scispace - formally typeset
Search or ask a question
Journal ArticleDOI

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.

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI
TL;DR: From the results obtained, it can be inferred that with the use of local available energy sources, the grid connected mode serves as more economical and reliable choice for the electrification of numerous villages when compared with the stand-alone hybrid energy system.
Abstract: This study presents proposed Pseudo-Inspired Gravitational Search Algorithm (PI-GSA) for solving complex Economic Dispatch (ED) problem in the power system and Optimal sizing of the components for a self-contained and grid connected hybrid energy system that meets the load demand of a particular village. This method can be scaled according to the need of the system under investigation. From the results obtained, it can be inferred that with the use of local available energy sources, the grid connected mode serves as more economical and reliable choice for the electrification of numerous villages when compared with the stand-alone hybrid energy system. To check the effectiveness and performance of proposed algorithm simulation results for Complex Economic Dispatch (Cases 1) are compared with other methods reported in literature and Optimal sizing of the components for self-contained and grid integrated renewable energy resources (Case 2) are compared with the results obtained from Hybrid Optimization Model for Electric Renewable (HOMER). A qualitative comparison of the obtained result with other standard population based meta-heuristic techniques manifests proposed technique's superiority.

3 citations

Journal ArticleDOI
TL;DR: In this paper , a new method to determine optimal well layouts of groundwater heat pumps using the adjoint approach, which is an efficient way to solve the underlying PDE-constrained optimization problem, is presented.

3 citations

Journal ArticleDOI
TL;DR: This paper proposes a clustering method referred to as quality-driven search for optimal partition (QDSOC) where the search process of the optimal partition is directly driven by a validity index instead of a proximity measure.
Abstract: Clustering is an important task in data analysis to find a partition on an unlabeled dataset based on similarity relationships among its elements. Typically, such similarity is determined by a proximity measure or distance. Then, the optimal partition is the one that minimizes the distance among elements belonging to the same subset and maximizes the distance among elements from different subsets. The way in which the optimal partition is found is called clustering method. The adequateness of the partition found is commonly determined in terms of a validity index. In this paper, we propose a clustering method referred to as quality-driven search for optimal partition (QDSOC) where the search process of the optimal partition is directly driven by a validity index instead of a proximity measure. Our approach allows to efficiently exploring a large solution space via a breed of genetic algorithm, the so-called eclectic genetic algorithm. Unlike existing clustering methods, the proposed QDSOC offers the optimal partition and provides the mathematical model of such partition in terms of a representation based on membership functions. This model describes the points that belong to the subsets in the partition found. Thus, by using this model, we can predict the membership of new objects without performing the search process again. As part of the experimental evaluation, our proposed QDSOC method is compared with k-means and self-organizing maps (SOMs), which are two well-known clustering approaches. The clustering methods were used to solve a wide sample of clustering problems, and using three different validity indices. From the obtained results, we demonstrate that QDSOC statistically outperforms k-means and SOMs. We also point out that our approach does not incur in excessive computational overhead with respect to such traditional clustering methods.

3 citations


Cites methods from "Penalty Function Methods for Constr..."

  • ...In order to focus the search process on the feasible region, heuristic methods discriminate among feasible and non-feasible solutions via a penalty function [51] applied to Q(5) as follows:...

    [...]

Proceedings ArticleDOI
11 Jul 2021
TL;DR: In this paper, the authors proposed an AI-based decision support system (AI-DSS) that integrates the results of a survey of 250 manufacturing companies in western Poland, the use of the Ensemble Neural Network (ENN) Model and a Genetic Algorithm (GA) to determine the profitability of investing in research laboratories, especially in additive manufacturing technologies.
Abstract: In the case of industrial solutions, in the context of Industry 4.0, Artificial Neural Networks (ANNs) currently dominate almost all tasks related to the optimisation of manufacturing processes. For manufacturing enterprises, a quick and precise response to customers needs is crucial for gaining a competitive advantage, therefore, managers should invest in new technologies, such as Additive Manufacturing (AM) technologies. However, these activities are very costly, so it seems that a good solution would be to encourage enterprises to cooperate with specialized research laboratories offering material research in the field of the AM technologies used. This paper proposes a new framework to determine the types and quantities of devices in the field of AM technologies, with which such a research laboratory should be equipped. The proposed AI-based Decision Support System (AI-DSS) integrates the results of a survey of 250 manufacturing companies in western Poland, the use of the Ensemble Neural Network (ENN) Model and the use of a Genetic Algorithm (GA) to determine the profitability of investing in research laboratories, especially in AM technologies. Firstly, in order to reduce variance and thus improve generalization of the proposed model, the combination of outputs of several networks forming ENN was proposed. For this purpose, the bootstrap technique was used, resulting in a model with 75% accuracy being obtained. Next, using the fitness function in a GA algorithm, the research laboratory optimal configuration was determined. Finally, its practicality is presented by applying AI-DSS in the design of the current and future workload of devices, in order to find the optimal configuration in the research laboratory.

3 citations

01 Jan 2011
TL;DR: The paper presents a Genetic Algorithm approach for solving constrained reliability redundancy optimization of general systems that uses a dynamic adaptive penalty function to consider the infeasible solutions also and guides the search to optimal or near optimal solution.
Abstract: The paper presents a Genetic Algorithm (GA) approach for solving constrained reliability redundancy optimization of general systems. The advanced GA technique uses a dynamic adaptive penalty function to consider the infeasible solutions also and guides the search to optimal or near optimal solution. The penalty technique is applied to keep a certain amount of infeasible solutions in each generation so as to enforce genetic search towards an optimal solution from both the sides of feasible and infeasible regions. The performance of the method is compared with GA tool Box of MATLAB.

3 citations


Cites background from "Penalty Function Methods for Constr..."

  • ...The detailed descriptions of all these have been presented in [2, 17, 27-37]....

    [...]

References
More filters
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

Journal ArticleDOI
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]...

    [...]

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