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Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization
, 1993
"... The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to a ..."
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Cited by 439 (12 self)
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The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to allow direct intervention of an external decision maker (DM). Finally, the MOGA is generalised further: the genetic algorithm is seen as the optimizing element of a multiobjective optimization loop, which also comprises the DM. It is the interaction between the two that leads to the determination of a satisfactory solution to the problem. Illustrative results of how the DM can interact with the genetic algorithm are presented. They also show the ability of the MOGA to uniformly sample regions of the tradeoff surface.
An Overview of Evolutionary Algorithms in Multiobjective Optimization
 Evolutionary Computation
, 1995
"... The application of evolutionary algorithms (EAs) in multiobjective optimization is currently receiving growing interest from researchers with various backgrounds. Most research in this area has understandably concentrated on the selection stage of EAs, due to the need to integrate vectorial performa ..."
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Cited by 360 (10 self)
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The application of evolutionary algorithms (EAs) in multiobjective optimization is currently receiving growing interest from researchers with various backgrounds. Most research in this area has understandably concentrated on the selection stage of EAs, due to the need to integrate vectorial performance measures with the inherently scalar way in which EAs reward individual performance, i.e., number of offspring. In this review, current multiobjective evolutionary approaches are discussed, ranging from the conventional analytical aggregation of the different objectives into a single function to a number of populationbased approaches and the more recent ranking schemes based on the definition of Paretooptimality. The sensitivity of different methods to
A Niched Pareto Genetic Algorithm for Multiobjective Optimization
 In Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence
, 1994
"... Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives have been combined ad hoc to form a scalar objective function, usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The genetic a ..."
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Cited by 278 (5 self)
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Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives have been combined ad hoc to form a scalar objective function, usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The genetic algorithm (GA), however, is readily modified to deal with multiple objectives by incorporating the concept of Pareto domination in its selection operator, and applying a niching pressure to spread its population out along the Pareto optimal tradeoff surface. We introduce the Niched Pareto GA as an algorithm for finding the Pareto optimal set. We demonstrate its ability to find and maintain a diverse "Pareto optimal population" on two artificial problems and an open problem in hydrosystems.
A Comprehensive Survey of EvolutionaryBased Multiobjective Optimization Techniques
 Knowledge and Information Systems
, 1998
"... . This paper presents a critical review of the most important evolutionarybased multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search cap ..."
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Cited by 210 (18 self)
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. This paper presents a critical review of the most important evolutionarybased multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described mentioning its advantages and disadvantages, their degree of applicability and some of their known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed. Keywords: multiobjective optimization, multicriteria optimization, vector optimization, genetic algorithms, evolutionary algorithms, artificial intelligence. 1 Introduction Since the pioneer work of Rosenberg in the late 60s regarding the possibility of using geneticbased search to deal with multiple objectives, this new area of research (now called evolutionary multiobjective optimization) has grown c...
A Genetic Algorithm for the Set Covering Problem
 European Journal of Operational Research
, 1996
"... In this paper we present a genetic algorithmbased heuristic for nonunicost set covering problems. We propose several modifications to the basic genetic procedures including a new fitnessbased crossover operator (fusion), a variable mutation rate and a heuristic feasibility operator tailored speci ..."
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Cited by 128 (4 self)
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In this paper we present a genetic algorithmbased heuristic for nonunicost set covering problems. We propose several modifications to the basic genetic procedures including a new fitnessbased crossover operator (fusion), a variable mutation rate and a heuristic feasibility operator tailored specifically for the set covering problem. The performance of our algorithm was evaluated on a large set of randomly generated problems. Computational results showed that the genetic algorithmbased heuristic is capable of producing highquality solutions. Keywords: genetic algorithms; set covering; optimisation. 1 Introduction The set covering problem (SCP) is the problem of covering the rows of a mrow, n column, zeroone matrix (a ij ) by a subset of the columns at minimal cost. Defining x j = 1 if column j (with cost c j ? 0) is in the solution and x j = 0 otherwise, the SCP is Minimise n X j=1 c j x j (1) Subject to n X j=1 a ij x j 1, i = 1; : : : ; m (2) x j 2 f0; 1g, j = 1; ...
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 120 (11 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...
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.
On the Use of NonStationary Penalty Functions to Solve Nonlinear Constrained Optimization Problems with GA's
 In
, 1994
"... In this paper we discuss the use of nonstationary penalty functions to solve general nonlinear programming problems (NP ) using realvalued GAs. The nonstationary penalty is a function of the generation number; as the number of generations increases so does the penalty. Therefore, as the penalty i ..."
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Cited by 99 (7 self)
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In this paper we discuss the use of nonstationary penalty functions to solve general nonlinear programming problems (NP ) using realvalued GAs. The nonstationary penalty is a function of the generation number; as the number of generations increases so does the penalty. Therefore, as the penalty increases it puts more and more selective pressure on the GA to find a feasible solution. The ideas presented in this paper come from two basic areas: calculusbased nonlinear programming and simulated annealing. The nonstationary penalty methods are tested on four NP test cases and the effectiveness of these methods are reported.. 1 Introduction Constrained function optimization is an extremely important tool used in almost every facet of engineering, operations research, mathematics, and etc. Constrained optimization can be represented as a nonlinear programming problem. The general nonlinear programming problem is defined as follows: (NP ) minimize f(X) subject to (nonlinear and linear)...
Coevolutionary Computation
"... This paper proposes a general framework for the use of coevolution to boost the performance of genetic search. It combines coevolution with yet another biologically inspired technique, called lifetime fitness evaluation (LTFE). Two unrelated problems  neural net learning and constraint satisfactio ..."
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Cited by 82 (3 self)
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This paper proposes a general framework for the use of coevolution to boost the performance of genetic search. It combines coevolution with yet another biologically inspired technique, called lifetime fitness evaluation (LTFE). Two unrelated problems  neural net learning and constraint satisfaction  are used to illustrate the approach. Both problems use predatorprey interactions to boost the search. In contrast with traditional "single population " genetic algorithms (GAs), two populations constantly interact and coevolve. However, the same algorithm can also be used with different types of coevolutionary interactions. As an example, the symbiotic coevolution of solutions and genetic representations is shown to provide an elegant solution to the problem of finding a suitable genetic representation. The approach presented here greatly profits from the partial and continuous nature of LTFE. Noise tolerance is one advantage. Even more important, LTFE is ideally suited to deal with co...
An Overview of Genetic Algorithms: Part 1, Fundamentals
, 1993
"... this article may be reproduced for commercial purposes. 1 Introduction ..."
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Cited by 79 (1 self)
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this article may be reproduced for commercial purposes. 1 Introduction