In this paper, we present a link between preference-based and multiobjective sequential decision-making. While transforming a multiobjective problem to a preference-based one is quite natural, the other direction is a bit less obvious. We present how this transformation (from preference-based to multiobjective) can be done under the classic condition that preferences over histories can be represented by additively decomposable utilities and that the decision criterion to evaluate policies in a state is based on expectation. This link yields a new source of multiobjective sequential decision-making problems (i.e., when reward values are unknown) and justifies the use of solving methods developed in one setting in the other one.
Still another approach to solve multiobjective problems is to assume the existence of a scalarizing function @math , which, given a vector @math , returns a scalar valuation. Two cases can be considered: @math can be either linear @cite_23 or nonlinear @cite_32 @cite_31 @cite_29 .
@cite_31 @cite_29 @cite_32 @cite_23
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We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Decomposition-based algorithms have become increasingly popular for evolutionary multiobjective optimization. However, the effect of scalarizing methods used in these algorithms is still far from being well understood. This paper analyzes a family of frequently used scalarizing methods, the @math methods, and shows that the @math value is crucial to balance the selective pressure toward the Pareto optimal and the algorithm robustness to Pareto optimal front (PF) geometries. It demonstrates that an @math method that can maximize the search ability of a decomposition-based algorithm exists and guarantees that, given some weight, any solution along the PF can be found. Moreover, a simple yet effective method called Pareto adaptive scalarizing (PaS) approximation is proposed to approximate the optimal @math value. In order to demonstrate the effectiveness of PaS, we incorporate PaS into a state-of-the-art decomposition-based algorithm, i.e., multiobjective evolutionary algorithm based on decomposition (MOEA D), and compare the resultant MOEA D-PaS with some other MOEA D variants on a set of problems with different PF geometries and up to seven conflicting objectives. Experimental results demonstrate that the PaS is effective. Abstract Irregular sampling and “stable sampling” of band-limited functions have been studied by H.J. Landau [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52]. We prove that quasicrystals are sets of stable sampling. To cite this article: B. Matei, Y. Meyer, C. R. Acad. Sci. Paris, Ser. I 346 (2008).