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Verified methods for computing Pareto sets: General algorithmic analysis

100%

Tóth B., Kreinovich V.

International Journal of Applied Mathematics and Computer Science

2009

tom 19

nr 3

369-380

In many engineering problems, we face multi-objective optimization, with several objective functions f₁,...,fₙ. We want to provide the user with the Pareto set-a set of all possible solutions x which cannot be improved in all categories (i.e., for which $f_j(x') ≥ f_j(x)$ for all j and $f_j(x ) > f_j(x)$ for some j is impossible). The user should be able to select an appropriate trade-off between, say, cost and durability. We extend the general results about (verified) algorithmic computability of maxima locations to show that Pareto sets can also be computed.

On a multi-objective optimization problem arising from production theory

100%

Roman M., Wieczorek A.

Applicationes Mathematicae

1998-1999

tom 25

nr 4

411-415

The paper presents a natural application of multi-objective programming to household production and consumption theory. A contribution to multi-objective programming theory is also included.

Niching mechanisms in evolutionary computations

63%

Kowalczuk Z., Białaszewski T.

International Journal of Applied Mathematics and Computer Science

2006

tom 16

nr 1

59-84

Different types of niching can be used in genetic algorithms (GAs) or evolutionary computations (ECs) to sustain the diversity of the sought optimal solutions and to increase the effectiveness of evolutionary multi-objective optimization solvers. In this paper four schemes of niching are proposed, which are also considered in two versions with respect to the method of invoking: a continuous realization and a periodic one. The characteristics of these mechanisms are discussed, while as their performance and effectiveness are analyzed by considering exemplary multi-objective optimization tasks both of a synthetic and an engineering (FDI) design nature.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Applicationes Mathematicae

1 Białaszewski T.

1 Kowalczuk Z.

1 Kreinovich V.

1 Roman M.

1 Tóth B.

1 Wieczorek A.

1 2009

1 2006

1 1999

Wyniki wyszukiwania

Verified methods for computing Pareto sets: General algorithmic analysis

On a multi-objective optimization problem arising from production theory

Niching mechanisms in evolutionary computations