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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 485 (13 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
Multiobjective Evolutionary Algorithms: Analyzing the StateoftheArt
, 2000
"... Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mideighties in an attempt to stochastically solve problems of this generic class. During the past decade, ..."
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Cited by 423 (7 self)
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Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mideighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of c...
Evolutionary Computation and Convergence to a Pareto Front
 Stanford University, California
, 1998
"... Research into solving multiobjective optimization problems (MOP) has as one of its an overall goals that of developing and defining foundations of an Evolutionary Computation (EC)based MOP theory. In this paper, we introduce relevant MOP concepts, and the notion of Pareto optimality, in particular. ..."
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Cited by 37 (1 self)
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Research into solving multiobjective optimization problems (MOP) has as one of its an overall goals that of developing and defining foundations of an Evolutionary Computation (EC)based MOP theory. In this paper, we introduce relevant MOP concepts, and the notion of Pareto optimality, in particular. Specific notation is defined and theorems are presented ensuring Paretobased Evolutionary Algorithm (EA) implementations are clearly understood. Then, a specific experiment investigating the convergence of an arbitrary EA to a Pareto front is presented. This experiment gives a basis for a theorem showing a specific multiobjective EA statistically converges to the Pareto front. We conclude by using this work to justify further exploration into the theoretical foundations of ECbased MOP solution methods. 1 Introduction Our research focuses on solving scientific and engineering multiobjective optimization problems (MOPs), contributing to the overall goal of developing and defining foundatio...
Finding a BetterthanClassical Quantum AND/OR Algorithm using Genetic Programming
, 1999
"... This paper documents the discovery of a new, betterthanclassical quantum algorithm for the depthtwo AND/OR tree problem. We describe the genetic programming system that was constructed specifically for this work, the quantum computer simulator that is used to evaluate the fitness of evolving quant ..."
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Cited by 36 (2 self)
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This paper documents the discovery of a new, betterthanclassical quantum algorithm for the depthtwo AND/OR tree problem. We describe the genetic programming system that was constructed specifically for this work, the quantum computer simulator that is used to evaluate the fitness of evolving quantum algorithms, and the newly discovered algorithm. 1 Introduction Quantum computers use the dynamics of atomicscale objects to store and manipulate information. The behavior of atomicscale objects is governed by quantum mechanics rather than by classical physics, and the quantum mechanical properties of these systems can be harnessed to compute certain functions more efficiently than is possible on any classical computer [1]. For example, Shor's quantum factoring algorithm finds the prime factors of an ndigit number in time O(n 2 log(n) log log(n)) [2], while the best known classical factoring algorithms require time O(2 n 1 3 log(n) 2 3 ) and many researchers doubt the existence...
Multiobjective Genetic Algorithms with Application to Control Engineering Problems
, 1995
"... Genetic algorithms (GAs) are stochastic search techniques inspired by the principles of natural selection and natural genetics which have revealed a number of characteristics particularly useful for applications in optimization, engineering, and computer science, among other fields. In control engin ..."
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Cited by 24 (1 self)
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Genetic algorithms (GAs) are stochastic search techniques inspired by the principles of natural selection and natural genetics which have revealed a number of characteristics particularly useful for applications in optimization, engineering, and computer science, among other fields. In control engineering, they have found application mainly in problems involving functions difficult to characterize mathematically or known to present difficulties to more conventional numerical optimizers, as well as problems involving nonnumeric and mixedtype variables. In addition, they exhibit a large degree of parallelism, making it possible to effectively exploit the computing power made available through parallel processing. Despite their early recognized potential for multiobjective optimization (almost all engineering problems involve multiple, often conflicting objectives), genetic algorithms have, for the most part, been applied to aggregations of the objectives in a singleobjective fashion, like conventional optimizers. Although alternative approaches based on the notion of Paretodominance have been suggested, multiobjective optimization with genetic algorithms has received comparatively
Preferences and their Application in Evolutionary Multiobjective Optimisation
, 2001
"... The paper describes a new preference method and its use in multiobjective optimisation. These preferences are developed with a goal to reduce the cognitive overload associated with the relative importance of a certain criterion within a multiobjective design environment involving large numbers of ob ..."
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Cited by 21 (3 self)
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The paper describes a new preference method and its use in multiobjective optimisation. These preferences are developed with a goal to reduce the cognitive overload associated with the relative importance of a certain criterion within a multiobjective design environment involving large numbers of objectives. Their successful integration with several genetic algorithmbased design search and optimisation techniques (weighted sums, weighted Pareto, weighted coevolutionary methods, and weighted scenarios) are described and theoretical results relating to complexity and sensitivity of the algorithm are presented and discussed. Its usefulness has been demonstrated in a realworld project of conceptual airframe design (a joint project with British Aerospace Systems).
Multiobjective Optimisation and Preliminary Airframe Design
, 1998
"... In this paper we explore established methods for optimising multiobjective functions whilst addressing the problem of preliminary design. Methods from the literature are investigated and new ones introduced. All methods are evaluated within a collaborative project with British Aerospace for whole s ..."
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Cited by 12 (6 self)
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In this paper we explore established methods for optimising multiobjective functions whilst addressing the problem of preliminary design. Methods from the literature are investigated and new ones introduced. All methods are evaluated within a collaborative project with British Aerospace for whole system airframe design and the basic problems and difficulties of preliminary design methodology are discussed. Our Genetic Algorithm is expanded to integrate different methods for optimising multiobjective functions. First, methods based on scalarisation and the utilisation of weights are addressed. Methods based on Pareto order are then analysed and two different sorting techniques (dominated/nondominated and Pareto rank) investigated. Finally, several variants of subpopulation based algorithms are presented. All presented methods are also analysed in the context of whole system design, discussing their advantages and disadvantages. 1 Introduction When dealing with industrial design ...
Genetic Programming for Quantum Computers
 In Genetic Programming
, 1998
"... Genetic programming can be used to automatically discover algorithms for quantum computers that are more efficient than any classical computer algorithms for the same problems. In this paper we exhibit the first evolved betterthanclassical quantum algorithm, for Deutsch’s “early promise ” problem. ..."
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Cited by 11 (0 self)
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Genetic programming can be used to automatically discover algorithms for quantum computers that are more efficient than any classical computer algorithms for the same problems. In this paper we exhibit the first evolved betterthanclassical quantum algorithm, for Deutsch’s “early promise ” problem. We also demonstrate a technique for evolving scalable quantum gate arrays and discuss other issues in the application of genetic programming to quantum computation and vice versa. 1. Quantum Computing Quantum computers are computational devices that use atomicscale objects, for example 2state particles, to store and manipulate information (Steane, 1997; for an elementary online tutorial see Braunstein, 1995; for an introduction for the general reader see Milburn, 1997). The physics of these devices allows them to do things that common digital (henceforth “classical”) computers cannot. Although quantum computers and classical computers appear to be bound by the same limits of Turing computability, physicists argue that quantum computers can solve certain problems using less resources (time and space) than classical computers are thought to require (Jozsa, 1997). For example, Shor’s quantum algorithm finds the prime factors of an ndigit number in time O(n 3), while the best known classical factoring algorithms
Evolutionary Design and Multiobjective Optimisation
 in '6th European Congress on Intelligent Techniques and Soft Computing EUFIT'98
, 1998
"... : In this paper we explore established methods for optimising multiobjective functions whilst addressing the problem of preliminary design. Methods from the literature are investigated and new ones introduced. All methods are evaluated within a collaborative project for whole system airframe design ..."
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Cited by 10 (3 self)
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: In this paper we explore established methods for optimising multiobjective functions whilst addressing the problem of preliminary design. Methods from the literature are investigated and new ones introduced. All methods are evaluated within a collaborative project for whole system airframe design and the basic problems and difficulties of preliminary design methodology are discussed (Cvetkovic, Parmee and Webb 1998). Our Genetic Algorithm is expanded to integrate different methods for optimising multiobjective functions. All presented methods are also analysed in the context of whole system design, discussing their advantages and disadvantages. The problem of qualitative versus quantitative characterisation of relative importance of objectives (such as `objective A is much more important then objective B') in multiobjective optimisation framework is also addressed and some relationships with fuzzy preferences (Fodor and Roubens 1994) and preference ordering established. Several ...
Genetic Algorithmbased Multiobjective Optimisation and Conceptual Engineering Design
 IN CONGRESS ON EVOLUTIONARY COMPUTATION  CEC99
, 1999
"... In this paper we present a genetic algorithm based system for conceptual engineering design. First, we present a method based on preference relations for transforming noncrisp (qualitative) relationships between objectives in multiobjective optimisation into quantitative attributes (numbers). This ..."
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Cited by 5 (1 self)
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In this paper we present a genetic algorithm based system for conceptual engineering design. First, we present a method based on preference relations for transforming noncrisp (qualitative) relationships between objectives in multiobjective optimisation into quantitative attributes (numbers). This is integrated with two multiobjective Genetic Algorithms: weighted sums GA and a method for combining the Pareto method with weights. Examples of preference relations application together with traditional Genetic Algorithms are also presented. A further method for dynamical inclusion and modification of extra constraints (not included in the mathematical model of the system) via scenarios is presented. Its use is discussed and potential applications indicated. Finally, some future work paths are mentioned.