Application and Assessment of Divide-and-Conquer-based Heuristic Algorithms for some Integer Optimization Problems

TL;DR

This paper develops and evaluates three divide-and-conquer heuristic algorithms for three integer optimization problems, analyzing their computational efficiency and accuracy through empirical experiments.

Contribution

It introduces new divide-and-conquer heuristics for d-KP, BPP, and TSP, with comprehensive performance assessment.

Findings

Algorithms show competitive computational times.

Heuristics achieve acceptable accuracy levels.

Performance varies across different problem instances.

Abstract

In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for three integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing Problem (BPP) and Travelling Salesman Problem (TSP). For each case, the algorithm is introduced, together with the design of numerical experiments, in order to empirically establish its performance from both points of view: its computational time and its numerical accuracy.