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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 ..."
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Cited by 515 (18 self)
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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.
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 292 (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...
A New Multiobjective Evolutionary Algorithm For Environmental Economic Power Dispatch
, 2001
"... In this paper, a new multiobjective evolutionary algorithm for Environmental/Economic power Dispatch (EED) optimization problem is presented. The EED problem is formulated as a nonlInear constrained multiobjective optimization problem with both equality and inequality constraints. A new Nondominated ..."
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Cited by 28 (1 self)
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In this paper, a new multiobjective evolutionary algorithm for Environmental/Economic power Dispatch (EED) optimization problem is presented. The EED problem is formulated as a nonlInear constrained multiobjective optimization problem with both equality and inequality constraints. A new Nondominated Sorting Genetic Algorithm (NSGA) based approach is proposed to handle the problem as a true multiobjective optimization problem with competing and noncommensurable objectives. The proposed approach employs a diversitypreserving technique to overcome the premature convergence and search bias problems and produce a welldistributed Paretooptimal set of nondominated solutions. A hierarchical clustering technique is also imposed to provide the decision maker with a representative and manageable Pareto optimal set. Several optimization runs of the proposed approach are carded out on a standard IEEE test system. The results demonstrate the capabilities of the proposed NSGA based approach to generate the true Paretooptimal set of nondominated solutions of the multiobjective EED problem in one single run. Simulation results with the proposed approach have been compared to those reported in the literature. The comparison shows the superiority of the proposed NSGA based approach and confirms its potential to solve the multiobjective EED problem.
Fuzzy multiple criteria decision making: Recent developments
 Fuzzy Sets and Systems
, 1996
"... Multiple Crtiple Decision Making (MCDM) shows signs of becoming a matur: field. Ther ar four quite distinct families of methods:(i) theoutr91 ing, (ii) the value and utilitytheor based, (iii) the multiple objectivepr68: ming, and (iv) gr): decision and negotiationtheor based methods. Fuzzy MCDM has ..."
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Cited by 16 (0 self)
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Multiple Crtiple Decision Making (MCDM) shows signs of becoming a matur: field. Ther ar four quite distinct families of methods:(i) theoutr91 ing, (ii) the value and utilitytheor based, (iii) the multiple objectivepr68: ming, and (iv) gr): decision and negotiationtheor based methods. Fuzzy MCDM has basically been developed along the same lines, although with the help of fuzzy settheor a number of innovations have been made possible; the most impor:1 t methods arr17 ed and a novelappr68 h  inter57 endence in MCDM  is intr duced. 1
Antonsson, “TradeOff strategies in engineering design
 Res. Eng. Design
, 1991
"... A formal method to allow designers to explicitly make tradeoff decisions is presented. The methodology can be used when an engineer wishes to rate the design by the weakest aspect, or by cooperatively considering the overall performance, or a combination of these strategies. The design problem is f ..."
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Cited by 16 (11 self)
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A formal method to allow designers to explicitly make tradeoff decisions is presented. The methodology can be used when an engineer wishes to rate the design by the weakest aspect, or by cooperatively considering the overall performance, or a combination of these strategies. The design problem is formulated with preference rankings, similar to a utility theory or fuzzy sets approach. This approach separates the design tradeoff strategy from the performance expressions. The details of the mathematical formulation are presented and discussed, along with two design examples: one from the preliminary design domain, and one from the parameter design domain. 1
Propagating Imprecise Engineering Design Constraints
 1995 IEEE International Conference on Fuzzy Systems
, 1995
"... Constraint based CAD systems are used to manipulate input and output variables by allowing a user to adjust the variables ’ crisp values. The different ..."
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Cited by 3 (0 self)
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Constraint based CAD systems are used to manipulate input and output variables by allowing a user to adjust the variables ’ crisp values. The different
Satisficing, Optimization, and Adaptive Systems
"... Abstract An aspect of complex adaptive systems is an observation that they typically operate far from equilibrium and optimality. This provokes investigation into frameworks into such decisionmaking processes. Satisficing describes a rational decision making process in economics where deciding age ..."
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Cited by 2 (0 self)
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Abstract An aspect of complex adaptive systems is an observation that they typically operate far from equilibrium and optimality. This provokes investigation into frameworks into such decisionmaking processes. Satisficing describes a rational decision making process in economics where deciding agents accept solutions that achieve a minimum level of satisfaction. This theory differs from previously traditional rational decisionmaking in which the agent seeks to maximise or optimize utility from the choices faced. This work investigates some of the impact this altered perspective on the decision making process has had in economics, game theory, control theory, and evolutionary biology. We see it is the latter case that that may be most interesting to the study of complex adaptive systems and resultant models, such as those used in biologically inspired computation.
A Location Problem with the Adistance in a Competitive Environment
 Proceedings of International MultiConference of Engineers and Computer Scientists 2008, V2
"... Abstract — This paper proposes a new location problem of competitive facilities, e.g. shops. In the most studies of competitive facility location, the distance between the facilities and their customers is represented as the Euclid distance. The proposing location problem introduces the Adistance, ..."
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Cited by 2 (2 self)
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Abstract — This paper proposes a new location problem of competitive facilities, e.g. shops. In the most studies of competitive facility location, the distance between the facilities and their customers is represented as the Euclid distance. The proposing location problem introduces the Adistance, proposed by Widmayer etc., for representing the situation that the directions which customers can move are given. For solving the formulated facility location problem efficiently, it is shown that the problem is reformulated as a combinatorial optimization problem, and its solving method based on genetic algorithms is proposed. The efficiency of the solving method is shown by applying to several examples of the competitive facility location problems.
Modeling Uncertainty Using Probabilistic Based Possibility Theory With Applications To Optimization
, 1998
"... It is shown that possibility distributions can be formulated within the context of probability theory and that membership values of fuzzy set theory can be interpreted as cumulative probabilities. The basic functions and operations of possibility theory are interpreted within this setting. The proba ..."
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Cited by 1 (1 self)
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It is shown that possibility distributions can be formulated within the context of probability theory and that membership values of fuzzy set theory can be interpreted as cumulative probabilities. The basic functions and operations of possibility theory are interpreted within this setting. The probabilistic information that can be derived from possibility distributions is examined. This leads to two functionals that provide estimates for the expected value of a random variable, the expected average of a single possibility distribution and the estimated expectation that requires two special possibility distributions to compute. Secondly, the space of fuzzy numbers is examined. It is shown that this space can be partitioned into a vector space and that the expected average functional motivates a norm on this space. It is shown that for most applications, Cauchy sequences converge in this space. Thirdly, applications of this theory to problems in optimization are examined. The concept of ...