Penalty Function Methods for Constrained Optimization with Genetic Algorithms
01 Apr 2005-Mathematical & Computational Applications (Association for Scientific Research)-Vol. 10, Iss: 1, pp 45-56
TL;DR: These penalty-based methods for handling constraints in Genetic Algorithms are presented and discussed and their strengths and weaknesses are discussed.
Abstract: Genetic Algorithms are most directly suited to unconstrained optimization. Application of Genetic Algorithms to constrained optimization problems is often a challenging effort. Several methods have been proposed for handling constraints. The most common method in Genetic Algorithms to handle constraints is to use penalty functions. In this paper, we present these penalty-based methods and discuss their strengths and weaknesses.
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TL;DR: In this paper, the authors present a methodology for the antenna reflector shape optimization, in which the cost function is the maximum value of the strain in the reflector and, where the radio-frequency (RF) and the actuation requirements are imposed as constraints.
Abstract: The active mechanical reshaping of the antenna reflector is considered a good candidate for in-orbit coverage reconfigurability that is required by the Telecom and Earth Observation missions since it features low cost, low mass and high power capability as compared to the active array antenna technology. However, to guarantee the stability and strength of the reflector under both constant actuation and exposure to the space environment, it is necessary to minimize the stresses and strains that arise when the reflector is reshaped. This article presents a methodology for the antenna reflector shape optimization, in which the cost function is the maximum value of the strain in the reflector and, where the radio-frequency (RF) and the actuation requirements are imposed as constraints. The performance at each iteration of actuator displacements is analyzed by the finite element method to compute the overall shape of the reflector, the strains arising and the actuator forces and by physical optics to compute the RF pattern radiated by the reflector shaping. Simulated annealing, as a global optimization method, has been selected for the optimization algorithm, since it allows escaping from local minima and benefits from the existence of starting points for the global optimization, that have resulted from pure RF optimization. A drastic reduction of strains in the reflector has been achieved, while the RF and actuation requirements have been met. These are key results to the development of actively reshapable reflectors.
7 citations
TL;DR: In this paper, a multistage planning method for active distribution networks (ADNs) considering multiple alternatives is introduced. But the authors do not consider the uncertainties of load, wind and solar generation.
Abstract: This paper introduces a multistage planning method for active distribution networks (ADNs) considering multiple alternatives. The uncertainties of load, wind and solar generation are taken into account and a chance constrained programming (CCP) model is developed to handle these uncertainties in the planning procedure. A method based on a k-means clustering technique is employed for the modelling of renewable generation and load demand. The proposed solution methodology, which is based on a genetic algorithm, considers multiple planning alternatives, such as the reinforcement of substations and distribution lines, the addition of new lines, and the placement of capacitors and it aims at minimizing the net present value of the total operation cost plus the total investment cost of the reinforcement and expansion plan. The active network management is incorporated into planning method in order to exploit the control capabilities of the output power of the distributed generation units. To validate its effectiveness and performance, the proposed method is applied to a 24-bus distribution system.
7 citations
TL;DR: Numerical results clearly prove the accuracy and efficiency of the proposed control process in comparison with other methods and lead to a new generation of the genetic algorithm, which is more reliable.
Abstract: This study focuses on a new active control method by improving specification of a well-known intelligent numerical search method, that is the genetic algorithm. The proposed scheme modifies the spe...
7 citations
Cites background from "Penalty Function Methods for Constr..."
...Indeed, equation (5) presents an additive penalty function (Yeniay, 2005)....
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...Indeed, equation (5) presents an additive penalty function (Yeniay, 2005)....
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23 Oct 2006
TL;DR: The kind of SVMs where C is determined automatically from the application of a GA a “Genetic SVM” or GSVM is called and the relevance of the problem, the algorithm, the experiments and the results obtained are discussed.
Abstract: We describe a methodology to train Support Vector Machines (SVM) where the regularization parameter (C) is determined automatically via an efficient Genetic Algorithm in order to solve multiple category classification problems. We call the kind of SVMs where C is determined automatically from the application of a GA a “Genetic SVM” or GSVM. In order to test the performance of our GSVM, we solved a representative set of problems by applying one-versus-one majority voting and one-versus-all winner-takes-all strategies. In all of these the algorithm displayed very good performance. The relevance of the problem, the algorithm, the experiments and the results obtained are discussed.
7 citations
Dissertation•
01 Jan 2010
TL;DR: This dissertation aims to demonstrate the power of data-driven, evidence-based learning to improve the quality of human experience in the natural world.
Abstract: Certified by. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hugh Herr Associate Professor of Health Sciences and Technology Associate Professor of Media Arts and Sciences Thesis Supervisor Certified by. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emery N. Brown Professor of Health Sciences and Technology Professor of Computational Neuroscience Thesis Supervisor
7 citations
Cites methods from "Penalty Function Methods for Constr..."
...We chose to use the simple and efficient penalty method to enforce our non-linear constraint [32]....
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References
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Book•
01 Sep 1988
TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.
Abstract: From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required
52,797 citations
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01 Jan 1992
TL;DR: GAs and Evolution Programs for Various Discrete Problems, a Hierarchy of Evolution Programs and Heuristics, and Conclusions.
Abstract: 1 GAs: What Are They?.- 2 GAs: How Do They Work?.- 3 GAs: Why Do They Work?.- 4 GAs: Selected Topics.- 5 Binary or Float?.- 6 Fine Local Tuning.- 7 Handling Constraints.- 8 Evolution Strategies and Other Methods.- 9 The Transportation Problem.- 10 The Traveling Salesman Problem.- 11 Evolution Programs for Various Discrete Problems.- 12 Machine Learning.- 13 Evolutionary Programming and Genetic Programming.- 14 A Hierarchy of Evolution Programs.- 15 Evolution Programs and Heuristics.- 16 Conclusions.- Appendix A.- Appendix B.- Appendix C.- Appendix D.- References.
12,212 citations
Book•
03 Mar 1993
TL;DR: The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques.
Abstract: COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED"Nonlinear Programming: Theory and Algorithms"--now in an extensively updated Third Edition--addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The "Third Edition" begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction.Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programmingOptimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditionsAlgorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problemsImportant features of the "Third Edition" include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and moreUpdated discussion and new applications in each chapterDetailed numerical examples and graphical illustrationsEssential coverage of modeling and formulating nonlinear programsSimple numerical problemsAdvanced theoretical exercisesThe book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.
6,259 citations
TL;DR: GA's population-based approach and ability to make pair-wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter to guide the search towards the constrained optimum.
3,495 citations
"Penalty Function Methods for Constr..." refers background in this paper
...These approaches can be grouped in four major categories [28]: Category 1: Methods based on penalty functions - Death Penalty [2] - Static Penalties [15,20] - Dynamic Penalties [16,17] - Annealing Penalties [5,24] - Adaptive Penalties [10,12,35,37] - Segregated GA [21] - Co-evolutionary Penalties [8] Category 2: Methods based on a search of feasible solutions - Repairing unfeasible individuals [27] - Superiority of feasible points [9,32] - Behavioral memory [34]...
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Book•
01 Jan 1996
TL;DR: In this work, the author compares the three most prominent representatives of evolutionary algorithms: genetic algorithms, evolution strategies, and evolutionary programming within a unified framework, thereby clarifying the similarities and differences of these methods.
2,679 citations