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: An adaptive penalty function that is easy to implement, free of parameter tuning, and guaranteed to find a solution for every problem at every run was used to impose constraints on the Shuffled Complex Evolution-University of Arizona algorithm to include constraints.
Abstract: Evolutionary algorithms are used to solve optimization problems in a wide range of fields and are considered to be global optimization algorithms. However, evolutionary algorithms are limited in that they cannot be used to solve optimization problems with constraints. Additional methods to implement constraints must be used with these algorithms when solving constrained optimization problems. The purpose of the study is to improve the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm to include constraints. An adaptive penalty function that is easy to implement, free of parameter tuning, and guaranteed to find a solution for every problem at every run was used to impose constraints on the SCE-UA. The modified SCE-UA was validated by application to two constrained optimization problems. The algorithm was also applied to an automatic calibration of the storm water management model (SWMM), which is a hydrological model. An automatic calibration by unconstrained optimization (the ori...
8 citations
Cites background from "Penalty Function Methods for Constr..."
...Constraints are most commonly implemented using penalty functions of various forms (Yeniay 2005)....
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TL;DR: In this paper, the optimal combination between the trajectory and the associated heat shield configuration, namely the locations and thicknesses of the ablative and reusable zones, was identified to maximize the allowable payload mass for a spacecraft.
Abstract: The aim of this paper was to identify, for a specific maneuver, the optimal combination between the trajectory and the associated heat shield configuration, namely the locations and thicknesses of the ablative and reusable zones, that maximize the allowable payload mass for a spacecraft. The analysis is conducted by considering the coupling between the trajectory's dynamics and the heat shield's thermal behavior while using a highly representative model of the heat shield. A global optimization procedure and original software were developed and implemented. The analyzed mission considers an aeroassisted transfer from two low Earth orbits with an assigned orbital plane change maneuver for a given delta wing vehicle equipped with a heat shield consisting of both ablative and reusable materials. The results indicate that the aeroassisted maneuver is more convenient than a "full propulsive" maneuver in the analyzed case, even considering the increased vehicle mass due to the presence of the heat shield.
8 citations
Cites background from "Penalty Function Methods for Constr..."
...4), where ‘j’ indexes the various constraints, is a stepped pyramidal function (Yeniay, 2005)....
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TL;DR: An Artificial Neural Network-Genetic Algorithm (ANN-GA) model was developed to further optimize the operating parameters to result in a product that would have the desired color and texture observed in kheer prepared conventionally as discussed by the authors.
Abstract: If rice is cooked in milk, starch–milk reaction results into a thick product, which is very popular in India known as kheer. Conventionally, kheer is prepared by cooking rice in milk in an open pan over low fire followed by addition of sugar toward the end. The present investigation aims to optimize the process parameters (operating pressure and cooking time) for designing the pressurized cooking section of a continuous kheer-making machine. Sensory trials of kheer prepared conventionally and using pressurized methods were carried out and the data was analyzed using Fuzzy Logic. Sensory results of open-pan samples indicated that there is a small range of Whiteness Index (WI) and Hardness (H) values that is desirable in kheer. An Artificial Neural Network-Genetic Algorithm (ANN-GA) model was developed to further optimize the operating parameters to result in a product that would have the desired color and texture observed in kheer prepared conventionally. The developed ANN-GA model was successful in providing with input conditions leading to desired WI and H values. Finally, from the set of optimal input conditions, operating pressure of 0.27 MPa and cooking time of 7.5 min was chosen for designing the pressurized cooking section of the continuous kheer-making machine.
8 citations
TL;DR: In this paper, a nonlinear programming model for abrasive waterjet machining is proposed, where kernel principal component regression (KPCR) is employed to overcome the weaknesses of second order polynomial regression.
8 citations
TL;DR: The innovative point of the proposed planning algorithm lies in that the satellite structure and control limitation are not considered as optimization constraints but are formulated into the cost function and is able to relieve the burden of the optimizer and increases the optimization efficiency.
Abstract: The planning algorithm to calculate a satellite’s optimal slew trajectory with a given keep-out constraint is proposed. An energy-optimal formulation is proposed for the Space-based multiband astronomical Variable Objects Monitor Mission Analysis and Planning (MAP) system. The innovative point of the proposed planning algorithm lies in that the satellite structure and control limitation are not considered as optimization constraints but are formulated into the cost function. This modification is able to relieve the burden of the optimizer and increases the optimization efficiency, which is the major challenge for designing the MAP system. Mathematical analysis is given to prove that there is a proportional mapping between the formulation and the satellite controller output. Simulations with different scenarios are given to demonstrate the efficiency of the developed algorithm.
8 citations
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