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: This paper reflects on Survival selection schemes specifically like Truncate Selection, Proportionate selection, Tournament Selection and Ranking Based Selection, and calculates the best fittest value among the populations which is generated.
Abstract: Algorithms are based on some influential principles like Survival of the Fittest and with some natural phenomena in Genetic Inheritance. The key for searching the solution in improved function optimization problems are based only on Selection and Mutation operators. This paper reflects on Survival selection schemes specifically like Truncate Selection, Proportionate Selection, Tournament Selection and Ranking Based Selection. In this paper we calculate the best fittest value among the populations which is generated.
1 citations
TL;DR: The shuffled frog‐leaping algorithm (SFLA) is superior to the differential evolution, artificial bee colony, and particle swarm optimization algorithms in terms of convergence speed and optimization accuracy, and the objective function is the least sensitive to the opening width of the parabola.
1 citations
13 Jun 2016
TL;DR: In this article, a genetic algorithm and an evolutionary structural optimization (ESO) heuristic were applied to the structural design of a 3D printed wing of a small UAV and benchmarked against manually designed internal structures.
Abstract: Aircraft wings have seen very few changes in the topological arrangement of the internal structures during the past decades. However, the traditional topology consisting of longitudinal spars and transverse ribs has not been conclusively shown to be the optimal. The purpose of this study is to develop a tool to explore the space of alternative internal structure topologies. We consider a pair of two-step optimization methods. First, a large set of potential structural members, i.e. a ground structure, is built inside the outer mold line of the wing. Second, an evolutionary optimization method is applied to search for the optimal subset of structural members. Two methods are used: a genetic algorithm (GA) and an evolutionary structural optimization (ESO) heuristic. The objective in both cases is to minimize the structural mass of the wing subject to stress and buckling constraints, which are evaluated by automated finite element analysis. The methods are applied to the structural design of the 3D printed wing of a small unmanned aerial vehicle (sUAV) and benchmarked against manually designed internal structures.
1 citations
24 Dec 2012
TL;DR: A specially-designed algorithm based on multi-objective comprehensive learning particle swarm optimizer (MOCLPSO) under the cooperative co-evolution framework is presented to handle this large scale, multi-Objective real-world optimization problem.
Abstract: With the increasing incidence of malfunctions of air transportation system due to severe weather, the Air Traffic Flow Network Rerouting (ATFNR) is playing an important role in improving the global efficiency of air traffic. This paper adopts a multi-objective optimization model to solve the ATFNR problem to make a tradeoff between the total delay costs and the airlines fairness. Meanwhile, a specially-designed algorithm based on multi-objective comprehensive learning particle swarm optimizer (MOCLPSO) under the cooperative co-evolution framework is presented to handle this large scale, multi-objective real-world optimization problem. The empirical studies show that the presented methodology is effective and outperforms an existing approach to ATFNR problem as well as two well-known Multi-Objective Optimization Algorithms.
1 citations
01 Jul 2018
TL;DR: The hybrid method combines the qualities of both the matching algorithm and the GA showing promising results is proposed, to find the best set of cloud computing providers that satisfies a customer's request, with the least amount of providers and the lowest price.
Abstract: The success of cloud computing technology has leveraged the emergence of a large number of new companies providing cloud computing services. Choosing which cloud providers are the most suitable to attend consumers desired quality of service has become a hard problem. In order to qualify such providers, performance indicators (PIs) are useful tools for systematic and synthesized information collection. Thus, the problem approached in this work is to find the best set of cloud computing providers that satisfies a customer's request, with the least amount of providers and the lowest price. Hence, this work proposes a hybrid Genetic Algorithm (GA) to address this problem. In experiments, three approaches, using PIs as input, are employed: a simple matching algorithm, a GA and the proposed hybrid matching-GA approach. The hybrid method combines the qualities of both the matching algorithm and the GA showing promising results.
1 citations
Cites background from "Penalty Function Methods for Constr..."
...Penalties significantly decrease the fitness value of the individual if it presents an inadequate solution to the problem [21]....
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...Penalties are a way for GAs to handle constrained optimization problems [21]....
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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
Book•
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