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.
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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.
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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.
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