Block local elimination algorithms for solving sparse discrete optimization problems

TL;DR

This paper introduces block local elimination algorithms for sparse discrete optimization, demonstrating their efficiency in solving large-scale problems faster than traditional methods through benchmarking and analysis.

Contribution

The paper presents a novel combination of block elimination algorithms with the SYMPHONY solver, enhancing the solution speed for large sparse integer linear programming problems.

Findings

Block elimination algorithms outperform standard solvers for large problems.

Efficiency depends on the number of blocks and separator sizes.

Postoptimal analysis improves solving efficiency for problem packages.

Abstract

Block elimination algorithms for solving sparse discrete optimization problems are considered. The numerical example is provided. The benchmarking is done in order to define real computational capabilities of block elimination algorithms combined with SYMPHONY solver. Analysis of the results show that for sufficiently large number of blocks and small enough size of separators between the blocks for staircase integer linear programming problem the local elimination algorithms in combination with a solver for solving subproblems in blocks allow to solve such problems much faster than used solver itself for solving the whole problem. Also the capabilities of postoptimal analysis (warm starting) are considered for solving packages of integer linear programming problems for corresponding blocks.