A Comparative Review of Parallel Exact, Heuristic, Metaheuristic, and Hybrid Optimization Techniques for the Traveling Salesman Problem

TL;DR

This paper reviews various parallel optimization techniques for the NP-hard Traveling Salesman Problem, comparing exact, heuristic, metaheuristic, and hybrid methods, and discusses future research directions including deep learning and quantum-inspired algorithms.

Contribution

It provides a comprehensive comparative evaluation of parallel TSP algorithms and introduces new evaluation metrics for cross-paradigm analysis.

Findings

Hybrid metaheuristics show improved scalability.

Task-specific metrics enable better method comparison.

Future directions include deep learning and quantum-inspired approaches.

Abstract

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances requires scalable and efficient algorithmic frameworks, often enabled by parallel computing. This literature review provides a comparative evaluation of parallel TSP optimization methods, including exact algorithms, heuristic-based approaches, hybrid metaheuristics, and machine learning-enhanced models. In addition, we introduce task-specific evaluation metrics to facilitate cross-paradigm analysis, particularly for hybrid and adaptive solvers. The review concludes by identifying research gaps and outlining future directions, including deep learning integration, exploring quantum-inspired algorithms, and establishing reproducible evaluation frameworks to support scalable and adaptive TSP optimization in real-world scenarios.