scholarly journals Harris Hawks Optimization for Optimum Design of Truss Structures with Discrete Variables

2021 ◽  
Vol 6 (4) ◽  
pp. 1157-1173
Author(s):  
Mustafa Al-Bazoon
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Population Based ◽  
Truss Structures ◽  
Discrete Variables ◽  
Structural Problems ◽  
Collaborative Behavior ◽  
Design Variables ◽  
Predatory Birds ◽  
The Mathematical Model

This article investigates the use of Harris Hawks Optimization (HHO) to solve planar and spatial trusses with design variables that are discrete. The original HHO has been used to solve continuous design variables problems. However, HHO is formulated to solve optimization problems with discrete variables in this research. HHO is a population-based metaheuristic algorithm that simulates the chasing style and the collaborative behavior of predatory birds Harris hawks. The mathematical model of HHO uses a straightforward formulation and does not require tuning of algorithmic parameters and it is a robust algorithm in exploitation. The performance of HHO is evaluated using five benchmark structural problems and the final designs are compared with ten state-of-the-art algorithms. The statistical outcomes (average and standard deviation of final designs) show that HHO is quite consistent and robust in solving truss structure optimization problems. This is an important characteristic that leads to better confidence in the final solution from a single run of the algorithm for an optimization problem.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

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.

Parametric Optimization for Structural Design Problems

2019 ◽  
Author(s):  
Krupakaran Ravichandran ◽  
Nafiseh Masoudi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Structural Design ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Nonlinear Constraint ◽  
Computational Performance ◽  
Design Variables ◽  
Input Parameters ◽  
Parametric Optimization Problem ◽  
Objective Function Values

Abstract Parametric Optimization is used to solve problems that have certain design variables as implicit functions of some independent input parameters. The optimal solutions and optimal objective function values are provided as functions of the input parameters for the entire parameter space of interest. Since exact solutions are available merely for parametric optimization problems that are linear or convex-quadratic, general non-convex non-linear problems require approximations. In the present work, we apply three parametric optimization algorithms to solve a case study of a benchmark structural design problem. The algorithms first approximate the nonlinear constraint(s) and then solve the optimization problem. The accuracy of their results and their computational performance are then compared to identify a suitable algorithm for structural design applications. Using the identified method, sizing optimization of a truss structure for varying load conditions such as a varying load direction is considered and solved as a parametric optimization problem to evaluate the performance of the identified algorithm. The results are also compared with non-parametric optimization to assess the accuracy of the solution and computational performance of the two methods.

A Two Level Parallel Evolution Strategy for Solving Mixed-Discrete Structural Optimization Problems

1995 ◽  
Author(s):  
Georg Thierauf ◽  
Jianbo Cai
Keyword(s):  
Parallel Computing ◽  
Structural Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Parallel Evolution ◽  
Evolution Strategy ◽  
Parallel Computer ◽  
Computing Architecture ◽  
Design Variables

Abstract A method for the solution of mixed-discrete structural optimization problems based on a two level parallel evolution strategy is presented. On the first level, the optimization problem is divided into two subproblems with discrete and continuous design variables, respectively. The two subproblems are solved simultaneously on a parallel computing architecture. On the second level, each subproblem is further parallelized by means of a parallel sub-evolution-strategy. Periodically, the design variables in the two groups axe exchanged. Examples are included to demonstrate the implementation of this method on a 8 nodes parallel computer.

Development of a Changeable Airfoil Optimization Model for Use in the Multidisciplinary Design of Unmanned Aerial Vehicles

2009 ◽  
Author(s):  
Scott Ferguson ◽  
Andrew H. Tilstra ◽  
Carolyn C. Seepersad ◽  
Kristin L. Wood
Keyword(s):  
Optimization Problem ◽  
Design Research ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Operating Conditions ◽  
Multidisciplinary Optimization ◽  
System Level ◽  
Airfoil Optimization ◽  
Design Variables ◽  
Subsystem Design

Complex systems need to perform in a variety of functional states and under varying operating conditions. Therefore, it is important to manage the different values of design variables associated with the operating states for each subsystem. The research presented in this paper uses multidisciplinary optimization (MDO) and changeable systems methods together in the design of a reconfigurable Unmanned Aerial Vehicle (UAV). MDO is a useful approach for designing a system that is composed of distinct disciplinary subsystems by managing the design variable coupling between the subsystem and system level optimization problems. Changeable design research addresses how changes in the physical configuration of products and systems can better meet distinct needs of different operating states. As a step towards the development of a realistic reconfigurable UAV optimization problem, this paper focuses on the performance advantage of using a changeable airfoil subsystem. Design principles from transformational design methods are used to develop concepts that determine how the design variables are allowed to change in the mathematical optimization problem. The performance of two changeable airfoil concepts is compared to a fixed airfoil design over two different missions that are defined by a sequence of mission segments. Determining the configurations of the static and changeable airfoils is accomplished using a genetic algorithm. Results from this study show that aircraft with changeable airfoils attain increased performance, and that the manner by which the system transforms is significant. For this reason, the changeable airfoil optimization developed in this paper is ready to be integrated into a complete MDO problem for the design of a reconfigurable UAV.

Practical Optimization Algorithm for Discrete Variables

2010 ◽  
Vol 42 ◽  
pp. 39-42
Author(s):  
De Sheng Wang ◽  
Ai Ping Zhou
Keyword(s):  
Objective Function ◽  
High Speed ◽  
Optimization Problems ◽  
Discrete Variables ◽  
Design Variables ◽  
Low Dimension ◽  
The Difference ◽  
Calculation Ability ◽  
Minimum Objective Function ◽  
Upper Boundary

In order to solve the optimization problems of discrete variable in mechanism design, beginning vertexes to meet all of performance restriction conditions can be given by the technician from upper boundary of design variables by means of man-machine interactive method. Objective function of each beginning vertex is calculated and arranged from small to large, the vertex of maximum and minimum of objective function are found. The difference between the vertex of minimum and maximum of objective function are calculated and new point is made up from the minimum point and the difference. The new point is used in stead of the vertex of the maximum objective function if the objective function of the new point is less than the maximum of beginning vertexes. The new composite figure is made up again and the new point is calculated until all design variables reach to under boundary. Then the vertex of minimum objective function is regarded to as the optimization point. This method is very fit for the optimization of discrete variables of low dimension and is higher calculation efficiency because the hominine brightness is combined with the high speed calculation ability.

Enhancing a twist beam suspension system conceptual design using population-based optimization methods

2020 ◽  
Vol 62 (7) ◽  
pp. 672-677 ◽  
Author(s):  
E. İ. Albak ◽  
E. Solmaz ◽  
F. Öztürk
Keyword(s):  
Mathematical Model ◽  
Conceptual Design ◽  
Optimization Methods ◽  
Population Based ◽  
Least Squares Regression ◽  
Stage Design ◽  
Beam Design ◽  
Design Variables ◽  
Optimization Study ◽  
The Mathematical Model

Abstract Twist beam suspension systems are usually used in middle segment vehicles due to certain advantages. Researchers have presented many studies on both lightweight and functional twist beam design. In this paper, an optimization study is presented for enhancing the conceptual design of the twist beam by defining design variables along the twist beam as subject to vehicle handling conditions.Toe and camber angles are essential parameters that determine vehicle behavior during maneuvering. In this study, opposite wheel travel analysis is performed to represent maneuvering behavior. Therefore, while the optimization study is presented in the form of weight reduction, it is aimed to keep the toe and camber angles at certain intervals. Ant lion optimizer and mothflame optimization methods, which are population-based optimization methods, are used in the optimization phase to evaluate the performance of the new algorithms as compared with genetic algorithm in terms of robustness and correctness in the case of twist beam design. A two stage approach is introduced for presenting the optimization model and analysis. In the first stage, design space is created via the Latin hypercube method; the mathematical model is obtained via the least squares regression method. Finally, the mathematical model is solved to enhance twist beam conceptual design using recently developed population based optimization algorithms.

Improved Harmony Search Algorithm for Solving Optimization Problem with Mixed Discrete Variables

2013 ◽  
Vol 325-326 ◽  
pp. 1485-1488
Author(s):  
Shi Ming Hao ◽  
Li Zhi Cheng
Keyword(s):  
Constrained Optimization ◽  
Optimization Design ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Harmony Search Algorithm ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Decision Variables

The classical harmony search algorithm (HSA) can only be used to solve the unconstrained optimization problems with continuous decision variables. Therefore, the classical HSA is not suitable for solving an engineering optimization problem with mixed discrete variables. In order to improve the classical HSA, an engineering method for dealing with mixed discrete decision variables is introduced and an exact non-differentiable penalty function is used to transform the constrained optimization design model into an unconstrained mathematical model. Based on above improvements, a program of improved HSA is designed and it can be used for solving the constrained optimization design problems with continuous variables, integer variables and non-equidistant discrete variables. Finally, an optimization design example of single-stage cylindrical-gear reducer with mixed-discrete variables is given. The example shows that the designed program runs steadily and the proposed method is effective in engineering design.

The Cheapest Shop Seeker : A New Algorithm For Optimization Problem in a Continous Space

2016 ◽  
Vol 5 (3) ◽  
pp. 119
Author(s):  
Peter Bamidele Shola
Keyword(s):  
Success Rate ◽  
Rate Of Convergence ◽  
Heuristic Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Population Based ◽  
Global Optimum ◽  
Optimum Point ◽  
Number Of Iterations

<div class="Section1"><p>In this paper a population-based meta-heuristic algorithm for optimization problems in a continous space is presented.The algorithm,here called cheapest shop seeker is modeled after a group of shoppers seeking to identify the cheapest shop (among many available) for shopping. The  algorithm was tested on many benchmark functions with the result  compared with those from some other methods. The algorithm appears to  have a better  success  rate of hitting the global optimum point  of a function  and of the rate of convergence (in terms of the number of iterations required to reach the optimum  value) for some functions  in spite  of its simplicity.</p></div>

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