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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02 Jun 2014
TL;DR: Results show a near-optimum performance of the genetic algorithm aided power control scheme based on the multi-objective fitness function.
Abstract: We address the power control problem in cognitive radio networks where secondary users exploit spatial spectrum opportunities without causing unacceptable interference to primary users. An optimization problem is formulated aiming at maximizing the utility of secondary users and to ensure the QoS for both primary and secondary users. To solve the power allocation problem a genetic algorithm is developed, and two fitness functions are proposed. The first is oriented towards minimizing the total transmit power consumption of the secondary network. The second is a multi-objective function and is oriented to the joint optimization of total capacity and transmit power consumption of the secondary network. Results show a near-optimum performance of the genetic algorithm aided power control scheme based on the multi-objective fitness function.
20 citations
Cites methods from "Penalty Function Methods for Constr..."
...The most common method to handle constraints in GAs is to use penalty functions [13]....
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TL;DR: The results gained from the presented probabilistic model and the available models in the literature show the fact that the developed approach can be a robust tool for engineering design and analysis of liquefaction as a natural disaster.
20 citations
Cites background from "Penalty Function Methods for Constr..."
...Hence, the corresponding objective function can be defined as follows (Yeniay, 2005):...
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...Hence, the corresponding objective function can be defined as follows (Yeniay, 2005): ẑ = z. (1 + αv) (16) v = max ( CRR CSR7....
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TL;DR: In this paper, an extension of previous simulation researches is presented to calculate the amount of SOx emissions from two marine diesel engines along their load diagrams based on the percentage of sulfur in the marine fuel used.
Abstract: Optimization procedures are required to minimize the amount of fuel consumption and exhaust emissions from marine engines. This study discusses the procedures to optimize the performance of any marine engine implemented in a 0D/1D numerical model in order to achieve lower values of exhaust emissions. From that point, an extension of previous simulation researches is presented to calculate the amount of SOx emissions from two marine diesel engines along their load diagrams based on the percentage of sulfur in the marine fuel used. The variations of SOx emissions are computed in g/kW·h and in parts per million (ppm) as functions of the optimized parameters: brake specific fuel consumption and the amount of air-fuel ratio respectively. Then, a surrogate model-based response surface methodology is used to generate polynomial equations to estimate the amount of SOx emissions as functions of engine speed and load. These developed non-dimensional equations can be further used directly to assess the value of SOx emissions for different percentages of sulfur of the selected or similar engines to be used in different marine applications.
20 citations
01 Oct 2016
TL;DR: The proposed model attempts to find balance between coverage and redundancy in a summary by solving the optimization problem a human learning optimization algorithm is utilized.
Abstract: In paper text summarization represented as a sentence scoring and selection process. The process is modeled as a multi-objective optimization problem. The proposed model attempts to find balance between coverage and redundancy in a summary. For solving the optimization problem a human learning optimization algorithm is utilized.
19 citations
Cites methods from "Penalty Function Methods for Constr..."
...This method applies an algorithm for unconstrained optimizations to the penalty function formulations of the constrained problems [15]....
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TL;DR: In this article, the back analysis of the geotechnical parameters is changed into an unconstrained optimisation problem, whereby the Nelder-Mead method can then be employed.
Abstract: The back analysis method has been widely used as an indirect method of determining geotechnical parameters based on field measurements. The number of parameters and their initial values greatly influence the reliability and efficiency of back analysis. Therefore, sensitivity analysis is often employed to select high sensitivity parameters that have more greater impact on measured back analysis values. The orthogonal design method was first utilized to select geotechnical parameters for back analysis. The optimized parameter values obtained from an orthogonal design table can be used as the initial back analysis values, so as to avoid optimisation algorithm searching in local parameter spaces. By introducing a penalty function to the objective function, back analysis of the geotechnical parameters is changed into an unconstrained optimisation problem, whereby the Nelder–Mead method can then be employed. To verify the feasibility of the proposed back analysis method, a case study was conducted to determine the rock mass parameters for the Houziyan underground powerhouse complex.
19 citations
Cites methods from "Penalty Function Methods for Constr..."
...In this study, the method based on a penalty function is employed; it can transform a constrained problem to an unconstrained one in two ways (Yeniay 2005)....
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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
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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