scholarly journals Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yue Wu ◽  
Qingpeng Li ◽  
Qingjie Hu ◽  
Andrew Borgart
Keyword(s):  
Topology Optimization ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimization Method ◽  
Structural Topology ◽  
Discrete Variables ◽  
And Topology ◽  
Design Variables ◽  
Improved Firefly Algorithm ◽  
Discrete Design Variables

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

scholarly journals A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

2020 ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

Abstract In this paper a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability of generating connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. Lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize firefly algorithm based section of the hybrid algorithm. Input parameters, number of fireflies and number function evaluations were determined before implementation of firefly algorithm to solve formulated problems. Since direct application of firefly algorithm cannot generate connected topologies, outputs from firefly algorithm were used as an initial input material distribution for OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using OC method. Weight percentage reduction, maximum stress induced, optimal material distribution and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies and generated topologies are free from interference of end users, which only dependence on boundary conditions or the design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to OC method.

scholarly journals A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

2020 ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

Abstract In this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and number function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies and generated topologies are free from the interference of end-users, which only dependence on boundary conditions or the design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to the OC method.

scholarly journals A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

2020 ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

Abstract In this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and the number of function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies which are free from the interference of end-users, and only depend on boundary conditions or design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to the OC method.

scholarly journals A firefly algorithm based hybrid method for structural topology optimization

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

AbstractIn this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and the number of function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies which are free from the interference of end-users, and only depend on boundary conditions or design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5 to 15% compared to the OC method.

A NEW ELEMENT-BASED METHOD FOR SOLVING STRUCTURAL TOPOLOGY OPTIMIZATION PROBLEMS WITH NON-UNIFORM MESHES

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Kuang-Wu Chou ◽  
Chang-Wei Huang
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Optimization Method ◽  
Optimal Topology ◽  
Evolutionary Stage ◽  
Structural Topology Optimization ◽  
Volume Constraint ◽  
Structural Topology ◽  
Exchange Method ◽  
Python Scripting

This study proposes a new element-based method to solve structural topology optimization problems with non-uniform meshes. The objective function is to minimize the compliance of a structure, subject to a volume constraint. For a structure of a fixed volume, the method is intended to find a topology that could almost conform to the compliance minimum. The method is refined from the evolutionary switching method, whose policy of exchanging elements is improved by replacing some empirical decisions with ones according to optimization theories. The method has the evolutionary stage and the element exchange stage to conduct topology optimization. The evolutionary stage uses the evolutionary structural optimization method to remove inefficient elements until the volume constraint is satisfied. The element exchange stage performs a procedure refined from the element exchange method. Notably, the procedures of both stages are refined to conduct non-uniform finite element meshes. The proposed method was implemented to use the Abaqus Python scripting interface to call the services of Abaqus such as running analysis and retrieving the output database of an analysis. Numerical examples demonstrate that the proposed optimization method could determine the optimal topology of a structure that is subject to a volume constraint and whose mesh is non-uniform.

Topology Optimization of Compliant Mechanisms Using Evolutionary Algorithm With Design Geometry Encoded as a Graph

2002 ◽  
Author(s):  
Shamim Akhtar ◽  
Kang Tai ◽  
Jitendra Prasad
Keyword(s):  
Topology Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Evolutionary Process ◽  
Optimization Procedure ◽  
Structural Topology ◽  
Mutation Operators ◽  
Design Variables ◽  
Straight Line

This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using an evolutionary algorithm (EA). The geometry representation scheme works by defining a skeleton which represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any EA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a graph which reflects this underlying topology so that the genetic crossover and mutation operators of the EA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point.

Product Optimization Incorporating Discrete Design Variables Based on Decomposition of Performance Characteristics

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Masataka Yoshimura ◽  
Yu Yoshimura ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Mathematical Programming ◽  
Optimization Problems ◽  
System Optimization ◽  
Optimization Method ◽  
Hierarchical Optimization ◽  
Standard Material ◽  
Design Variables ◽  
Hierarchical Levels ◽  
Discrete Design Variables ◽  
Product Optimization

This paper proposes a system optimization method for product designs incorporating discrete design variables, in which hierarchical product optimization methodologies are constructed based on decomposition of characteristics and/or extraction of simpler characteristics from original characteristics. The method is constructed to take advantage of hierarchical optimization procedures, enabling the incorporation of discrete design variables. The proposed method can be applied to machine product designs that include discrete design variables such as material types, machining methods, standard material forms, and specifications. The optimizations begin at the lowest levels of the hierarchical optimization structure and proceed to the higher levels. Discrete design variables are efficiently selected and optimized in the form of small suboptimization problems at the lowest hierarchical levels, and optimum solutions for the entire problem are ultimately obtained using conventional mathematical programming methods. Practical optimization procedures for machine product optimization problems that include several types of discrete design variables are constructed, and applied examples are provided to demonstrate their effectiveness.

Structure Analysis and Topology Optimization of a Bent-Bar-Frame Piston Based on the Variable Density Approach

2014 ◽  
Author(s):  
Jie Zhao ◽  
Farong Du ◽  
Wei Yao
Keyword(s):  
Topology Optimization ◽  
Thermal Loading ◽  
Coupled Model ◽  
Variable Density ◽  
Structural Topology ◽  
Connecting Rod ◽  
And Topology ◽  
Design Variables ◽  
Cylinder Piston ◽  
Optimized Model

The iterative algorithm of design variables for structural topology optimization is derived by using variable density approach and Finite Element Method. A coupled model of bent-bar-frame piston is built considering the contact between piston and cylinder, piston and piston pin, piston pin and connecting rod. Based on this model, the deformation and stress of piston are analyzed under each of mechanical or thermal loading. Taking structural weight as the objective function of optimization, three desired regions of piston are optimized by using variable density approach in commercial FEA software HYPERMESH and ANSYS. Finally, the deformation and temperature of the optimized model are compared with prototype by using the same loading and boundary conditions. The results show that the weight of piston is reduced by 12.5% while meeting the required specifications.

scholarly journals Reliability-Based Design Optimization of Trusses with Linked-Discrete Design Variables using the Improved Firefly Algorithm

2016 ◽  
Vol 6 (2) ◽  
pp. 964-971
Author(s):  
N. M. Okasha
Keyword(s):  
Design Optimization ◽  
Firefly Algorithm ◽  
Structural Reliability ◽  
Solution Process ◽  
Truss Structures ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Design Variables ◽  
Improved Firefly Algorithm ◽  
Discrete Design Variables

In this paper, an approach for conducting a Reliability-Based Design Optimization (RBDO) of truss structures with linked-discrete design variables is proposed. The sections of the truss members are selected from the AISC standard tables and thus the design variables that represent the properties of each section are linked. Latin hypercube sampling is used in the evaluation of the structural reliability. The improved firefly algorithm is used for the optimization solution process. It was found that in order to use the improved firefly algorithm for efficiently solving problems of reliability-based design optimization with linked-discrete design variables; it needs to be modified as proposed in this paper to accelerate its convergence.

scholarly journals A Brief Review of Firefly Algorithm: Application in Structural Optimization Problem

2019 ◽  
Vol 15 (2) ◽  
pp. 183-191
Author(s):  
Sujan Tripathi
Keyword(s):  
Particle Swarm Optimization ◽  
Structural Engineering ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Heuristic Method ◽  
Particle Swarm ◽  
Research Area ◽  
Swarm Optimization ◽  
Design Variables ◽  
Discrete Design Variables

 Firefly Algorithm is a recently developed meta-heuristic algorithm, which is inspired by the flashing behaviour of Firefly. Initially, Firefly algorithm was used to solve the optimization problems of continuous search domain. Further, many researchers have successfully implemented this algorithm in several discrete optimization problems. Although the firefly algorithm behaves like another meta-heuristic method (i.e. Particle Swarm Optimization particle), however, the firefly is robust than that. Due to the presence of an exponential term in its movement equation, firefly algorithm is capable to search optimum value more efficiently than others. This study is, mainly, focused to show the strength of the firefly algorithm to solve the complex problems and to explore the possible research area on the structural engineering field. This study shows about the robustness of the firefly algorithm on the basis of recently published papers that was used to solve the size, shape and topology optimization of the spatial truss structure with discrete design variables. The review result shows that the performance of the Firefly Algorithm is remarkable compared to other nature-inspired-algorithms, such as particle swarm optimization. This study concludes with some remarkable points that will be more beneficial to the future researchers of this area.

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