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.
Citations
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TL;DR: The economic statistical design of an Auto-Regressive Moving Average (ARMA) control chart for autocorrelated data has been investigated and a Modified Fitness-based Self-Adaptive Differential Evolution algorithm, named MF-SADE, has been developed.
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TL;DR: In this article, a multi-objective genetic algorithm for economic statistical design (MOGAESD) is proposed for identifying the Pareto optimal solutions of control chart design, and the preferred solution is selected by the designer.
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Cites methods from "Penalty Function Methods for Constr..."
...Yeniay [23] classified the proposed approaches for optimizing the constraint problem using a GA into four categories, among them the penalty function is the most common....
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01 Jan 2012
TL;DR: This research is proposing a novel bi-objective facility location problem within batch arrival queuing framework under capacity, budget, and nearest-facility constraints and proposed an adaptive version of particle swarm optimization to be tuned the parameters of the algorithm.
Abstract: With regards to the many decisions which are made every day in service and industrial applications, we focus on determination of the number of required facilities along with the relevant allocation process. Goal of this research is proposing a novel bi-objective facility location problem within batch arrival queuing framework under capacity, budget, and nearest-facility constraints. Two objective functions are considered which are minimizing sum of the travel time and waiting and minimizing maximum of ideal time pertinent to each facility, respectively. Second objective causes to obtain the best combination of the facilities which are more equilibrium for the proposed model solutions. Since this type of problem is strictly NPhard, an efficient meta-heuristic algorithm namely particle swarm optimization algorithm with considering a specific representation process has been proposed. Since the output quality of the metaheuristic algorithms is severely depending on its parameters, we proposed an adaptive version of particle swarm optimization to be tuned the parameters of the algorithm. At the end, the results analysis represents the applicability of the proposed methodology.
18 citations
Additional excerpts
...As regards to the general form of constraints as , the penalty value of a chromosome is calculated as follows (Yeniay and Ankare (2005): where , U, and indicate combined objective function value, a large number, constraint, and penalty value of chromosome x, respectively....
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01 Jan 2020
TL;DR: This paper presents a new approach for dispatch generating powers of thermal plants based on ion motion optimization algorithm (IMA), and preliminary results shows that the proposed plan offers higher effect performance.
Abstract: This paper presents a new approach for dispatch generating powers of thermal plants based on ion motion optimization algorithm (IMA) Electrical power systems are determined by optimization in power balancing, transporting loss, and generating capacity The scheduling power generating units for stabilizing different dynamic responses of the control power system are mathematically modeled for the objective function Economic load dispatch (ELD) gains as the objective function is optimized by applying IMA In the experimental section, several cases of different units of thermal plants are used to test the performance of the proposed approach The preliminary results are compared with the other methods in the literature shows that the proposed plan offers higher effect performance
18 citations
TL;DR: A genetic algorithm based on insertion heuristics for the vehicle routing problem with constraints using a random insertion heuristic to construct initial solutions and to reconstruct the existing ones is proposed.
Abstract: In the paper we propose a genetic algorithm based on insertion heuristics for the vehicle routing problem with constraints. A random insertion heuristic is used to construct initial solutions and to reconstruct the existing ones. The location where a randomly chosen node will be inserted is selected by calculating an objective function. The process of random insertion preserves stochas- tic characteristics of the genetic algorithm and preserves feasibility of generated individuals. The defined crossover and mutation operators incorporate random insertion heuristics, analyse individ- uals and select which parts should be reinserted. Additionally, the second population is used in the mutation process. The second population increases the probability that the solution, obtained in the mutation process, will survive in the first population and increase the probability to find the global optimum. The result comparison shows that the solutions, found by the proposed algorithm, are similar to the optimal solutions obtained by other genetic algorithms. However, in most cases the proposed algorithm finds the solution in a shorter time and it makes this algorithm competitive with others.
18 citations
Cites background or methods from "Penalty Function Methods for Constr..."
...The stop criterion can be either the maximum time defined for calculation or maximum number of iterations without improvement of the current best solution found (Reid, 2000; Hong et al., 2002; Jung and Moon, 2002; Yeniay, 2005)....
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...VRPPD instances include the central depot, time window constraints, pick-up and delivery nodes and the maximal travel time for a single vehicle....
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...However, for highly constrained problems the algorithm can suffer a degradation when trying to search for feasible solutions and if the feasible solution is found, the search may prevent to find a better one (Yeniay, 2005)....
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...In the experimental evaluation, parameter values in the genetic algorithm are defined as follows: PS1 = 100, PL1 = 10, IL1 = 50, TL1 = 5 min, MP = 0.1, PS2 = 20, IL2 = 5, PL2 = 2....
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...The handling time window constraint involves additional check for any violations occurring in a partial route after inserting a new node....
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References
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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
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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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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