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: A new hybrid cuckoo search and genetic algorithm optimization method using a novel adaptive penalty function was proposed to solve the economic dispatch (ED) problem in smart grid and the efficiency of the developed algorithm is proven theoretically and experimentally.
Abstract: In this work, a new hybrid cuckoo search and genetic algorithm optimization method using a novel adaptive penalty function was proposed to solve the economic dispatch (ED) problem in smart grid. Please check and confirm the edit made in article title. This method was also paralyzed in order to solve the problem within specific time suitable to solve Energy management Problems. Three improvements are achieved through this combination. First, parallelism allows further reduction of the execution time. Second, the hybridization of both cuckoo search and genetic algorithm methods allows better diversification and exploration of search space which increases the solution quality. Third, the new adaptive penalty function was developed to discard infeasible solutions and to choose near-optimal ones within a short time. The efficiency of the developed algorithm is proven theoretically and experimentally. Three scenarios are considered to prove experimentally the out-performance of the developed method: (1) the proposed method is compared with Cuckoo Search and Genetic Algorithm methods using a set of benchmark functions. (2) A comparative study is carried out by applying the method to the ED continuous problem optimization case study. (3) The method is compared with Cuckoo search to solve discrete demand side management problem, considering each consumer as an independent parameter. The performance evaluation was conducted using Matlab data parallelism library.
7 citations
04 May 2012
TL;DR: A partir de esta hipotesis, desarrolla un nuevo algoritmo with una codificacion mixta, adaptada a cada grupo de variables de diseno, donde los diferentes operadores se definen and actuan de forma independiente para grupo as discussed by the authors.
Abstract: La optimizacion de estructuras ha sido una disciplina muy estudiada por numerosos investigadores durante los ultimos cuarenta anos. A pesar de que durante los primeros veinte anos las tecnicas de Programacion Matematica fueron la herramienta fundamental en este campo, estas han ido perdiendo fuelle frente a un nuevo conjunto de tecnicas metaheuristicas basadas en la Computacion Evolutiva. De entre destacan, de manera significativa, los Algoritmos Geneticos. La irrupcion de estas nuevas tecnicas en el campo de la optimizacion de estructuras es debida, en gran medida, a las dificultades de la programacion matematica para realizar la optimizacion simultanea de las variables de diseno debido a la elevada alinealidad de estas y sus restricciones El objetivo fundamental del presente trabajo es ir un poco mas alla en el proceso de la optimizacion simultanea de las variables de diseno, definiendo un algoritmo que no parte de una estructura predefinida y que incorpora los parametros que determinan la geometria. A diferencia de los metodos actuales, el algoritmo desarrollado no requiere de ningun tipo de estructura inicial ni otro tipo de informacion adicional, aparte de la definicion de los puntos de aplicacion de las cargas, los puntos de apoyo y el tipo de apoyo. El nuevo algoritmo desarrollado se justifica segun la siguiente hipotesis: La definicion previa de la forma, geometria, regla o modelo preconcebido en una estructura suponen restricciones del diseno en si mismas y por lo tanto aquel algoritmo que no se encuentre sujeto a estas debera poder generar disenos necesariamente mejores, o al menos tan buenos como los existentes. A partir de esta hipotesis se desarrolla un nuevo algoritmo con una codificacion mixta, adaptada a cada grupo de variables de diseno, donde los diferentes operadores se definen y actuan de forma independiente para grupo.
7 citations
Cites background from "Penalty Function Methods for Constr..."
...Otros investigadores [34, 56, 140, 183, 283, 319, 386, 423] han empleado funciones de penalización basadas en la distancia al espacio de soluciones factibles, pero en todos los casos hacen falta parámetros de penalización que impiden su generalización al ser dependientes del problema....
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TL;DR: A mixed-integer mathematical model is developed to optimize the logistics costs of MSCs, concerning retailer/job-order allocation, production scheduling, and MF routing, and a neighborhood search and an evolutionary algorithm are developed to solve the problem in large-scale data sets.
7 citations
TL;DR: The present study is aimed to calculate and obtain the optimal values of the cycle length and backorders quantity for every product in order to achieve the minimum total cost of system considering machine capacity, service level, warehouse space, and budget constraints.
Abstract: The present work investigates a manufacturing-inventory system with a single machine and multiple products, featuring returns on sales and backorders. In the proposed model, some imperfect items, including scrapped and defective items, are produced by the manufacturer. Such items can be classified, based on the severity of the failure, into several categories; as a result, the rework process is carried out at different rates. Moreover, the implementation of the quality control policy requires monitoring and checking the items during the production and reworking processes via an inspection process. The present study is aimed to calculate and obtain the optimal values of the cycle length and backorders quantity for every product in order to achieve the minimum total cost of system considering machine capacity, service level, warehouse space, and budget constraints. To solve the presented model, given as a Nonlinear Programming (NLP) problem, the GAMS software as well as four commonly used algorithms, which are categorized among the meta-heuristic algorithms, is used. These algorithms include the GA (Genetic Algorithm), IWO (Invasive Weed Optimization), GWO (Grey Wolf Optimizer) and HHO (Harris Hawks Optimization) algorithms. Along with these algorithms, the Response Surface Methodology (RSM) is applied to calibrate the parameters of the proposed algorithms. Finally, several numeric problems are solved, the results of which are then compared with each other. Moreover, an analytical hierarchy process (AHP) technique for order performance by similarity to ideal solution (TOPSIS), which is a hybrid method of decision making with multiple attributes, is used for ranking the algorithms.
7 citations
01 Nov 2014
TL;DR: In this paper, a mono objective approach based on harmony search algorithm is proposed, which later is able to get a near optimal composition, by leveraging various movements such as local search, memory based movements, random walk etc.
Abstract: Retrieving most suitable web services from large collection of instances is very crucial for decision makers, In this context QoS properties may play a central role in selecting web service compositions that serve complex requests. A number of approaches have been proposed to resolve Web service selection problem, we distinguish several classes such as the mono objective selection, the multi-objective selection and the hybrid selection. In this paper, we propose a mono objective approach based on harmony search algorithm, this later is able to get a near optimal composition, by leveraging various movements such as local search, memory based movements, random walk etc. Experimental results are very encouraging, and show that the proposed algorithm is more effective than the genetic and bees algorithms.
7 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.
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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