Multi-objective evolutionary computation and fuzzy optimization

Jiménez, Fernando; Cadenas, José Manuel; Sánchez, Gracia; Gómez‐Skarmeta, Antonio F.; Verdegay, José L.

doi:10.1016/j.ijar.2006.02.001

Cited by 42 publications

(16 citation statements)

References 13 publications

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“…Nowadays, these algorithms are often used, leading to good results and performance, in the solution of structural problems, in the characterization of constitutive models, etc. (Lagaros et al, 2005;Jiménez et al, 2006). A recent review of evolutionary software can be found in the work of Mantere and Alander (2005).…”

Section: Introductionmentioning

confidence: 99%

On the determination of material parameters for internal variable thermoelastic–viscoplastic constitutive models

Andrade‐Campos

Thuillier

Pilvin

et al. 2007

International Journal of Plasticity

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Section: Introductionmentioning

confidence: 99%

On the determination of material parameters for internal variable thermoelastic–viscoplastic constitutive models

Andrade‐Campos

Thuillier

Pilvin

et al. 2007

International Journal of Plasticity

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“…The problem in some import-export companies in the south of Spain, described in Table 2, was taken from of (Jiménez et al, 2006). The same parameters and uncertainties of this real-world problem were used in here, but uncertainties were inserted in the parameters of the objective functions.…”

Section: Real-world Problemmentioning

confidence: 99%

Application of an iterative method and an evolutionary algorithm in fuzzy optimization

2012

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ABSTRACT. This work develops two approaches based on the fuzzy set theory to solve a class of fuzzy mathematical optimization problems with uncertainties in the objective function and in the set of constraints. The first approach is an adaptation of an iterative method that obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. The second one is a metaheuristic approach that adapts a standard genetic algorithm to use fuzzy numbers. Both approaches use a decision criterion called satisfaction level that reaches the best solution in the uncertain environment. Selected examples from the literature are presented to compare and to validate the efficiency of the methods addressed, emphasizing the fuzzy optimization problem in some import-export companies in the south of Spain.

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“…On the other hand, some works describe a fuzzy optimization problem in a classical problem, and they use the classical theory to find the Pareto optimal set. In Jiménez et al (2006), a fuzzy single objective problem is transformed into a classical multiple objective one, and the number of objectives is defined by fuzzy coefficients from the fuzzy problem.…”

Section: Introductionmentioning

confidence: 99%

The use of possibility theory in the definition of fuzzy Pareto-optimality

Silva

Yamakami

2010

Fuzzy Optim Decis Making

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Pareto-optimality conditions are crucial when dealing with classic multiobjective optimization problems. Extensions of these conditions to the fuzzy domain have been discussed and addressed in recent literature. This work presents a novel approach based on the definition of a fuzzily ordered set with a view to generating the necessary conditions for the Pareto-optimality of candidate solutions in the fuzzy domain. Making use of the conditions generated, one can characterize fuzzy efficient solutions by means of carefully chosen mono-objective problems and Karush-Kuhn-Tucker conditions to fuzzy non-dominated solutions. The uncertainties are inserted into the formulation of the studied fuzzy multi-objective optimization problem by means of fuzzy coefficients in the objective function. Some numerical examples are analytically solved to illustrate the efficiency of the proposed approach.

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Multi-objective evolutionary computation and fuzzy optimization

Cited by 42 publications

References 13 publications

On the determination of material parameters for internal variable thermoelastic–viscoplastic constitutive models

On the determination of material parameters for internal variable thermoelastic–viscoplastic constitutive models

Application of an iterative method and an evolutionary algorithm in fuzzy optimization

The use of possibility theory in the definition of fuzzy Pareto-optimality

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