scholarly journals Heuristic-Based Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
M. Fernanda P. Costa ◽  
Ana Maria A. C. Rocha ◽  
Rogério B. Francisco ◽  
Edite M. G. P. Fernandes
Keyword(s):  
Firefly Algorithm ◽  
Optimization Problems ◽  
Search Space ◽  
Benchmark Problems ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Continuous Space ◽  
Two Parameters ◽  
Dynamic Updating ◽  
Simple Heuristics

Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper, we address the practical testing of a heuristic-based FA (HBFA) for computing optima of discrete nonlinear optimization problems, where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid “erf” function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid “erf” function with “movements in continuous space” is the best, in terms of both computational requirements and accuracy.

scholarly journals A comparison of mixed-variables Bayesian optimization approaches

2021 ◽  
Author(s):  
Jhouben Janyk Cuesta Ramirez ◽  
Rodolphe Le Riche ◽  
Olivier Roustant ◽  
Guillaume Perrin ◽  
Cedric Durantin ◽  
...  
Keyword(s):  
Latent Variables ◽  
Optimization Problems ◽  
Practical Interest ◽  
Search Space ◽  
Optimization Techniques ◽  
Bayesian Optimization ◽  
Augmented Lagrangians ◽  
Discrete Variables ◽  
Continuous Space ◽  
Beam Design

Abstract Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.

scholarly journals Differential Evolution with Population and Strategy Parameter Adaptation

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
V. Gonuguntla ◽  
R. Mallipeddi ◽  
Kalyana C. Veluvolu
Keyword(s):  
Differential Evolution ◽  
Population Size ◽  
Optimization Problems ◽  
Search Space ◽  
Benchmark Problems ◽  
Parameter Adaptation ◽  
De Algorithm ◽  
Probabilistic Technique ◽  
Number Of Individuals ◽  
Strategy Parameters

Differential evolution (DE) is simple and effective in solving numerous real-world global optimization problems. However, its effectiveness critically depends on the appropriate setting of population size and strategy parameters. Therefore, to obtain optimal performance the time-consuming preliminary tuning of parameters is needed. Recently, different strategy parameter adaptation techniques, which can automatically update the parameters to appropriate values to suit the characteristics of optimization problems, have been proposed. However, most of the works do not control the adaptation of the population size. In addition, they try to adapt each strategy parameters individually but do not take into account the interaction between the parameters that are being adapted. In this paper, we introduce a DE algorithm where both strategy parameters are self-adapted taking into account the parameter dependencies by means of a multivariate probabilistic technique based on Gaussian Adaptation working on the parameter space. In addition, the proposed DE algorithm starts by sampling a huge number of sample solutions in the search space and in each generation a constant number of individuals from huge sample set are adaptively selected to form the population that evolves. The proposed algorithm is evaluated on 14 benchmark problems of CEC 2005 with different dimensionality.

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.

Taguchi-Particle Swarm Optimization for Numerical Optimization

2012 ◽  
pp. 44-59
Author(s):  
T. O. Ting ◽  
H. C. Ting ◽  
T. S. Lee
Keyword(s):  
Particle Swarm Optimization ◽  
Taguchi Method ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Particle Swarm ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Swarm Optimization ◽  
Continuous And Discrete Variables

In this work, a hybrid Taguchi-Particle Swarm Optimization (TPSO) is proposed to solve global numerical optimization problems with continuous and discrete variables. This hybrid algorithm combines the well-known Particle Swarm Optimization Algorithm with the established Taguchi method, which has been an important tool for robust design. This paper presents the improvements obtained despite the simplicity of the hybridization process. The Taguchi method is run only once in every PSO iteration and therefore does not give significant impact in terms of computational cost. The method creates a more diversified population, which also contributes to the success of avoiding premature convergence. The proposed method is effectively applied to solve 13 benchmark problems. This study’s results show drastic improvements in comparison with the standard PSO algorithm involving continuous and discrete variables on high dimensional benchmark functions.

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.

Differential Operators Embedded Artificial Bee Colony Algorithm

2013 ◽  
pp. 149-163
Author(s):  
Tarun Kumar Sharma ◽  
Millie Pant
Keyword(s):  
Global Optimization ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Differential Operators ◽  
Optimization Problems ◽  
Numerical Results ◽  
Benchmark Problems ◽  
Continuous Space ◽  
Abc Algorithm ◽  
Bee Colony

Artificial Bee Colony (ABC) is one of the most recent nature inspired (NIA) algorithms based on swarming metaphor. Proposed by Karaboga in 2005, ABC has proven to be a robust and efficient algorithm for solving global optimization problems over continuous space. However, it has been observed that the structure of ABC is such that it supports exploration more in comparison to exploitation. In order to maintain a balance between these two antagonist factors, this paper suggests incorporation of differential evolution (DE) operators in the structure of basic ABC algorithm. The proposed algorithm called DE-ABC is validated on a set of 10 benchmark problems and the numerical results are compared with basic DE and basic ABC algorithm. The numerical results indicate that the presence of DE operators help in a significant improvement in the performance of ABC algorithm.

scholarly journals Improved Particle Swarm Optimization with a Collective Local Unimodal Search for Continuous Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
Martins Akugbe Arasomwan ◽  
Aderemi Oluyinka Adewumi
Keyword(s):  
Particle Swarm Optimization ◽  
Local Search ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Continuous Optimization ◽  
Search Space ◽  
Benchmark Problems ◽  
Search Technique ◽  
Swarm Optimization ◽  
Particle Position

A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value in the location of its randomly selected dimension from its personal best. After constructing the potential particle position, some local search is done around its neighbourhood in comparison with the current swarm global best position. It is then used to replace the global best particle position if it is found to be better; otherwise no replacement is made. Using some well-studied benchmark problems with low and high dimensions, numerical simulations were used to validate the performance of the improved algorithms. Comparisons were made with four different PSO variants, two of the variants implement different local search technique while the other two do not. Results show that the improved algorithms could obtain better quality solution while demonstrating better convergence velocity and precision, stability, robustness, and global-local search ability than the competing variants.

scholarly journals Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics

2017 ◽  
Vol 5 (2) ◽  
pp. 198-214 ◽  
Author(s):  
Ghanshyam G. Tejani ◽  
Vimal J. Savsani ◽  
Vivek K. Patel ◽  
Poonam V. Savsani
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Search Space ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Truss Topology Optimization ◽  
Random Mutation ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Space Trusses

Abstract In this study, simultaneous size, shape, and topology optimization of planar and space trusses are investigated. Moreover, the trusses are subjected to constraints for element stresses, nodal displacements, and kinematic stability conditions. Truss Topology Optimization (TTO) removes the superfluous elements and nodes from the ground structure. In this method, the difficulties arise due to unacceptable and singular topologies; therefore, the Grubler's criterion and the positive definiteness are used to handle such issue. Moreover, the TTO is challenging due to its search space, which is implicit, non-convex, non-linear, and often leading to divergence. Therefore, mutation-based metaheuristics are proposed to investigate them. This study compares the performance of four improved metaheuristics (viz. Improved Teaching–Learning-Based Optimization (ITLBO), Improved Heat Transfer Search (IHTS), Improved Water Wave Optimization (IWWO), and Improved Passing Vehicle Search (IPVS)) and four basic metaheuristics (viz. TLBO, HTS, WWO, and PVS) in order to solve structural optimization problems. Highlights Improvements in four recently designed metaheuristics. Use of random mutation-based search technique. Applications on challenging/benchmark problems of simultaneous size, shape, and topology optimization of truss structures. Improvements effective over basic metaheuristics.

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.

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