FLSSS: A Novel Algorithmic Framework for Combinatorial Optimization Problems in the Subset Sum Family

TL;DR

FLSSS introduces a flexible, efficient algorithmic framework implemented in R for solving complex subset sum and related combinatorial optimization problems, emphasizing adaptability, speed, and low memory usage.

Contribution

The paper presents a novel, adaptive combinatorial space compression algorithmic framework, including multidimensional extensions and multithreading support, for solving subset sum and related problems.

Findings

Provides exact solutions for multidimensional knapsack and generalized assignment problems.

Achieves rapid convergence through combinatorial space compression and data-driven adaptations.

Supports multithreading with trivial space complexity data structures.

Abstract

This article details the algorithmics in FLSSS, an R package for solving various subset sum problems. The fundamental algorithm engages the problem via combinatorial space compression adaptive to constraints, relaxations and variations that are often crucial for data analytics in practice. Such adaptation conversely enables the compression algorithm to drain every bit of information a sorted superset could bring for rapid convergence. Multidimensional extension follows a novel decomposition of the problem and is friendly to multithreading. Data structures supporting the algorithms have trivial space complexity. The framework offers exact algorithms for the multidimensional knapsack problem and the generalized assignment problem.