Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Rabab Alkhalifa, Fatima Alkhomayes, Boushra Almazroua, Dana Alhaidan, Maryam Alothman, Jumana Almuhaidib

TL;DR

This paper addresses the scalability gap in solving the Traveling Salesman Problem (TSP) by surveying parallel approaches across exact, heuristic, hybrid, and emerging ML-augmented methods. It details parallel exact solvers (e.g., branch-and-bound) and their memory/time limits, alongside parallel heuristics (GA, ACO, SA, TS) with GPU and multi-core acceleration. Hybrid metaheuristics and emerging techniques (ML-guided policies, Graph Neural Networks, reinforcement learning, and quantum-inspired methods) are highlighted as promising for large-scale TSP, supported by discussions of integration strategies and performance metrics. The work emphasizes standardized benchmark datasets, diverse evaluation measures, and open challenges (load balancing, generalization, benchmarking), advocating adaptive, data-driven, and quantum-classical hybrid solvers for scalable real-world optimization. Overall, the findings suggest that GPU-accelerated hybrids offer the strongest practical balance between solution quality and efficiency, while exact methods remain valuable for small-to-moderate instances and for validating optimality.

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.

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

TL;DR

This paper addresses the scalability gap in solving the Traveling Salesman Problem (TSP) by surveying parallel approaches across exact, heuristic, hybrid, and emerging ML-augmented methods. It details parallel exact solvers (e.g., branch-and-bound) and their memory/time limits, alongside parallel heuristics (GA, ACO, SA, TS) with GPU and multi-core acceleration. Hybrid metaheuristics and emerging techniques (ML-guided policies, Graph Neural Networks, reinforcement learning, and quantum-inspired methods) are highlighted as promising for large-scale TSP, supported by discussions of integration strategies and performance metrics. The work emphasizes standardized benchmark datasets, diverse evaluation measures, and open challenges (load balancing, generalization, benchmarking), advocating adaptive, data-driven, and quantum-classical hybrid solvers for scalable real-world optimization. Overall, the findings suggest that GPU-accelerated hybrids offer the strongest practical balance between solution quality and efficiency, while exact methods remain valuable for small-to-moderate instances and for validating optimality.

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.

Paper Structure

This paper contains 31 sections, 13 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Parallel Optimization Techniques in TSP
  3. Parallel Exact Algorithms
  4. Parallel Heuristic and Metaheuristic Algorithms
  5. Genetic Algorithms (GA)
  6. Ant Colony Optimization (ACO)
  7. Simulated Annealing (SA)
  8. Tabu Search (TS)
  9. Hybrid Metaheuristics & Emerging Techniques
  10. Benchmark Datasets for Parallel TSP Optimization
  11. Evaluation Measures for Parallel TSP Optimization
  12. General Performance Metrics
  13. Execution Time and Speedup
  14. Scalability Metrics
  15. Solution Optimality
  16. ...and 16 more sections

Figures (1)

  • Figure 1: Modeling intercity distances as weighted edges in a complete graph. Example cities across Saudi Arabia serve as vertices with edges weighted by travel costs.