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.

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 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 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.

An inner-point modification of PSO for constrained optimization

2015 ◽  
Vol 32 (7) ◽  
pp. 2005-2019 ◽  
Author(s):  
Daniele Peri
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Real Life ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Parallel Structure ◽  
Feasible Region ◽  
Content Type ◽  
Design Variables ◽  
Particle Level

Purpose – The purpose of this paper is to propose a modification of the original PSO algorithm in order to avoid the evaluation of the objective function outside the feasible set, improving the parallel performances of the algorithm in the view of its application on parallel architectures. Design/methodology/approach – Classical PSO iteration is repeated for each particle until a feasible point is found: the global search is performed by a set of independent sub-iteration, at the particle level, and the evaluation of the objective function is performed only once the full swarm is feasible. After that, the main attractors are updated and a new sub-iteration is initiated. Findings – While the main qualities of PSO are preserved, a great advantage in terms of identification of the feasible region and detection of the best feasible solution is obtained. Furthermore, the parallel structure of the algorithm is preserved, and the load balance improved. The results of the application to real-life optimization problems, where constraint satisfaction sometime represents a problem itself, gives the measure of this advantage: an improvement of about 10 percent of the optimal solution is obtained by using the modified version of the algorithm, with a more precise identification of the optimal design variables. Originality/value – Differently from the standard approach, utilizing a penalty function in order to discharge unfeasible points, here only feasible points are produced, improving the exploration of the feasible region and preserving the parallel structure of the algorithm.

Optimization of Multibody Dynamics Using Pointwise Constraints and Arbitrary Functions

1996 ◽  
Author(s):  
Javier Urruzola ◽  
Alejo Avello ◽  
Juan T. Celigüeta
Keyword(s):  
Objective Function ◽  
Multibody Dynamics ◽  
Symbolic Computation ◽  
Optimization Problems ◽  
Variable Method ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Design Variables ◽  
Complex Optimization ◽  
Pointwise Constraints

Abstract Multibody dynamics optimization requires the computation of sensitivities of the objective function and the constraints. This calculation can be done by two methods, direct differentiation and adjoint variable method, that are reviewed in this paper. In either cases, the complexity of the terms that appear in the formulation makes almost a need the use of symbolic computation for the derivation of sensitivities. An existing symbolic manipulator designed for multibody optimization has been enhanced with new and more powerful capabilities. The use of arbitrary functions as design variables and pointwise constraints permits the solution of more complex optimization problems. Some illustrative examples prove the capacity of the method to handle complex optimization problems.

scholarly journals Least-Cost Structural Optimization Oriented Preliminary Design

2001 ◽  
Vol 17 (04) ◽  
pp. 202-215 ◽  
Author(s):  
Philippe Rigo
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Plate Thickness ◽  
Construction Cost ◽  
Global Structure ◽  
Design Stage ◽  
Preliminary Design ◽  
Labor Costs ◽  
Rational Analysis ◽  
Design Variables

A computer design package is presented that provides optimum midship scantlings(plating, longitudinal members and frames). Basic characteristics such as L,B,T,Cb, the global structure layout, and applied loads are the requested data. It is not necessary to provide a feasible initial scantling. Within about one hour of computation time with a usual PC or laptop the LBR-5software automatically provides a rational optimum design. This software is an optimization tool dedicated to preliminary design. Its main advantages, in the early stage of design, are ease of structural modeling, rapid 3-D rational analysis of a ship's hold, and scantling optimization. Preliminary design is the most relevant and the least expensive time to modify design scantling and to compare different alternatives. Unfortunately, it is often too early for efficient use of many commercial software systems, such as FEM. This paper explains how it is now possible to perform optimization at the early design stage, including a 3-D numerical structural analysis. LBR-5 is based on the Module Oriented Approach. Design variables are the dimensions of the longitudinal and transversal members, plate thickness and spacing between members. The software contains three major modules. First, the Cost Module to assess the construction cost which is the objective function (least construction cost). So, unit material costs (Euro/kg or $/kg), welding, cutting, fairing, productivity (man-hours/m) and basic labor costs(Euro/man-hour) have to be specified by the user to define an explicit objective function. Then, there is the Constraint Module to perform a rational analysis of the global structure. This structure is modeled using stiffened plate and stiffened cylindrical shell elements. Finally, the Opti Module which contains a mathematical programming code (CONLIN) to solve constrained nonlinear optimization problems with a reduced number of re-analyses. Usually less than 15 analyses are required even with hundreds of design variables and hundreds of constraints. Optimum analysis of a FSO unit (Floating Storage Offloading) is presented as an example of the performance of the LBR-5 tool.

Discrete Variable Structural Optimization of Systems under Stochastic Earthquake Excitation

2012 ◽  
pp. 51-75 ◽  
Author(s):  
Héctor Jensen ◽  
Marcos Valdebenito ◽  
Juan Sepúlveda ◽  
Luis Becerra
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Optimization Strategy ◽  
Earthquake Excitation ◽  
Hybrid Form ◽  
Reliability Based Design ◽  
Passive Energy Dissipation ◽  
Design Variables ◽  
Stochastic Sensitivity Analysis

The reliability-based design optimization of structural systems under stochastic excitation involving discrete sizing type of design variables is considered. The design problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The excitation is modeled as a non-stationary stochastic process with uncertain model parameters. The problem is solved by a sequential approximate optimization strategy cast into the framework of conservative convex and separable approximations. To this end, the objective function and the reliability constraints are approximated by using a hybrid form of linear, reciprocal, and quadratic approximations. The approximations are combined with an effective stochastic sensitivity analysis in order to generate explicit expressions of the reliability constraints in terms of the design variables. The explicit approximate sub-optimization problems are solved by an appropriate discrete optimization technique. Two example problems that consider structures with passive energy dissipation systems under earthquake excitation are presented to illustrate the effectiveness of the approach reported herein.

scholarly journals Optimization while limiting the number of design variables

2021 ◽  
Vol 11 (2) ◽  
pp. 227-238
Author(s):  
V.P. Ofitserov ◽  
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Nonlinear Function ◽  
Optimal Solution ◽  
Correct Operation ◽  
New Approach ◽  
Design Variables ◽  
Optimal Value ◽  
Distribution Of Resources ◽  
Finite Set

A new approach to the formulation and solution of optimization problems of linear and nonlinear type is stated in this article. The problem statement under consideration differs from the classical linear programming problem of the opti-mal distribution of limited resources between given processes by the need to choose a limited number of processes from a certain finite set and allocate resources over these processes. The goal is to obtain the optimal value of the objective function in relation to other options for choosing the number of processes from the same set and the distribution of resources between them. The objective function can be either linear or non-linear. A nonlinear function must have cer-tain properties for the correct operation of the proposed algorithm for finding the optimal solution. The described method is based on the development of Bellman's ideas of dynamic programming. The proofs of the optimality of the obtained solutions are provided. The article gives an estimate of the computational complexity of the algorithm and a comparison with classical methods for solving the problems under consideration. The types of applied problems solved using the proposed method are characterized. Computer implementations of the described algorithm can be used in automated decision support systems.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

Case study: Prediction and field tests of railway noise and effects of a low-height noise barrier

2020 ◽  
Vol 68 (4) ◽  
pp. 303-314
Author(s):  
Yuna Park ◽  
Hyo-In Koh ◽  
University of Science and Technology, Transpo ◽  
University of Science and Technology, Transpo ◽  
University of Science and Technology, Transpo ◽  
...  
Keyword(s):  
High Speed ◽  
Field Tests ◽  
Residential Areas ◽  
Railway Systems ◽  
Railway Noise ◽  
Sound Levels ◽  
Noise Barrier ◽  
The Difference ◽  
Reduction Effect ◽  
The Impact

Railway noise is calculated to predict the impact of new or reconstructed railway tracks on nearby residential areas. The results are used to prepare adequate counter- measures, and the calculation results are directly related to the cost of the action plans. The calculated values were used to produce noise maps for each area of inter- est. The Schall 03 2012 is one of the most frequently used methods for the production of noise maps. The latest version was released in 2012 and uses various input para- meters associated with the latest rail vehicles and track systems in Germany. This version has not been sufficiently used in South Korea, and there is a lack of standard guidelines and a precise manual for Korean railway systems. Thus, it is not clear what input parameters will match specific local cases. This study investigates the modeling procedure for Korean railway systems and the differences between calcu- lated railway sound levels and measured values obtained using the Schall 03 2012 model. Depending on the location of sound receivers, the difference between the cal- culated and measured values was within approximately 4 dB for various train types. In the case of high-speed trains, the value was approximately 7 dB. A noise-reducing measure was also modeled. The noise reduction effect of a low-height noise barrier system was predicted and evaluated for operating railway sites within the frame- work of a national research project in Korea. The comparison of calculated and measured values showed differences within 2.5 dB.

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