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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Dissertation•
01 Jul 2012
TL;DR: It can be shown, that the here developed approach is not only fully competitive with established MINLP algorithms, but is even able to outperform those regarding global optimization capabilities and cpu runtime performance.
Abstract: In this thesis a new algorithm for mixed integer nonlinear programming (MINLP) is developed and applied to several real world applications with special focus on space applications. The algorithm is based on two main components, which are an extension of the Ant Colony Optimization metaheuristic and the Oracle Penalty Method for constraint handling. A sophisticated implementation (named MIDACO) of the algorithm is used to numerically demonstrate the usefulness and performance capabilities of the here developed novel approach on MINLP. An extensive amount of numerical results on both, comprehensive sets of benchmark problems (with up to 100 test instances) and several real world applications, are presented and compared to results obtained by concurrent methods. It can be shown, that the here developed approach is not only fully competitive with established MINLP algorithms, but is even able to outperform those regarding global optimization capabilities and cpu runtime performance. Furthermore, the algorithm is able to solve challenging space applications, that are considered here as mixed integer problems for the very first time.
30 citations
Cites background from "Penalty Function Methods for Constr..."
...The burden of a good parameter selection for advanced penalty functions in metaheuristics is a well known problem (see [10] or [53])....
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20 May 2019
TL;DR: The simulation results validate that the proposed fog based computation offloading with the heuristic algorithm can complete the computing task effectively with the minimal energy consumption under the requirements of latency and reliability.
Abstract: Due to the limited computing resources of swarm of drones, it is difficult to handle computation-intensive tasks locally, hence the cloud based computation offloading is widely adopted. However, for the business which requires low latency and high reliability, the cloud-based solution is not suitable, because of the slow response time caused by long distance data transmission. Therefore, to solve the problem mentioned above, in this paper, we introduce fog computing into swarm of drones (FCSD). Focusing on the latency and reliability sensitive business scenarios, the latency and reliability is constructed as the constraints of the optimization problem. And in order to enhance the practicality of the FCSD system, we formulate the energy consumption of FCSD as the optimization target function, to decrease the energy consumption as far as possible, under the premise of satisfying the latency and reliability requirements of the task. Furthermore, a heuristic algorithm based on genetic algorithm is designed to perform optimal task allocation in FCSD system. The simulation results validate that the proposed fog based computation offloading with the heuristic algorithm can complete the computing task effectively with the minimal energy consumption under the requirements of latency and reliability.
30 citations
Cites methods from "Penalty Function Methods for Constr..."
...Therefore, we adopt exterior penalty function method [20] to transform the constrained problem into an unconstrained optimization problem....
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01 Mar 2021
TL;DR: The simulated results in MATLAB revealed that the proposed protocol performs better than the contemporary system in the context of the system sum-throughput, reservation ratio, and the average health packet delay with performance gains of about 9.2%, 9.5%, and 9.6% respectively.
Abstract: This study proposes a hybrid MAC protocol that can efficiently and effectively optimize the communication channel access of a WBAN multi-class system. The proposed protocol consists of two major processes that include the contention phase (CP) and the transmission phase (TP). In the CP, only the biomedical devices that have health packets to transmit randomly contend with equal probabilities using a slotted ALOHA scheme for transmission opportunities and the successful biomedical devices are allocated a transmission time-slot by employing a reservation-based time division multiple access (TDMA) scheme in the transmission phase. A multi-objective optimization problem was formulated to maximize the system sum-throughput, packet success-access-ratio, as well as the reservation ratio, and solved by the controller (i.e., access point) to determine the optimal length of the CP and the number of biomedical devices that can transmit in the TP. Monte Carlo simulation was performed and the optimization solution improved the proposed protocol’s performances. For validation purposes, the simulated results in MATLAB revealed that the proposed protocol performs better than the contemporary system in the context of the system sum-throughput, reservation ratio, and the average health packet delay with performance gains of about 9.2%, 9.5%, and 9.6% respectively.
30 citations
Cites methods from "Penalty Function Methods for Constr..."
...over methods like the GA, which is not really efficient for handling optimization problems with constraints [33]....
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TL;DR: Optimization parameters and their effectiveness for artificial lighting design problems and the nature of their rugged fitness and constraint landscapes are explored.
30 citations
Cites methods from "Penalty Function Methods for Constr..."
...Among these methods, the penalty function method [36] is used widely....
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TL;DR: The experiments show that the proposed solution method competes well against commercial software and that can be competitive with specialized procedures in some problem classes.
Abstract: The goal of this work is the development of a black-box solver based on the scatter search methodology. In particular, we seek a solver capable of obtaining high quality outcomes to optimization problems for which solutions are represented as a vector of integer values. We refer to these problems as integer optimization problems. We assume that the decision variables are bounded and that there may be constraints that require that the black-box evaluator is called in order to know whether they are satisfied. Problems of this type are common in operational research areas of applications such as telecommunications, project management, engineering design and the like.Our experimental testing includes 171 instances within four classes of problems taken from the literature. The experiments compare the performance of the proposed method with both the best context-specific procedures designed for each class of problem as well as context-independent commercial software. The experiments show that the proposed solution method competes well against commercial software and that can be competitive with specialized procedures in some problem classes.
29 citations
Additional excerpts
... In order to establish search directions, the solver builds a penalized function of the form , where is the penalty term....
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... (Yeniay, 2005) describes the merits of a fairly extensive family of penalty functions of the following form: max 0, Clearly, if is feasible then ....
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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