically adapted parameter is utilized to select an appropriate mutation scheme for an effective trade-off between the global and local search abilities. An elitist technique is applied to the selection phase to choose the best individuals. Accordingly, the convergence rate is significantly improved with the high solution accuracy. Six numerical examples are examined for the validity of the present algorithm.

Truss optimization with multiple frequency constraints and automatic member grouping

This paper deals with sizing and shape structural optimization problems with respect to the minimization of the masses of truss structures considering multiple natural frequencies as the constraints of the problems. The sizing and shape design variables are discrete and continuous, respectively. It can be attractive to use a reduced number of distinct cross-sectional areas minimizing costs of fabrication, transportation, storing, checking, welding, and so on. Also, it is expected a labor-saving when the structure is welded, checked and so on. On the other hand, one can observe that the task of discovering the optimum member grouping is not trivial and leads to an exhaustive trial-and-error process. Cardinality constraints are adopted in order to obtain an automatic variable linking searching for the best member grouping of the bars of the trusses analyzed in this paper. A CRPSO (Craziness based Particle Swarm Optimization) is the search algorithm adopted in this paper. This algorithm uses a modified velocity expression and an operator called “craziness velocity” in order to avoid premature convergence. An Adaptive Penalty Method is adopted to handle the constraints. Six truss structures are analyzed, presenting very interesting results providing curves of tradeoff between the optimized weights versus the number of distinct cross-sectional areas used in these solutions.