J. G. Lin. Maximal vectors and multi objective optimization. Journal of Optimization Theory and Application, 18(1):41 64, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....method that would translate qualitative specification into quantitative. Without this combination, our modified Pareto method suffers from the same problem as the weighted sum method: how to specify weights in the case of 15 20 or more objectives. 4. 2 Definition of weighted Pareto method Lin [16] distinguishes between orders on k dimensional vectors: x y ifandonlyif (Vi ( k) xi Yi) 7) xy ifandonlyif (x y) X(3j k) xj yj) 8) He notes that the orders (7) and (8) are definable in terms of each other and therefore ordering a set in R k by is equivalent to ordering a set by [16, ....

J. G. Lin. Maximal vectors and multi objective optimization. Journal of Optimization Theory and Application, 18(1):41 64, 1976.

....definition of dominance could be obtained by setting z = 1 and w . w = 1 k. Note that in the standard definition of dominance it is required that at least one of the xi Yi inequalities is strict. However this is not a problem since these two orders are definable in terms of each other [51]. Definition 2: Weighted Pareto front) The (w, z) Paretofront is defined as a maximal (i.e. the largest according to C order) set of nondominated elements according to a given order z w. In the following text we will usually set z = 1 and write .w instead of .z w. The corresponding ....

J. G. Lin, "Maximal vectors and multi objective optimization," Journal of Optimization Theory and Application, vol. 18, no. 1, pp. 414, 1976.

....not available, then the task will be to identify a set of nondominated solutions. In this case, strong preference can only be concluded if there exists enough evidence that one of the vectors is clearly dominating the vector against which it is compared. Weak preference (modelled as weak dominance [26]) on the other hand, expresses a certain lack of conviction. Indifference means that both vectors are equivalent and that it does not matter which of them is selected. It is important to distinguish this indifference from the incomparability used with outranking methods, since the second ....

J. G. Lin. Maximal vectors and multi-objective optimization. Journal of Optimization Theory and Applications, 18(1):41--64, jan 1976.

....to agree upon a further concept of absolute optimality in this context, in case the designer desires a single final solution. For the scope of this paper, we will adopt the concept of min max optimum for that purpose. Osyczka provides in his book [40] an algorithm based on the contact theorem [37], which can identify Pareto optimal solutions from a given set of feasible solutions. This algorithm was implemented by the authors of this paper and incorporated in MOSES together with another one that finds the optimum in the min max sense [10] 4.1 Monte Carlo Methods We also implemented the ....

J. G. Lin. Maximal vectors and multi-objective optimization. Journal of Optimization Theory and Applications, 18(1):41--64, jan 1976.

....in this case, has also been exploited more recently by other researchers [96, 4, 30] 4. 7 Use of the Contact Theorem to Detect Pareto Optimal Solutions Osyczka and Kundu [62] proposed the use of an algorithm based on the contact theorem (one of the main theorems in multiobjective optimization [49]) to determine relative distances of a solution vector with respect to the Pareto set. In this paper [62] the contact theorem was used to determine the fitness of each individual in the population. This approach is in a way, very similar to the Min Max approach previously described, only that in ....

J. G. Lin. Maximal vectors and multi-objective optimization. Journal of Optimization Theory and Applications, 18(1):41--64, jan 1976.

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Lin, J. G. 1976. Maximal vectors and multi-objective optimization. Journal of Optimization Theory and Applications 18, 1 (jan), 41--64.

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