Tree decomposition and postoptimality analysis in discrete optimization

TL;DR

This paper explores how tree decomposition and postoptimality analysis can be used to efficiently solve large, sparse discrete optimization problems with tree-structured graphs by generating related problems and exploiting their structure.

Contribution

It introduces local decomposition algorithms for tree-structured DOPs and applies postoptimality techniques to solve related problems efficiently.

Findings

Effective decomposition of large DOPs with tree structure

Utilization of postoptimality analysis for related problem families

Improved solution efficiency for sparse discrete optimization problems

Abstract

Many real discrete optimization problems (DOPs) are $NP$-hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special tructure using decomposition approaches. An important example of decomposition approaches is tree decomposition with local decomposition algorithms using the special block matrix structure of constraints which can exploit sparsity in the interaction graph of a discrete optimization problem. In this paper, discrete optimization problems with a tree structural graph are solved by local decomposition algorithms. Local decomposition algorithms generate a family of related DO problems which have the same structure but differ in the right-hand sides. Due to this fact, postoptimality techniques in DO are applied.