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A Hybrid Genetic Algorithm with Type-Aware Chromosomes for Traveling Salesman Problems with Drone

Sasan Mahmoudinazlou, Changhyun Kwon

TL;DR

The paper presents a Hybrid Genetic Algorithm with Type-Aware Chromosomes (HGA-TAC) to solve the Traveling Salesman Problem with Drone (TSPD) and Flying Sidekick TSP (FSTSP). It introduces a three-layer architecture where GA handles truck/drone sequencing via a Type-Aware Chromosome, DP (Join) computes optimal drone rendezvous points with $O(n^2)$ complexity, and LS provides local improvements, yielding faster and more exploration-rich solutions. Empirical results on five benchmark sets show competitive performance, with the method solving the largest number of instances to date and achieving new best solutions in many cases; an escape strategy further improves performance on larger instances. The work demonstrates the effectiveness of dividing decision-making across GA, DP, and LS, and introduces TAC, TOX crossovers, and new LS neighborhoods as core innovations, with potential for extension to multiple drones or fleets.

Abstract

There are emerging transportation problems known as the Traveling Salesman Problem with Drone (TSPD) and the Flying Sidekick Traveling Salesman Problem (FSTSP) that involve using a drone in conjunction with a truck for package delivery. This study presents a hybrid genetic algorithm for solving TSPD and FSTSP by incorporating local search and dynamic programming. Similar algorithms exist in the literature. Our algorithm, however, considers more sophisticated chromosomes and less computationally complex dynamic programming to enable broader exploration by the genetic algorithm and efficient exploitation through dynamic programming and local search. The key contribution of this paper is the discovery of how decision-making processes for solving TSPD and FSTSP should be divided among the layers of genetic algorithm, dynamic programming, and local search. In particular, our genetic algorithm generates the truck and the drone sequences separately and encodes them in a type-aware chromosome, wherein each customer is assigned to either the truck or the drone. We apply local search to each chromosome, which is decoded by dynamic programming for fitness evaluation. Our new algorithm is shown to outperform existing algorithms on most benchmark instances in both quality and time. Our algorithms found the new best solutions for 538 TSPD instances out of 920 and 74 FSTSP instances out of 132.

A Hybrid Genetic Algorithm with Type-Aware Chromosomes for Traveling Salesman Problems with Drone

TL;DR

The paper presents a Hybrid Genetic Algorithm with Type-Aware Chromosomes (HGA-TAC) to solve the Traveling Salesman Problem with Drone (TSPD) and Flying Sidekick TSP (FSTSP). It introduces a three-layer architecture where GA handles truck/drone sequencing via a Type-Aware Chromosome, DP (Join) computes optimal drone rendezvous points with complexity, and LS provides local improvements, yielding faster and more exploration-rich solutions. Empirical results on five benchmark sets show competitive performance, with the method solving the largest number of instances to date and achieving new best solutions in many cases; an escape strategy further improves performance on larger instances. The work demonstrates the effectiveness of dividing decision-making across GA, DP, and LS, and introduces TAC, TOX crossovers, and new LS neighborhoods as core innovations, with potential for extension to multiple drones or fleets.

Abstract

There are emerging transportation problems known as the Traveling Salesman Problem with Drone (TSPD) and the Flying Sidekick Traveling Salesman Problem (FSTSP) that involve using a drone in conjunction with a truck for package delivery. This study presents a hybrid genetic algorithm for solving TSPD and FSTSP by incorporating local search and dynamic programming. Similar algorithms exist in the literature. Our algorithm, however, considers more sophisticated chromosomes and less computationally complex dynamic programming to enable broader exploration by the genetic algorithm and efficient exploitation through dynamic programming and local search. The key contribution of this paper is the discovery of how decision-making processes for solving TSPD and FSTSP should be divided among the layers of genetic algorithm, dynamic programming, and local search. In particular, our genetic algorithm generates the truck and the drone sequences separately and encodes them in a type-aware chromosome, wherein each customer is assigned to either the truck or the drone. We apply local search to each chromosome, which is decoded by dynamic programming for fitness evaluation. Our new algorithm is shown to outperform existing algorithms on most benchmark instances in both quality and time. Our algorithms found the new best solutions for 538 TSPD instances out of 920 and 74 FSTSP instances out of 132.
Paper Structure (23 sections, 1 theorem, 2 equations, 8 figures, 11 tables, 4 algorithms)

This paper contains 23 sections, 1 theorem, 2 equations, 8 figures, 11 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Problem Statement
  4. Common Assumptions
  5. Problem-Specific Assumptions
  6. A Hybrid Genetic Algorithm with Type-Aware Chromosomes
  7. Type-Aware Chromosome Encoding
  8. Generating Initial Subpopulations
  9. Decoding and Evaluating Chromosomes by Dynamic Programming
  10. Parent Selection, Crossover, and Mutation
  11. Improvement by Local Search
  12. Population Management
  13. Penalty adjustment.
  14. Diversification.
  15. Escape Strategy
  16. ...and 8 more sections

Key Result

Lemma 1

By using the Join algorithm for a given chromosome where the sequence and types of the vehicles are known, TSPD (or FSTSP) solutions can be determined in time $O(n^2)$.

Figures (8)

  • Figure 1: A network with one depot and 5 customers solved by TSP and TSPD.
  • Figure 2: For a network of one depot and 10 customers, the figure in (a) is the solution representation, and (b) is the same solution shown on network.
  • Figure 3: An instance illustrating the notation used in the DP approach
  • Figure 4: Comparing the structure of our approach to TSP-ep-all in agatz2018optimization and HGA20 in ha2020hybrid
  • Figure 5: Examples of the type-aware order crossover operations, TOX1 and TOX2
  • ...and 3 more figures

Theorems & Definitions (1)

  • Lemma 1