Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Comparative study on the localization of adult Schistosoma mansoni worms in albino mice anesthetized with pentobarbital sodium, ether or chlorophorm Estudo comparativo sobre a localização de vermes adultos de Schistosoma mansoni em camundongos albinos anestesiados com pentobarbital sódico, éter ou clorofórmio

The effect of anesthetic drugs on the localization of adult worms in albino mice was compared. The animals with 56 days of infection were anesthetized with pentobarbital sodium, ether or chlorophorm. Perfusion was carried out immediately after, recovering the worms and classifying them in relation to their localization on the liver or portal vein and the mesenteric veins. Our results showed that pentobarbital sodium produced a greater displacement of the worms to the liver (89%) than ether (76%) and chlorophorm (34%) did, when compared to the control group (22%). The difference between pentobarbital sodium and ether was significant (p < 0.05). We suggest that anesthetic drugs may not be used in studies on the distribution of adult worms in several hosts.<br>Comparou-se o efeito de drogas anestésicas na localização de vermes adultos em camundongos albinos. Com 56 dias de infecção os animais foram anestesiados com pentobarbital sódico, éter ou clorofórmio. Imediatamente realizou-se a perfusão, sendo os vermes recolhidos e classificados quanto à localização em fígado ou veia porta e nos vasos mesentéricos. Nossos resultados demonstraram que o pentobarbital sódico produziu maior deslocamento dos vermes para o fígado (89%) do que o éter (76%) e o clorofórmio (34%) quando comparados com o grupo controle (22%). As diferenças para o pentobarbital sódico e o éter foram significativas (P < 0,05). Sugerimos que os anestésicos não sejam utilizados nos estudos sobre a distribuição de vermes adultos nos hospedeiros