RESUMEN
Abstract The averaged Hausdorff distance Δ p is an inframetric, recently introduced in evolutionary multiobjective optimization (EMO) as a tool to measure the optimality of finite size approximations to the Pareto front associated to a multiobjective optimization problem (MOP). Tools of this kind are called performance indicators, and their quality depends on the useful criteria they provide to evaluate the suitability of different candidate solutions to a given MOP. We present here a purely theoretical study of the compliance of the Δ p -indicator to the notion of Pareto optimality. Since Δ p is defined in terms of a modified version of other well-known indicators, namely the generational distance GDp , and the inverted generational distance IGDp , specific criteria for the Pareto compliance of each one of them is discussed in detail. In doing so, we review some previously available knowledge on the behavior of these indicators, correcting inaccuracies found in the literature, and establish new and more general results, including detailed proofs and examples of illustrative situations.
Resumen La distancia promedio de Hausdorff Δp es una inframétrica recientemente introducida en optimización multiobjetivo evolutiva (EMO) como una herramienta para medir la optimalidad de aproximaciones finitas al frente de Pareto asociado con un problema de optimización multiobjetivo (MOP). Presentamos aquí un estudio puramente teórico sobre la sujeción del indicador Δp a la noción de optimalidad de Pareto. Puesto que Δp está definida en términos de una versión modificada de otros indicadores bien conocidos como lo son la distancia generacional GD p y la distancia generacional invertida IGD p , discutimos en detalle criterios específicos para la sujeción de tipo Pareto de cada uno de ellos. Adicionalmente, presentamos una revisión del comportamiento previamente conocido de estos indicadores, corrigiendo imprecisiones que se encuentran en la literatura y establecemos resultados nuevos y más generales, incluyendo pruebas detalladas y ejemplos ilustrativos.
Resumo A distância média de Hausdorff Δp é uma inframétrica introduzida recentemente em otimização multiobjetivo evolucionária (EMO) como uma ferramenta para medir a otimalidade de aproximações finitas para o frente de Pareto associado com um problema de optimização multiobjetivo (MOP). Apresentamos aqui um estudo puramente teórico sobre a sujeição do indicador Δp à noção de otimalidade de Pareto. Desde Δp é definido em termos de uma versão modificada de outros indicadores bem conhecidos, tais como a distância geraçional GD p ∈ a distância geraçional invertida IGD p , discutimos em detalhes critérios específicos para a sujeição de Pareto de cada um deles. Além disso, apresentamos uma revisão do comportamento previamente conhecido desses indicadores, corrigindo imprecisões encontradas na literatura ∈ estabelecemos novos ∈ mais gerais resultados, incluindo testes detalhados ∈ exemplos ilustrativos.
RESUMEN
This paper analyzed medical dispute litigation from the view of game theory.The adoption of mediation strategy for both hospital and patient was the Pareto optimal of this model.The adoption of court decision for both hospital and patient was the Nash equilibrium and its overall benefit was the Pareto suboptimal of this model.The communication of patient's lawyer can prompt the reconciliation between hospital and patient.On the one hand,it let the hospital realize the responsibilities they should bear,on the other hand let patients be willing to make concessions on the basis of the original claims,and finally made the two sides reach a reconciliation agreement,thus to make conflict between hospital and patient end in litigation and the overall benefits maximize.
RESUMEN
The meta-analysis has become a widely used tool for many applications in bioinformatics, including genome-wide association studies. A commonly used approach for meta-analysis is the fixed effects model approach, for which there are two popular methods: the inverse variance-weighted average method and weighted sum of z-scores method. Although previous studies have shown that the two methods perform similarly, their characteristics and their relationship have not been thoroughly investigated. In this paper, we investigate the optimal characteristics of the two methods and show the connection between the two methods. We demonstrate that the each method is optimized for a unique goal, which gives us insight into the optimal weights for the weighted sum of z-scores method. We examine the connection between the two methods both analytically and empirically and show that their resulting statistics become equivalent under certain assumptions. Finally, we apply both methods to the Wellcome Trust Case Control Consortium data and demonstrate that the two methods can give distinct results in certain study designs.