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152
An Efficient Constraint Handling Method for Genetic Algorithms
 Computer Methods in Applied Mechanics and Engineering
, 1998
"... Many realworld search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods hav ..."
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Cited by 225 (15 self)
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Many realworld search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods have been the most popular approach, because of their simplicity and ease of implementation. However, since the penalty function approach is generic and applicable to any type of constraint (linear or nonlinear), their performance is not always satisfactory. Thus, researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization. However, the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum. In this paper, GA's populationbased approach and ability to make pairwise comparison in tournament selection operator are explo...
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods
 SIAM REVIEW VOL. 45, NO. 3, PP. 385–482
, 2003
"... Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked ..."
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Cited by 222 (15 self)
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Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis. Nonetheless, users remained loyal to these methods, most of which were easy to program, some of which were reliable. In the past fifteen years, these methods have seen a revival due, in part, to the appearance of mathematical analysis, as well as to interest in parallel and distributed computing. This review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited. Our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results. The underlying principles allow generalization to handle bound constraints and linear constraints. We also discuss extensions to problems with nonlinear constraints.
Stochastic Ranking for Constrained Evolutionary Optimization
, 2000
"... Penalty functions are often used in constrained optimization. However, it is very difficult to strike the right balance between objective and penalty functions. This paper introduces a novel approach to balance objective and penalty functions stochastically, i.e., stochastic ranking, and presents a ..."
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Cited by 199 (11 self)
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Penalty functions are often used in constrained optimization. However, it is very difficult to strike the right balance between objective and penalty functions. This paper introduces a novel approach to balance objective and penalty functions stochastically, i.e., stochastic ranking, and presents a new view on penalty function methods in terms of the dominance of penalty and objective functions. Some of the pitfalls of naive penalty methods are discussed in these terms. The new ranking method is tested using a (µ, ) evolution strategy on 13 benchmark problems. Our results show that suitable ranking alone (i.e., selection), without the introduction of complicated and specialized variation operators, is capable of improving the search performance significantly.
Theoretical and Numerical ConstraintHandling Techniques used with Evolutionary Algorithms: A Survey of the State of the Art
, 2002
"... This paper provides a comprehensive survey of the most popular constrainthandling techniques currently used with evolutionary algorithms. We review approaches that go from simple variations of a penalty function, to others, more sophisticated, that are biologically inspired on emulations of the imm ..."
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Cited by 178 (26 self)
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This paper provides a comprehensive survey of the most popular constrainthandling techniques currently used with evolutionary algorithms. We review approaches that go from simple variations of a penalty function, to others, more sophisticated, that are biologically inspired on emulations of the immune system, culture or ant colonies. Besides describing briefly each of these approaches (or groups of techniques), we provide some criticism regarding their highlights and drawbacks. A small comparative study is also conducted, in order to assess the performance of several penaltybased approaches with respect to a dominancebased technique proposed by the author, and with respect to some mathematical programming approaches. Finally, we provide some guidelines regarding how to select the most appropriate constrainthandling technique for a certain application, ad we conclude with some of the the most promising paths of future research in this area.
Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization
 Evolutionary Computation
, 1999
"... During the last ve years, several methods have been proposed for handling nonlinear constraints by evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify them into four categories (preservation of feasibility, penalty functions, searching for feasibility, a ..."
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Cited by 89 (2 self)
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During the last ve years, several methods have been proposed for handling nonlinear constraints by evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify them into four categories (preservation of feasibility, penalty functions, searching for feasibility, and other hybrids).
A Sqp Method For General Nonlinear Programs Using Only Equality Constrained Subproblems
 MATHEMATICAL PROGRAMMING
, 1993
"... In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [34] it is much simpler to implement and allows any kind of changes of the working s ..."
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Cited by 69 (2 self)
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In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [34] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SQPmethods, as demonstrated by extensive numerical tests.
Particle Swarm Optimization Method for Constrained Optimization Problems
 In Proceedings of the EuroInternational Symposium on Computational Intelligence 2002
, 2002
"... The performance of the Particle Swarm Optimization method in coping with Constrained Optimization problems is investigated in this contribution. In the adopted approach a nonstationary multistage assignment penalty function is incorporated, and several experiments are performed on wellknow ..."
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Cited by 61 (7 self)
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The performance of the Particle Swarm Optimization method in coping with Constrained Optimization problems is investigated in this contribution. In the adopted approach a nonstationary multistage assignment penalty function is incorporated, and several experiments are performed on wellknown and widely used benchmark problems. The obtained results are reported and compared with those obtained through differentevolutionary algorithms, suchasEvolution Strategies and Genetic Algorithms. Conclusions are derived and directions of future research are exposed.
Radioptimization  Goal Based Rendering
 In Computer Graphics Proceedings, Annual Conference Series
, 1993
"... This paper presents a method for designing the illumination in an environment using optimization techniques applied to a radiosity based image synthesis system. An optimization of lighting parameters is performed based on user specified constraints and objectives for the illumination of the envir ..."
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Cited by 56 (0 self)
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This paper presents a method for designing the illumination in an environment using optimization techniques applied to a radiosity based image synthesis system. An optimization of lighting parameters is performed based on user specified constraints and objectives for the illumination of the environment. The system solves for the "best" possible settings for: light source emissivities, element reflectivities, and spot light directionality parameters so that the design goals, suchastominimize energy or to give the the room an impression of privacy, are met. The system absorbs much of the burden for searching the design space allowing the user to focus on the goals of the illumination design rather than the intricate details of a complete lighting specification. A software implementation is described and some results of using the system are reported.
Treating Constraints As Objectives For SingleObjective Evolutionary Optimization
 Engineering Optimization
, 1999
"... This paper presents a new approach to handle constraints using evolutionary algorithms. The new technique treats constraints as objectives, and uses a multiobjective optimization approach to solve the restated singleobjective optimization problem. The new approach is compared against other numeric ..."
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Cited by 55 (16 self)
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This paper presents a new approach to handle constraints using evolutionary algorithms. The new technique treats constraints as objectives, and uses a multiobjective optimization approach to solve the restated singleobjective optimization problem. The new approach is compared against other numerical and evolutionary optimization techniques in several engineering optimization problems with different kinds of constraints. The results obtained show that the new approach can consistently outperform the other techniques using relatively small subpopulations, and without a significant sacrifice in terms of performance.
Use of a SelfAdaptive Penalty Approach for Engineering Optimization Problems
 Computers in Industry
, 1999
"... This paper introduces the notion of using coevolution to adapt the penalty factors of a fitness function incorporated in a genetic algorithm for numerical optimization. The proposed approach produces solutions even better than those previously reported in the literature for other (GAbased and math ..."
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Cited by 44 (4 self)
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This paper introduces the notion of using coevolution to adapt the penalty factors of a fitness function incorporated in a genetic algorithm for numerical optimization. The proposed approach produces solutions even better than those previously reported in the literature for other (GAbased and mathematical programming) techniques that have been particularly finetuned using a normally lengthy trial and error process to solve a certain problem or set of problems. The present technique is also easy to implement and suitable for parallelization, which is a necessary further step to improve its current performance. Key words: genetic algorithms, constraint handling, coevolution, penalty functions, selfadaptation, evolutionary optimization, numerical optimization. 1 Introduction The importance of genetic algorithms (GAs) as a powerful tool for engineering optimization has been widely shown in the last few years through a vast amount of applications ([1,2]). However, even when GAs hav...