scholarly journals Evolutionary Algorithms for Constrained Parameter Optimization Problems

1996 ◽  
Vol 4 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Zbigniew Michalewicz ◽  
Marc Schoenauer
Keyword(s):  
Nonlinear Programming ◽  
Evolutionary Algorithms ◽  
Evolutionary Computation ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Test Cases ◽  
Nonlinear Constraints ◽  
Nonlinear Programming Problem ◽  
General Nonlinear Programming

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

scholarly journals Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization

1999 ◽  
Vol 7 (1) ◽  
pp. 19-44 ◽  
Author(s):  
Slawomir Koziel ◽  
Zbigniew Michalewicz
Keyword(s):  
Evolutionary Algorithms ◽  
Parameter Optimization ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Search Space ◽  
Test Cases ◽  
Nonlinear Constraints ◽  
New Approach ◽  
Survey Papers ◽  
Dimensional Cube

During the last five years, several methods have been proposed for handling nonlinear constraints using evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify these methods into four categories: preservation of feasibility, penalty functions, searching for feasibility, and other hybrids. In this paper we investigate a new approach for solving constrained numerical optimization problems which incorporates a homomorphous mapping between n-dimensional cube and a feasible search space. This approach constitutes an example of the fifth decoder-based category of constraint handling techniques. We demonstrate the power of this new approach on several test cases and discuss its further potential.

scholarly journals Lifecycle-Based Swarm Optimization Method for Numerical Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hai Shen ◽  
Yunlong Zhu ◽  
Xiaodan Liang
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Benchmark Problems ◽  
Swarm Optimization ◽  
Individual Organism ◽  
Engineering Problems ◽  
Mechanical Design Problem

Bioinspired optimization algorithms have been widely used to solve various scientific and engineering problems. Inspired by biological lifecycle, this paper presents a novel optimization algorithm called lifecycle-based swarm optimization (LSO). Biological lifecycle includes four stages: birth, growth, reproduction, and death. With this process, even though individual organism died, the species will not perish. Furthermore, species will have stronger ability of adaptation to the environment and achieve perfect evolution. LSO simulates Biological lifecycle process through six optimization operators: chemotactic, assimilation, transposition, crossover, selection, and mutation. In addition, the spatial distribution of initialization population meets clumped distribution. Experiments were conducted on unconstrained benchmark optimization problems and mechanical design optimization problems. Unconstrained benchmark problems include both unimodal and multimodal cases the demonstration of the optimal performance and stability, and the mechanical design problem was tested for algorithm practicability. The results demonstrate remarkable performance of the LSO algorithm on all chosen benchmark functions when compared to several successful optimization techniques.

Introduction

2010 ◽  
pp. 1-12 ◽  
Author(s):  
Monica Chis
Keyword(s):  
Software Engineering ◽  
Computer Science ◽  
Evolutionary Computation ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Science Literature ◽  
Computation Techniques

This chapter aims to present a part of the computer science literature in which the evolutionary computation techniques, optimization techniques and other bio-inspired techniques are used to solve different search and optimization problems in the area of software engineering.

Optimization With Discrete Variables Via Recursive Quadratic Programming: Part 1—Concepts and Definitions

1989 ◽  
Vol 111 (1) ◽  
pp. 124-129 ◽  
Author(s):  
J. Z. Cha ◽  
R. W. Mayne
Keyword(s):  
Nonlinear Programming ◽  
Quadratic Programming ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Optimization Techniques ◽  
Discrete Variables ◽  
Convergence Criteria ◽  
Recursive Quadratic Programming ◽  
Analytical Properties ◽  
Discrete Optimization Problems

Although a variety of algorithms for discrete nonlinear programming have been proposed, the solution of discrete optimization problems is far from mature compared to continuous optimization techniques. This paper focuses on the recursive quadratic programming strategy which has proven to be efficient and robust for continuous optimization. The procedure is adapted to consider a class of mixed discrete nonlinear programming problems and utilizes the analytical properties of functions and constraints. This first part of the paper considers definitions, concepts, and possible convergence criteria. Part II includes the development and testing of the algorithm.

scholarly journals A Comparison of Evolutionary Computation Techniques for IIR Model Identification

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Erik Cuevas ◽  
Jorge Gálvez ◽  
Salvador Hinojosa ◽  
Omar Avalos ◽  
Daniel Zaldívar ◽  
...  
Keyword(s):  
Evolutionary Computation ◽  
Impulse Response ◽  
Optimization Problems ◽  
Finite Impulse Response ◽  
Model Identification ◽  
Optimization Techniques ◽  
Infinite Impulse Response ◽  
Computation Techniques ◽  
Recent Developments ◽  
Complex Optimization

System identification is a complex optimization problem which has recently attracted the attention in the field of science and engineering. In particular, the use of infinite impulse response (IIR) models for identification is preferred over their equivalent FIR (finite impulse response) models since the former yield more accurate models of physical plants for real world applications. However, IIR structures tend to produce multimodal error surfaces whose cost functions are significantly difficult to minimize. Evolutionary computation techniques (ECT) are used to estimate the solution to complex optimization problems. They are often designed to meet the requirements of particular problems because no single optimization algorithm can solve all problems competitively. Therefore, when new algorithms are proposed, their relative efficacies must be appropriately evaluated. Several comparisons among ECT have been reported in the literature. Nevertheless, they suffer from one limitation: their conclusions are based on the performance of popular evolutionary approaches over a set of synthetic functions with exact solutions and well-known behaviors, without considering the application context or including recent developments. This study presents the comparison of various evolutionary computation optimization techniques applied to IIR model identification. Results over several models are presented and statistically validated.

Multiobjective Design Optimization of an IACC Sailing Yacht by Means of CFD High-Fidelity Solvers

2005 ◽  
Author(s):  
Daniele Peri ◽  
Fabrizio Mandolesi
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Design Team ◽  
Course Of Action ◽  
Multiobjective Optimization Problems ◽  
Sailing Yacht ◽  
America’S Cup ◽  
The One ◽  
Multiobjective Design

Performance differences in box rule racing yachts, such as the International America’s Cup Class (IACC), have progressively decreased, and the gap between the winner and the loser is on the order of a percentage point. Numerical optimization techniques can help the design team by identifying the best course of action for improving the design. However, optimization techniques must fulfill two major requirements; reliability and efficiency. Reliability is obtained by applying edge class CFD solvers, like RANSE solvers. Efficiency is gained by utilizing popular algorithms for local optimization using Global Optimization (GO) techniques. In this context, two different multiobjective optimization problems are formulated and solved. The outcome of this optimization process is a suite of optimal solutions. In this way, the design team is not compelled to accept a single final solution, but will be able to evaluate the trade-off between the different alternatives, selecting the one that represents the best compromise among all the requirements.

scholarly journals Efficient Conical Area Differential Evolution with Biased Decomposition and Dual Populations for Constrained Optimization

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Weiqin Ying ◽  
Bin Wu ◽  
Yu Wu ◽  
Yali Deng ◽  
Hainan Huang ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Differential Evolution ◽  
Constrained Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
Early Stage ◽  
Test Cases ◽  
Constrained Optimization Problems ◽  
Handling Methods ◽  
Cone Decomposition

The constraint-handling methods using multiobjective techniques in evolutionary algorithms have drawn increasing attention from researchers. This paper proposes an efficient conical area differential evolution (CADE) algorithm, which employs biased decomposition and dual populations for constrained optimization by borrowing the idea of cone decomposition for multiobjective optimization. In this approach, a conical subpopulation and a feasible subpopulation are designed to search for the global feasible optimum, along the Pareto front and the feasible segment, respectively, in a cooperative way. In particular, the conical subpopulation aims to efficiently construct and utilize the Pareto front through a biased cone decomposition strategy and conical area indicator. Neighbors in the conical subpopulation are fully exploited to assist each other to find the global feasible optimum. Afterwards, the feasible subpopulation is ranked and updated according to a tolerance-based rule to heighten its diversity in the early stage of evolution. Experimental results on 24 benchmark test cases reveal that CADE is capable of resolving the constrained optimization problems more efficiently as well as producing solutions that are significantly competitive with other popular approaches.

A comparative analysis of evolutionary algorithms in the design of laminated composite structures

2017 ◽  
Vol 24 (1) ◽  
pp. 13-21 ◽  
Author(s):  
Pavel Y. Tabakov ◽  
Sibusiso Moyo
Keyword(s):  
Evolutionary Algorithms ◽  
Design Optimization ◽  
Composite Structures ◽  
Optimization Problems ◽  
Laminated Composite ◽  
Design Sensitivity ◽  
Optimization Techniques ◽  
Full Potential ◽  
Analysis And Design ◽  
Laminated Composite Structures

AbstractThe increased use of composite materials and structures in many engineering applications led to the need for a more accurate analysis and design optimization. While methods of stress-strain analysis developed faster, optimization techniques have been lagging behind. As a result, many designed structures do not fulfill their full potential. The present study demonstrates the major achievements in recent years in an application of evolutionary algorithms to the design optimization of fiber-reinforced laminated composite structures. Such structures are of much interest due to high structural design sensitivity to fiber orientations as well as complex multidimensional discrete optimization problems. Using an anisotropic multilayered cylindrical pressure vessel and an exact elasticity solution as an example, we show how the optimum, or near–optimum, solution can be found in a more efficient way.

A Note on the Extended Rosenbrock Function

2006 ◽  
Vol 14 (1) ◽  
pp. 119-126 ◽  
Author(s):  
Yun-Wei Shang ◽  
Yu-Huang Qiu
Keyword(s):  
Theoretical Analysis ◽  
Evolutionary Algorithms ◽  
Numerical Optimization ◽  
Local Minimum ◽  
Optimization Problems ◽  
Higher Dimensions ◽  
High Dimensional ◽  
Two Dimensional ◽  
Local Minima ◽  
Unimodal Function

The Rosenbrock function is a well-known benchmark for numerical optimization problems, which is frequently used to assess the performance of Evolutionary Algorithms. The classical Rosenbrock function, which is a two-dimensional unimodal function, has been extended to higher dimensions in recent years. Many researchers take the high-dimensional Rosenbrock function as a unimodal function by instinct. In 2001 and 2002, Hansen and Deb found that the Rosenbrock function is not a unimodal function for higher dimensions although no theoretical analysis was provided. This paper shows that the n-dimensional (n = 4 ∼ 30) Rosenbrock function has 2 minima, and analysis is proposed to verify this. The local minima in some cases are presented. In addition, this paper demonstrates that one of the “local minima” for the 20-variable Rosenbrock function found by Deb might not in fact be a local minimum.

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