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265
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
, 2000
"... In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in conver ..."
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Cited by 605 (39 self)
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In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Paretooptimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.
Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms
 Evolutionary Computation
, 1994
"... In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about t ..."
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Cited by 524 (4 self)
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In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Paretooptimal points, instead of a single point. Since genetic algorithms(GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias towards some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Paretooptimal points sim...
Multicriteria Optimization
, 2005
"... n Using some realworld examples I illustrate the important role of multiobjective optimization in decision making and its interface with preference handling. I explain what optimization in the presence of multiple objectives means and discuss some of the most common methods of solving multiobjectiv ..."
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Cited by 312 (4 self)
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n Using some realworld examples I illustrate the important role of multiobjective optimization in decision making and its interface with preference handling. I explain what optimization in the presence of multiple objectives means and discuss some of the most common methods of solving multiobjective optimization problems using transformations to singleobjective optimization problems. Finally, I address linear and combinatorial optimization problems with multiple objectives and summarize techniques for solving them. Throughout the article I
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.
Behavior Coordination Mechanisms  Stateoftheart
, 1999
"... In behaviorbased robotics the control of a robot is shared between a set of purposive perceptionaction units, called behaviors. Based on selective sensory information, each behavior produces immediate reactions to control the robot with respect to a particular objective, i.e., a narrow aspect of t ..."
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Cited by 69 (6 self)
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In behaviorbased robotics the control of a robot is shared between a set of purposive perceptionaction units, called behaviors. Based on selective sensory information, each behavior produces immediate reactions to control the robot with respect to a particular objective, i.e., a narrow aspect of the robot's overall task such as obstacle avoidance or wall following. Behaviors with di erent and possibly incommensurable objectives may produce con icting actions that are seemingly irreconcilable. Thus a major issue in the design of behaviorbased control systems is the formulation of e ective mechanisms for coordination of the behaviors' activities into strategies for rational and coherent behavior. This is known as the action selection problem (also refereed to as the behavior coordination problem) and is the primary focus of this overview paper. Numerous action selection mechanisms have been proposed over the last decade and the main objective of this document istogive a qualitative overview of these approaches. 2 1
Multiple Objective Action Selection & Behavior Fusion using Voting
 Department of Medical
, 1998
"... In the behaviorbased approach the control of a robot is shared between multiple behaviors with different and possibly incommensurable objectives. In most cases when deciding what next action to take, multiple conflicting objectives should be considered simultaneously. Thus one faces the problem of ..."
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Cited by 60 (8 self)
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In the behaviorbased approach the control of a robot is shared between multiple behaviors with different and possibly incommensurable objectives. In most cases when deciding what next action to take, multiple conflicting objectives should be considered simultaneously. Thus one faces the problem of deciding what next action to select. This is known as the action selection problem and is the primary focus of this dissertation. In particular, two aspects of the action selection problem, that are subject to investigation consist of 1) the formulation of effective mechanisms for coordination of the behaviors' activities into strategies for rational and coherent behavior and 2) the construction of faulttolerant behaviors from a multitude of less reliable ones. Regarding the first issue, it is demonstrated that multiple objective decision theory provides a suitable formalism to encompass ideas from behaviorbased system synthesis and control, where each behavior is cast as an objective fun...
Evolutionary Algorithms for MultiCriterion Optimization in Engineering Design
, 1999
"... this paper, we briefly outline the principles of multiobjective optimization. Thereafter, we discuss why classical search and optimization methods are not adequate for multicriterion optimization by discussing the working of two popular methods. We then outline several evolutionary methods for han ..."
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Cited by 53 (0 self)
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this paper, we briefly outline the principles of multiobjective optimization. Thereafter, we discuss why classical search and optimization methods are not adequate for multicriterion optimization by discussing the working of two popular methods. We then outline several evolutionary methods for handling multicriterion optimization problems. Of them, we discuss one implementation (nondominated sorting GA or NSGA [38]) in somewhat greater details. Thereafter, we demonstrate the working of the evolutionary methods by applying NSGA to three test problems having constraints and discontinuous Paretooptimal region. We also show the efficacy of evolutionary algorithms in engineering design problems by solving a welded beam design problem. The results show that evolutionary methods can find widely different yet nearParetooptimal solutions in such problems. Based on the above studies, this paper also suggests a number of immediate future studies which would make this emerging field more mature and applicable in practice. 1.2 PRINCIPLES OF MULTICRITERION OPTIMIZATION
Running Time Analysis of a MultiObjective Evolutionary Algorithm on a Simple Discrete Optimization Problem
, 2002
"... For the first time, a running time analysis of a multiobjective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudoBoolean problem (Lotz: leading ones  trailing zeroes) is defined and a populationbased optimization algorithm (FEMO). We show, that the ..."
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Cited by 52 (8 self)
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For the first time, a running time analysis of a multiobjective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudoBoolean problem (Lotz: leading ones  trailing zeroes) is defined and a populationbased optimization algorithm (FEMO). We show, that the algorithm performs a black box optimization in #(n 2 log n) function evaluations where n is the number of binary decision variables. 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 49 (6 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.
IEMO: An interactive evolutionary multiobjective optimization tool
 In Pattern Recognition and Machine Intelligence: First International Conference (PReMI2005
, 2005
"... Abstract. With the advent of efficient techniques for multiobjective evolutionary optimization (EMO), realworld search and optimization problems are being increasingly solved for mulitple conflicting objectives. During the past decade of research and application, most emphasis has been spent on fi ..."
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Cited by 43 (10 self)
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Abstract. With the advent of efficient techniques for multiobjective evolutionary optimization (EMO), realworld search and optimization problems are being increasingly solved for mulitple conflicting objectives. During the past decade of research and application, most emphasis has been spent on finding the complete Paretooptimal set, although EMO researchers were always aware of the importance of procedures which would help choose one particular solution from the Paretooptimal set for implementation. This is also one of the main issues on which the classical and EMO philosophies are divided on. In this paper, we address this longstanding issue and suggest an interactive EMO procedure which, for the first time, will involve a decisionmaker in the evolutionary optimization process and help choose a single solution at the end. This study is the culmination of many year’s of research on EMO and would hopefully encourage both practitioners and researchers to pay more attention in viewing the multiobjective optimization as a aggregate task of optimization and decisionmaking. 1