Inter Programming Models for the Target Visitation Problem

The target visitation problem (TVP) is concerned with finding a route to visit a set of targets starting from and returning to some base. In addition to the distance traveled a tour is evaluated by taking also preferences into account which address the sequence in which the targets are visited. The problem thus is a combination of two well-known combinatorial optimization problems: the traveling salesman and the linear ordering problem. In this paper we point out some polyhedral properties and develop a branch-andcut algorithm for solving the TVP to optimality. Some computational results are presented.

[1]  Dinggang Shen,et al.  Sampling the spatial patterns of cancer: Optimized biopsy procedures for estimating prostate cancer volume and Gleason Score , 2009, Medical Image Anal..

[2]  Kari Tanderup,et al.  Applicator reconstruction in MRI 3D image-based dose planning of brachytherapy for cervical cancer. , 2009, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[3]  N. Reed,et al.  A Review of Recent Developments in Image-Guided Radiation Therapy in Cervix Cancer , 2012, Current Oncology Reports.

[4]  Richard Pötter,et al.  Image-guided brachytherapy sets benchmarks in advanced radiotherapy. , 2009, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[5]  Christos Davatzikos,et al.  Multilevel Functional Principal Component Analysis for High-Dimensional Data , 2011, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[6]  Yen-Wei Chen,et al.  Appearance Models for Medical Volumes with Few Samples by Generalized 3D-PCA , 2007, ICONIP.

[7]  W. Eric L. Grimson,et al.  Coupling Statistical Segmentation and PCA Shape Modeling , 2004, MICCAI.

[8]  Kevin J. Parker,et al.  Analysis of the spatial distribution of prostate cancer obtained from histopathological images , 2013, Medical Imaging.

[9]  M. B. Opell,et al.  Investigating the distribution of prostate cancer using three-dimensional computer simulation , 2002, Prostate Cancer and Prostatic Diseases.

[10]  Edward Jones,et al.  Investigation of Classifiers for Early-Stage Breast Cancer Based on Radar Target Signatures , 2010 .

[11]  Luis Mateus Rocha,et al.  Singular value decomposition and principal component analysis , 2003 .