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: The proposed adaptive pattern nulling approach of half-wave dipole uniform linear arrays (DULA), inspired by binary bat algorithm (BBA)-based beamformers and the phase-only control of array excitation weights, demonstrates greater efficiency and higher speed than those using binary particle swarm optimization (BPSO).
Abstract: In this study, an adaptive pattern nulling approach of half-wave dipole uniform linear arrays (DULA), inspired by binary bat algorithm (BBA)-based beamformers and the phase-only control of array ex...
6 citations
6 citations
TL;DR: A novel repair heuristic based on the tendency function and a genetic search for the function approximation is introduced to find good feasible solutions for the MMKP instances, for which feasible solutions rarely exist.
Abstract: We propose a memetic algorithm for the multiple-choice multidimensional knapsack problem (MMKP). In this study, we focus on finding good solutions for the MMKP instances, for which feasible solutions rarely exist. To find good feasible solutions, we introduce a novel repair heuristic based on the tendency function and a genetic search for the function approximation. Even when the density of feasible solutions over the entire solution space is very low, the proposed repair heuristic could successfully change infeasible solutions into feasible ones. Based on the proposed repair heuristic and effective local search, we designed a memetic algorithm that performs well on problem instances with a low density of feasible solutions. By performing experiments, we could show the superiority of our method compared with previous genetic algorithms.
6 citations
01 Jan 2008
TL;DR: This thesis makes a genuine endeavor to develop topology generation tools individually for both passive analog circuits involving R, L, and C components and active circuits that involve additional MOS devices and a graph grammar based framework.
Abstract: In today’s world, with ever increasing design complexity and constantly shrinking device sizes, the microelectronics industry faces the need to develop an entire system on a single chip (SoC). This need gives rise to the responsibility of developing mature Computer-Aided-Design (CAD) tools to tackle such complexities. Unlike digital CAD tools, automated synthesis tools for the irreplaceable analog sections are still immature. Circuit-level analog synthesis comprises of two steps—Topology formation and Sizing of the topology. Topology selection and topology generation are two approaches to topology formation. Research in topology selection has almost been discontinued owing to heavy designer dependency. But with the advent of evolutionary techniques like Genetic Algorithm (GA) and Genetic Programming (GP), topology generation gained popularity. Topology generation is the art of generating device level circuit schematics satisfying user specifications. This thesis makes a genuine endeavor to develop topology generation tools individually for both passive analog circuits involving R, L, and C components and active circuits that involve additional MOS devices.
For passive circuits, we present a GA-based synthesis framework, where the component values for the first set of circuits are set through a deterministic computational technique. Further, the crossover technique for breeding off-springs from parent solutions obeys certain constraints to ensure the formation of structurally correct circuits. The work has been further extended with the introduction of novel selection and crossover strategies. The above techniques have been successful in synthesizing various low-pass and high-pass filter designs.
In the pursuit of developing an active circuit topology generator, we have developed a self-learning optimization algorithm involving multiple design variables. To measure the effectiveness of this technique, we applied it first to a relatively easier domain viz. MPLS computer network topology design. The tool produced optimal solutions for most of the test cases considered.
Drawing inspiration from the above work, we have extended the technique to active analog circuit synthesis. Here, we use a building block library that is adaptively formed based on the self-learning approach. It starts with basic elements like PMOS and NMOS and gradually includes bigger and functionally more meaningful blocks as the synthesis run progresses. Our next work on active synthesis incorporates the advantages of both a conventional GA as well as an augmented version of the dynamically formed building block library. Using the above techniques, we have synthesized two opamp and ring oscillator designs.
Finally, to strengthen the analog circuit topology design approach and increase its universal appeal further, we have developed a graph grammar based framework. Appropriate production rules are used to generate circuits through derivation trees. Our approach has certain advantages when compared to other tree-based techniques like GP. The framework also incorporates the concept of dynamic extraction and subsequent use of better building blocks. The work has been extended further to replace the numerical techniques used in quantifying the suitability of a block, with a fuzzy logic based inference system. The developed tool has been successful in synthesizing opamp and vco designs, producing both manual-like designs as well as novel designs.
6 citations
Cites methods from "Penalty Function Methods for Constr..."
...Here, since we are unaware of the feasible proportion of the search space, we use the widely known exterior additive penalty method [Yeni 05]....
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TL;DR: Numerical experiments show that the population based dual sequence PNPA is more effective than its counterparts and with the random seed dual sequence Non-Penalty Annealing, the standard single sequence Penalty Annealing.
Abstract: We propose a Population based dual-sequence Non-Penalty Annealing algorithm (PNPA) for solving the general nonlinear constrained optimization problem. The PNPA maintains a population of solutions that are intermixed by crossover to supply a new starting solution for simulated annealing throughout the search. Every time the search gets stuck at a local optimum, this crossover procedure is triggered and simulated annealing search re-starts from a new subspace. In both the crossover and simulated annealing procedures, the objective function value and the total solution infeasibility degrees are treated as separate performance criteria. Feasible solutions are assessed according to their objective function values and infeasible solutions are assessed with regard to their absolute degree of constraint infeasibility. In other words, in the proposed approach, there exist two sequences of solutions: the feasible sequence and the infeasible sequence. We compare the population based dual sequence PNPA with the standard single sequence Penalty Annealing (the PA), and with the random seed dual sequence Non-Penalty Annealing (NPA). Numerical experiments show that PNPA is more effective than its counterparts.
6 citations
Cites background from "Penalty Function Methods for Constr..."
...A review of different penalty methods in GAs and a discussion on their advantages and disadvantages can be found in (Yeniay, 2005)....
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...Further details and discussion of the penalty function formulae mentioned above can be found in (Yeniay, 2005)....
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...The penalty function is defined as, p(x) = f(x)e √ temp −TIF(x) (2.7) Further details and discussion of the penalty function formulae mentioned above can be found in (Yeniay, 2005)....
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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
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
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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