Results 1  10
of
37
Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach
 IEEE Transactions on Evolutionary Computation
, 1999
"... Abstract—Evolutionary algorithms (EA’s) are often wellsuited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in ..."
Abstract

Cited by 493 (17 self)
 Add to MetaCart
Abstract—Evolutionary algorithms (EA’s) are often wellsuited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EA’s are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the Strength Pareto EA (SPEA), that combines several features of previous multiobjective EA’s in a unique manner. It is characterized by a) storing nondominated solutions externally in a second, continuously updated population, b) evaluating an individual’s fitness dependent on the number of external nondominated points that dominate it, c) preserving population diversity using the Pareto dominance relationship, and d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proofofprinciple results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware–software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Paretooptimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EA’s on the 0/1 knapsack problem. Index Terms — Clustering, evolutionary algorithm, knapsack problem, multiobjective optimization, niching, Pareto optimality.
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 ..."
Abstract

Cited by 278 (5 self)
 Add to MetaCart
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.
Niching Methods for Genetic Algorithms
, 1995
"... Niching methods extend genetic algorithms to domains that require the location and maintenance of multiple solutions. Such domains include classification and machine learning, multimodal function optimization, multiobjective function optimization, and simulation of complex and adaptive systems. This ..."
Abstract

Cited by 191 (1 self)
 Add to MetaCart
Niching methods extend genetic algorithms to domains that require the location and maintenance of multiple solutions. Such domains include classification and machine learning, multimodal function optimization, multiobjective function optimization, and simulation of complex and adaptive systems. This study presents a comprehensive treatment of niching methods and the related topic of population diversity. Its purpose is to analyze existing niching methods and to design improved niching methods. To achieve this purpose, it first develops a general framework for the modelling of niching methods, and then applies this framework to construct models of individual niching methods, specifically crowding and sharing methods. Using a constructed model of crowding, this study determines why crowding methods over the last two decades have not made effective niching methods. A series of tests and design modifications results in the development of a highly effective form of crowding, called determin...
Multiobjective Optimization Using Evolutionary Algorithms  A Comparative Case Study
, 1998
"... . Since 1985 various evolutionary approaches to multiobjective optimization have been developed, capable of searching for multiple solutions concurrently in a single run. But the few comparative studies of different methods available to date are mostly qualitative and restricted to two approaches. I ..."
Abstract

Cited by 132 (9 self)
 Add to MetaCart
. Since 1985 various evolutionary approaches to multiobjective optimization have been developed, capable of searching for multiple solutions concurrently in a single run. But the few comparative studies of different methods available to date are mostly qualitative and restricted to two approaches. In this paper an extensive, quantitative comparison is presented, applying four multiobjective evolutionary algorithms to an extended 0/1 knapsack problem. 1 Introduction Many realworld problems involve simultaneous optimization of several incommensurable and often competing objectives. Usually, there is no single optimal solution, but rather a set of alternative solutions. These solutions are optimal in the wider sense that no other solutions in the search space are superior to them when all objectives are considered. They are known as Paretooptimal solutions. Mathematically, the concept of Paretooptimality can be defined as follows: Let us consider, without loss of generality, a multio...
New Methods for Competitive Coevolution
 Evolutionary Computation
, 1996
"... We consider "competitive coevolution," in which fitness is based on direct competition among individuals selected from two independently evolving populations of "hosts" and "parasites." Competitive coevolution can lead to an "arms race," in which the two populations reciprocally drive one another to ..."
Abstract

Cited by 121 (3 self)
 Add to MetaCart
We consider "competitive coevolution," in which fitness is based on direct competition among individuals selected from two independently evolving populations of "hosts" and "parasites." Competitive coevolution can lead to an "arms race," in which the two populations reciprocally drive one another to increasing levels of performance and complexity. We use the games of Nim and 3D TicTacToe as test problems to explore three new techniques in competitive coevolution. "Competitive fitness sharing" changes the way fitness is measured, "shared sampling" provides a method for selecting a strong, diverse set of parasites, and the "hall of fame" encourages arms races by saving good individuals from prior generations. We provide several different motivations for these methods, and mathematical insights into their use. Experimental comparisons are done, and a detailed analysis of these experiments is presented in terms of testing issues, diversity, extinction, arms race progress measurements, a...
Massive Multimodality, Deception, and Genetic Algorithms
, 1992
"... This paper considers the use of genetic algorithms (GAs) for the solution of problems that are both averagesense misleading (deceptive) and massively multimodal. An archetypical multimodaldeceptive problem, here called a bipolar deceptive problem, is defined and two generalized constructions of su ..."
Abstract

Cited by 113 (25 self)
 Add to MetaCart
This paper considers the use of genetic algorithms (GAs) for the solution of problems that are both averagesense misleading (deceptive) and massively multimodal. An archetypical multimodaldeceptive problem, here called a bipolar deceptive problem, is defined and two generalized constructions of such problems are reviewed, one using reflected trap functions and one using loworder Walsh coefficients; sufficient conditions for bipolar deception are also reviewed. The Walsh construction is then used to form a 30bit, ordersix bipolardeceptive function by concatenating five, sixbit bipolar functions. This test function, with over five million local optima and 32 global optima, poses a difficult challenge to simple and niched GAs alike. Nonetheless, simulations show that a simple GA can reliably find one of the 32 global optima if appropriate signaltonoiseratio population sizing is adopted. Simulations also demonstrate that a niched GA can reliably and simultaneously find all 32 global solutions if the population is roughly sized for the expected niche distribution and if the function is appropriately scaled to emphasize global solutions at the expense of suboptimal ones. These results immediately recommend the application of niched GAs using appropriate population sizing and scaling. They also suggest a number of avenues for generalizing the notion of deception.
Multiobjective Optimization Using the Niched Pareto Genetic Algorithm
, 1993
"... Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives (i.e., attributes or criteria) 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 ..."
Abstract

Cited by 111 (4 self)
 Add to MetaCart
Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives (i.e., attributes or criteria) 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 most recent development in the field of decision analysis has yielded a rigorous technique for combining attributes multiplicatively (thereby incorporating nonlinearity), and for handling uncertainty in the attribute values. But MultiAttribute Utility Analysis (MAUA) provides only a mapping from a vectorvalued objective function to a scalarvalued function, and does not address the difficulty of searching large problem spaces. Genetic algorithms (GAs), on the other hand, are well suited to searching intractably large, poorly understood problem spaces, but have mostly been used to optimize a single objective. The direct combination of MAUA and GAs is a logical next step...
Implicit Niching in a Learning Classifier System: Nature's Way
 EVOLUTIONARY COMPUTATION
, 1994
"... We approach the difficult task of analyzing the complex behavior of even the simplest learning classifier system (LCS) by isolating one crucial subfunction in the LCS learning algorithm: covering through niching. The LCS must maintain a population of diverse rules that together solve a problem (e.g. ..."
Abstract

Cited by 56 (9 self)
 Add to MetaCart
We approach the difficult task of analyzing the complex behavior of even the simplest learning classifier system (LCS) by isolating one crucial subfunction in the LCS learning algorithm: covering through niching. The LCS must maintain a population of diverse rules that together solve a problem (e.g., classify examples). To maintain a diverse population while applying the GA's selection operator, the LCS must incorporate some kind of niching mechanism. The natural way to accomplish niching in an LCS is to force competing rules to share resources (i.e., rewards). This implicit LCS fitness sharing is similar to the explicit fitness sharing used in many niched GAs. Indeed, the LCS implicit sharing algorithm can be mapped onto explicit fitness sharing with a onetoone correspondence between algorithm components. This mapping is important because several studies of explicit fitness sharing, and of niching in GAs generally, have produced key insights and analytical tools for understanding th...
Genetic Algorithms with Dynamic Niche Sharing for Multimodal Function Optimization
 IEEE International Conference on Evolutionary Computation
, 1996
"... Genetic algorithms utilize populations of individual hypotheses that converge over time to a single optimum, even within a multimodal domain. This paper examines methods that enable genetic algorithms to identify multiple optima within multimodal domains by maintaining population members within the ..."
Abstract

Cited by 42 (0 self)
 Add to MetaCart
Genetic algorithms utilize populations of individual hypotheses that converge over time to a single optimum, even within a multimodal domain. This paper examines methods that enable genetic algorithms to identify multiple optima within multimodal domains by maintaining population members within the niches defined by the multiple optima. A new mechanism, Dynamic Niche Sharing, is developed that is able to efficiently identify and search multiple niches (peaks) in a multimodal domain. Dynamic niche sharing is shown to perform better than two other methods for multiple optima identification, Standard Sharing and Deterministic Crowding. To further improve performance, mating restrictions are used to increase the likelihood of producing highly fit offspring. Two new mating restriction mechanisms, Dynamic Line Breeding and Dynamic Inbreeding, are introduced that utilize dynamic niche sharing to proportionately populate local optima in a multimodal domain. Experiments presented in this paper ...