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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 100 (21 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.
A Parallel Genetic Algorithm for the Set Partitioning Problem
, 1994
"... In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problema difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed stea ..."
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Cited by 66 (1 self)
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In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problema difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed steadystate genetic algorithm in conjunction with a specialized local search heuristic for solving the set partitioning problem. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steadystate genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty realworld set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, highquality integer feasible solutions were found for problems with 36,699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints.
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 61 (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).
Reliability Optimization of SeriesParallel Systems Using a Genetic Algorithm
 IEEE Transactions on Reliability
, 1996
"... This paper describes the use of a genetic algorithm (GA) to determine solutions to the redundancy allocation problem for a seriesparallel system. In this problem formulation, there is a specified number of subsystems and, for each subsystem, there are multiple component choices which can be selecte ..."
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Cited by 56 (17 self)
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This paper describes the use of a genetic algorithm (GA) to determine solutions to the redundancy allocation problem for a seriesparallel system. In this problem formulation, there is a specified number of subsystems and, for each subsystem, there are multiple component choices which can be selected, with replacement, and used in parallel. For those systems designed using offtheshelf component types, with known cost, reliability and weight, system design and component selection becomes a combinatorial 2
Evolutionary Algorithms for Engineering Applications
, 1997
"... This paper focuses on the issue of evaluation of constraints handling methods, as the advantages and disadvantages of various methods are not well understood. The general way of dealing with constraints  whatever the optimization method  is by penalizing infeasible points. However, there are no ..."
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Cited by 52 (3 self)
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This paper focuses on the issue of evaluation of constraints handling methods, as the advantages and disadvantages of various methods are not well understood. The general way of dealing with constraints  whatever the optimization method  is by penalizing infeasible points. However, there are no guidelines on designing penalty functions. Some suggestions for evolutionary algorithms are given in [37], but they do not generalize. Other techniques that can be used to handle constraints in are more or less problem dependent. For instance, the knowledge about linear constraints can be incorporated into specific operators [24], or a repair operator can be designed that projects infeasible points onto feasible ones [30]
An Evolutionary Approach to Combinatorial Optimization Problems
 PROCEEDINGS OF THE 22ND ANNUAL ACM COMPUTER SCIENCE CONFERENCE
, 1994
"... The paper reports on the application of genetic algorithms, probabilistic search algorithms based on the model of organic evolution, to NPcomplete combinatorial optimization problems. In particular, the subset sum, maximum cut, and minimum tardy task problems are considered. Except for the fitness ..."
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Cited by 39 (5 self)
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The paper reports on the application of genetic algorithms, probabilistic search algorithms based on the model of organic evolution, to NPcomplete combinatorial optimization problems. In particular, the subset sum, maximum cut, and minimum tardy task problems are considered. Except for the fitness function, no problemspecific changes of the genetic algorithm are required in order to achieve results of high quality even for the problem instances of size 100 used in the paper. For constrained problems, such as the subset sum and the minimum tardy task, the constraints are taken into account by incorporating a graded penalty term into the fitness function. Even for large instances of these highly multimodal optimization problems, an iterated application of the genetic algorithm is observed to find the global optimum within a number of runs. As the genetic algorithm samples only a tiny fraction of the search space, these results are quite encouraging.
Evolutionary computation at the edge of feasibility
 In Proc. of 4th Parallel Problem Solving from Nature
, 1996
"... Numerical optimization problems enjoy a significant popularity in evolutionary computation community; all major evolutionary techniques use such problems for various tests and experiments. However, many of these techniques (as well as other, classical optimization methods) encounter difficulties in ..."
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Cited by 38 (8 self)
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Numerical optimization problems enjoy a significant popularity in evolutionary computation community; all major evolutionary techniques use such problems for various tests and experiments. However, many of these techniques (as well as other, classical optimization methods) encounter difficulties in solving some realworld problems which include nontrivial constraints. This paper discusses a new development which is based on the observation that very often the global solution lies on the boundary of the feasible region. Thus, for many constrained numerical optimization problems it might be beneficial to limit the search to that boundary, using problemspecific operators. Two test cases illustrate this approach: specific operators are designed from the simple analytical expression of the constraints. Some possible generalizations to larger classes of constraints are discussed as well. 1
Evolutionary computation in structural design
 Journal of Engineering with Computers
, 2001
"... Evolutionary computation is emerging as a new engineering computational paradigm, which may significantly change the present structural design practice. For this reason, an extensive study of evolutionary computation in the context of structural design has been conducted in the Information Technolog ..."
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Cited by 32 (5 self)
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Evolutionary computation is emerging as a new engineering computational paradigm, which may significantly change the present structural design practice. For this reason, an extensive study of evolutionary computation in the context of structural design has been conducted in the Information Technology and Engineering School at George Mason University and its results are reported here. First, a general introduction to evolutionary computation is presented and recent developments in this field are briefly described. Next, the field of evolutionary design is introduced and its relevance to structural design is explained. Further, the issue of creativity/novelty is discussed and possible ways of achieving it during a structural design process are suggested. Current research progress in building engineering systems ’ representations, one of the key issues in evolutionary design, is subsequently discussed. Next, recent developments in constrainthandling methods in evolutionary optimization are reported. Further, the rapidly growing field of evolutionary multiobjective optimization is presented and briefly described. An emerging subfield of coevolutionary design is subsequently introduced and its current advancements reported. Next, a comprehensive review of the applications of evolutionary computation in structural design is provided and chronologically classified. Finally, a summary of the current research status and a discussion on the most promising paths of future research are also presented.
A Survey of Constraint Handling Techniques used with Evolutionary Algorithms
 Laboratorio Nacional de Informática Avanzada
, 1999
"... Despite the extended applicability of evolutionary algorithms to a wide range of domains, the fact that these algorithms are unconstrained optimization techniques leaves open the issue regarding how to incorporate constraints of any kind (linear, nonlinear, equality and inequality) into the fitness ..."
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Cited by 29 (0 self)
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Despite the extended applicability of evolutionary algorithms to a wide range of domains, the fact that these algorithms are unconstrained optimization techniques leaves open the issue regarding how to incorporate constraints of any kind (linear, nonlinear, equality and inequality) into the fitness function as to search efficiently. The main goal of this paper is to provide a detailed and comprehensive survey of the many constraint handling approaches that have been proposed for evolutionary algorithms, analyzing in each case their advantages and disadvantages, and concluding with some of the most promising paths of research.
Adaptive Penalty Methods For Genetic Optimization Of Constrained Combinatorial Problems
 INFORMS Journal on Computing
, 1996
"... The application of genetic algorithms (GA) to constrained optimization problems has been hindered by the inefficiencies of reproduction and mutation when feasibility of generated solutions is impossible to guarantee and feasible solutions are very difficult to find. Although several authors have ..."
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Cited by 26 (12 self)
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The application of genetic algorithms (GA) to constrained optimization problems has been hindered by the inefficiencies of reproduction and mutation when feasibility of generated solutions is impossible to guarantee and feasible solutions are very difficult to find. Although several authors have suggested the use of both static and dynamic penalty functions for genetic search, this paper presents a general adaptive penalty technique which makes use of feedback obtained during the search along with a dynamic distance metric. The effectiveness of this method is illustrated on two diverse combinatorial applications; (1) the unequalarea, shapeconstrained facility layout problem and (2) the seriesparallel redundancy allocation problem to maximize system reliability given cost and weight constraints. The adaptive penalty function is shown to be robust with regard to random number seed, parameter settings, number and degree of constraints, and problem instance. 1. Introduction ...