Fifty Years of Integer Programming: A Review of the Solution Approaches

Abstract

Many scientific, industrial engineering and economic problems may be cast into an integer-programming model. This paper attempts to review various approaches that have been developed for solving this model, emphasizing on the methodological view. For the sake of space, we restrict ourselves mainly to the pure integer-programming problem. The paper is expository in nature and it includes many references to give credit to essential results in the field and help readers obtain more detailed information on issues of interest.

Parameterizing the Angular Distribution of Emission: A model for TOF-PET low counts reconstruction

“…The parametrization of the PADE model enables a more accurate use of the integer nature of counts by circumventing the R ji λ i approximation in the log-likelihood term. While the number of variables for the PADE model is definitely in the high end for integer programming, which is known as a NP-Hard problem, multiple heuristic methods have been successfully developed for diverse integer optimization problems and an in-depth investigation of its state-of-the-art might provide fruitful solutions [23], [24]. Other approaches could also be investigated, such as origin ensemble that was already applied to TOF-PET reconstruction [25] or machine learning methods which have already shown their potential for PET reconstruction [26].…”

Computational Enhancement in the Application of the Branch and Bound Method for Linear Integer Programs and Related Models

“…Many approaches have been developed to reduce computational effort and time required to get to the optimal solution. Some of the well-known approaches for integer programming problems are by Kelley (1960), Mitten (1970), Taha (2003), Kumar et al (2010), Kumar and Munapo (2012). For larger integer programs, see the column generation procedure by Barnhart et al (2018).…”