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 model- and optimization-based heuristic method is employed to compute the control policy that results in the collision-free motion of the vehicles at the intersection and, at the same time, minimizes their delay.
Abstract: This paper considers the motion coordination problem of autonomous vehicles in an intersection of a traffic network. The featured challenge is the design of an intersection traffic manager, in the form of a supervisory control algorithm, that regulates the motion of the autonomous vehicles in the intersection. We cast the multivehicle coordination task as an optimization problem, with a one-dimensional search-space. A model- and optimization-based heuristic method is employed to compute the control policy that results in the collision-free motion of the vehicles at the intersection and, at the same time, minimizes their delay. Our approach depends on a computation framework that makes the need for complex analytical derivations obsolete. A complete account of the computational complexity of the algorithm, parameterized by the configuration parameters of the problem, is provided. Extensive numerical simulations validate the applicability and performance of the proposed autonomous intersection traffic manager.
29 citations
Cites background from "Penalty Function Methods for Constr..."
...(e penalty function can be designed as static or nonstatic [58, 59]....
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TL;DR: A bi-objective RFLP with multiple capacity levels in a three echelon supply chain management while there is a constraint on the coverage levels and the adapted concepts of expected value of perfect information and the value of stochastic solution (VSS) in order to validate 2-SSP.
Abstract: This paper develops a bi-objective reliable facility location problems (RFLP).There is a constraint on DCs based on both their distance and capacity level.There is a provider-side uncertainty for distribution-centers (DCs).Three tuned-parameter metaheuristic algorithms are employed to solve the model.An exact method via GAMS is used to validate solutions as well. The stochastic process is one the most important tools to overcome uncertainties of supply chain problems. Being a lack of studies on constrained reliable facility location problems (RFLP) with multiple capacity levels, this paper develops a bi-objective RFLP with multiple capacity levels in a three echelon supply chain management while there is a constraint on the coverage levels. Moreover, there is a provider-side uncertainty for distribution-centers (DCs). The aim of this paper is to find a near-optimal solution including suitable locations of DCs and plants, the fraction of satisfied customer demands, and the fraction of items sent to DCs to minimize the total cost and to maximize fill rate, simultaneously. As the proposed model belongs to NP-Hard problems, a meta-heuristic algorithm called multi-objective biogeography-based optimization (MOBBO) is employed to find a near-optimal Pareto solution. Since there is no benchmark in the literature to compare provided solutions, a non-dominated ranking genetic algorithm (NRGA) and a multi objective simulated annealing (MOSA) are used to verify the solution obtained by MOBBO while a two-stage stochastic programming (2-SSP) is employed to capture randomness of DCs. This paper uses the adapted concepts of expected value of perfect information (EVPI) and the value of stochastic solution (VSS) in order to validate 2-SSP. Moreover, the parameters of algorithms are tuned by the response surface methodology (RSM) in the design of experiments. Besides, an exact method, called branch-and-bound method via GAMS optimization software, is used to compare lower and upper bounds of Pareto fronts to optimize two single-objective problems separately.
28 citations
TL;DR: The simulation results suggest UDA can choose the proper cluster shape to get the maximum underwater wireless sensor network lifetime approximately, and nodes closer to sinks are possible to bear a heavier data-relaying mission.
Abstract: Underwater sensor networks will find many oceanic applications in near future, and the deployment problem in 3D sensor networks has not been paid enough attention at present. In order to maximize the network lifetime, a deployment algorithm (UDA) for underwater sensor networks in ocean environment is proposed. UDA can determine and select the best cluster shape, then partition the space into layers and clusters while maintaining full coverage and full connectivity. In addition, nodes closer to sinks are possible to bear a heavier data-relaying mission. UDA sets different node deployment densities at different layers in response to the potential relay discrepancy. The simulation results suggest UDA can choose the proper cluster shape to get the maximum underwater wireless sensor network lifetime approximately.
28 citations
TL;DR: The adaptive UDD method can lead to optimum design solutions with significantly lower computational costs compared to both GA and coupled UDD-GA methods and it is shown that frames optimised under a single spectrum-compatible earthquake can efficiently satisfy the predefined performance targets under a set of synthetic earthquakes representing the design spectrum.
28 citations
Cites background from "Penalty Function Methods for Constr..."
...Different penalty functions have been proposed to solve the constraint problems such as Death Penalty, Static Penalties, Dynamic Penalties, Annealing Penalties and Adaptive Penalties [67]....
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...In the first case, GA will converge to a feasible solution very quickly even if it is far from the optimum, while in the latter case, GA would converge to an infeasible answer [67]....
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TL;DR: The presented way of constructing the penalty function is to some extent problem specific, but the applied scheme may be adapted to other global search and optimisation problems, in particular to those requiring identification of multiple deep local minima.
28 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.
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