scholarly journals Unconstrained numerical optimization using real-coded genetic algorithms: a study case using benchmark functions in R from Scratch

2019 ◽  
Vol 11 (3) ◽  
pp. 1-11
Author(s):  
Omar Andres Carmona Cortes ◽  
Josenildo Costa da Silva
Keyword(s):  
Genetic Algorithms ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Practical Applications ◽  
R Language ◽  
Mutation Operators ◽  
Design Variables ◽  
Study Case ◽  
Selection Mechanisms ◽  
Real Coded Genetic Algorithms

Unconstrained numerical problems are common in solving practical applications that, due to its nature, are usually devised by several design variables, narrowing the kind of technique or algorithm that can deal with them. An interesting way of tackling this kind of issue is to use an evolutionary algorithm named Genetic Algorithm. In this context, this work is a tutorial on using real-coded genetic algorithms for solving unconstrained numerical optimization problems. We present the theory and the implementation in R language. Five benchmarks functions (Rosenbrock, Griewank, Ackley, Schwefel, and Alpine) are used as a study case. Further, four different crossover operators (simple, arithmetical, non-uniform arithmetical, and Linear), two selection mechanisms (roulette wheel and tournament), and two mutation operators (uniform and non-uniform) are shown. Results indicate that non-uniform mutation and tournament selection tend to present better outcomes.

scholarly journals A Novel Parent Centric Crossover with the Log-Logistic Probabilistic Approach Using Multimodal Test Problems for Real-Coded Genetic Algorithms

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Ehtasham ul Haq ◽  
Ishfaq Ahmad ◽  
Ibrahim M. Almanjahie
Keyword(s):  
Optimization Problems ◽  
Probabilistic Approach ◽  
Population Diversity ◽  
Test Problems ◽  
Crossover Operator ◽  
Local Optima ◽  
Mutation Operators ◽  
Multiple Comparison Test ◽  
Power Mutation ◽  
Real Coded Genetic Algorithms

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems.

scholarly journals Autonomous Planning of Multigravity-Assist Trajectories with Deep Space Maneuvers Using a Differential Evolution Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ossama Abdelkhalik
Keyword(s):  
Genetic Algorithms ◽  
Differential Evolution ◽  
Optimization Problems ◽  
Optimal Number ◽  
Deep Space ◽  
Biologically Inspired ◽  
Autonomous Planning ◽  
Design Variables ◽  
Planning Problems ◽  
Evolution Approach

The biologically inspired concept of hidden genes has been recently introduced in genetic algorithms to solve optimization problems where the number of design variables is variable. In multigravity-assist trajectories, the hidden genes genetic algorithms demonstrated success in searching for the optimal number of swing-bys and the optimal number of deep space maneuvers. Previous investigations in the literature for multigravity-assist trajectory planning problems show that the standard differential evolution is more effective than the standard genetic algorithms. This paper extends the concept of hidden genes to differential evolution. The hidden genes differential evolution is implemented in optimizing multigravity-assist space trajectories. Case studies are conducted, and comparisons to the hidden genes genetic algorithms are presented in this paper.

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.

scholarly journals Optimization in a realistic structural engineering context: redesign of the Market Hall in Ghent

2021 ◽  
Author(s):  
Wouter Dillen ◽  
Geert Lombaert ◽  
Ruben Mertens ◽  
Hanne Van Beurden ◽  
Dirk Jaspaert
Keyword(s):  
Structural Design ◽  
Numerical Optimization ◽  
Structural Engineering ◽  
Steel Structure ◽  
Construction Cost ◽  
Metaheuristic Algorithms ◽  
Complex Structures ◽  
Original Design ◽  
Practical Applications ◽  
Design Variables

<p>Numerical optimization has a large potential in the context of structural design, but practical applications remain scarce. Even metaheuristic algorithms, which are easy to use, are rarely adopted in practice. Possible explanations are the fact that for problems with many design variables, metaheuristic algorithms converge slowly, and that structural optimization often leads to very complex structures, resulting in a high construction cost. The aim of this paper is to illustrate the potential of numerical optimization in a realistic design context. The focus is on the steel structure of the Ghent Market Hall, which is redesigned using a genetic algorithm. The structural member groups from the original design are maintained, such that the number of design variables is sufficiently low, and that the complexity of the design remains limited. Using this approach, a design is obtained that consumes 15 % less material than the original design.</p>

A Literature Review: Solving Constrained Non-Linear Bi-Level Optimization Problems With Classical Methods

2019 ◽  
Author(s):  
Arpan Biswas ◽  
Christopher Hoyle
Keyword(s):  
Literature Review ◽  
Optimization Problems ◽  
Classical Method ◽  
Optimization Methods ◽  
Function Evaluation ◽  
Practical Applications ◽  
Design Variables ◽  
Non Linear ◽  
Upper Level ◽  
Work Done

Abstract Bi-level optimization is an emerging scope of research which consists of two optimization problems, where the lower-level optimization problem is nested into the upper-level problem as a constraint. Bi-level programming has gained much attention recently for practical applications. Bi-level Programming Problems (BLPP) can be solved with classical and heuristic optimization methods. However, applying heuristic methods, though easier to formulate for realistic complex design, are likely to be too computationally expensive for solving bi-level problems, especially when the problem has high function evaluation cost associated with handling large number of constraint functions. Thus, classical approaches are investigated in this paper. As we present, there appears to be no universally best classical method for solving any kind of NP-hard BLPP problem in terms of accuracy to finding true optimal solutions and minimal computational costs. This could cause a dilemma to the researcher in choosing an appropriate classical approach to solve a BLPP in different domains and levels of complexities. Therefore, this motivates us to provide a detailed literature review and a comparative study of the work done to date on applying different classical approaches in solving constrained non-linear, bi-level optimization problems considering continuous design variables and no discontinuity in functions.

An improved class of real-coded Genetic Algorithms for numerical optimization✰

2018 ◽  
Vol 275 ◽  
pp. 155-166 ◽  
Author(s):  
Mostafa Z. Ali ◽  
Noor H. Awad ◽  
Ponnuthurai N. Suganthan ◽  
Ali M. Shatnawi ◽  
Robert G. Reynolds
Keyword(s):  
Genetic Algorithms ◽  
Numerical Optimization ◽  
Real Coded Genetic Algorithms
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