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: In this paper, the optimization of fuel rod design parameters such as plenum length, gap thickness, cladding thickness, and fuel rod internal pressure using the genetic algorithm was studied.
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20 Oct 2013
TL;DR: Empirical studies using the real data of China airspace demonstrate that MOEA/D outperforms or performs similarly to three well-acknowledged Multi-Objective Evolutionary Algorithms MOEAs on ATFNRP.
Abstract: Air Traffic Flow Network Rerouting Problem ATFNRP, which aims to alleviate the flight delays caused by the increasing traffic and extreme weather, has become more and more serious in air traffic flow management. This paper proposes a multi-objective general rerouting model considering both total delay cost and airlines fairness and adopts Multi-Objective Evolutionary Algorithm based on Decomposition MOEA/D for ATNFRP. Empirical studies using the real data of China airspace demonstrate that MOEA/D outperforms or performs similarly to three well-acknowledged Multi-Objective Evolutionary Algorithms MOEAs on ATFNRP.
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TL;DR: A Poisson regression approach for analyzing customer preferences and a genetic algorithm for determining preference-based default products are presented and the basis for this is transaction data.
Abstract: Today, more and more companies are providing web-based product configuration systems in order to better meet individual customer preferences. In many cases, pre-defined product specifications are additionally offered to facilitate the corresponding choice decisions. Against this background, we present a Poisson regression approach for analyzing customer preferences and a genetic algorithm for determining preference-based default products. The basis for this is transaction data, as they are automatically generated when configuring a product online. The potentials of the suggested methodology are demonstrated by means of two case studies referring to different product categories.
4 citations
Cites background from "Penalty Function Methods for Constr..."
...A common approach to deal with constraints within the GA framework is to use penalty functions that penalize infeasible solutions by reducing the value of the objective function (Equation 9) in proportion to the degree of constraint violation [42]....
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TL;DR: In this article , link-level slice enforcement is formulated as a resource allocation problem that minimizes radio resource consumption while ensuring link-layer soft slice isolation, guaranteeing users diverse QoS requirements, and conforming to slicing policies.
Abstract: Considering network slicing in a cellular network, one of the most intriguing tasks is slice enforcement over air interfaces across multiple cells. The challenges lie in several aspects. First, resources allocated to different slices must achieve soft isolation at the link level. Second, users’ diverse QoS requirements must be satisfied even when communication links experience fading and interference. Third, long-term slicing policies must be conformed, no matter how unbalanced they are. To address these challenges, link-level slice enforcement is first formulated as a resource allocation problem that minimizes radio resource consumption while ensuring link-level soft slice isolation, guaranteeing users’ diverse QoS requirements, and conforming to slicing policies. Next, this problem is tackled via a deep reinforcement learning (DRL) based approach, through which LinkSlice is designed as an iterative two-stage algorithm. The first stage determines transmission rates for each link based on DRL. It is embedded with a graph neural network (GNN) to characterize link interference. Based on the transmission rates from the first stage, the second stage allocates resources to each slice. Performance results show that LinkSlice converges quickly to a near-optimal solution. It gracefully tackles the three challenges of link-level slice enforcement while further improving throughput by 18.5%.
4 citations
09 Jul 2022
TL;DR: Evolutionary Algorithms have been found successful in the solution of a wide variety of optimization problems, however, EAs are unconstrained search techniques.
Abstract: Evolutionary Algorithms (EAs) have been found successful in the solution of a wide variety of optimization problems. However, EAs are unconstrained search techniques. Thus, incorporating constraints into the fitness function of an EA is an open research area.
4 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
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