Learning-Guided Iterated Local Search for Minmax Multiple Traveling Salesman Problem

Belangrijkste concepten

Proposing a learning-guided iterated local search approach for the minmax multiple traveling salesman problem to achieve high-quality solutions efficiently.

Samenvatting

This article introduces a novel approach to solving the minmax multiple traveling salesman problem using a learning-guided iterated local search algorithm. The algorithm combines aggressive local search with probabilistic acceptance criteria and a multi-armed bandit algorithm for operator selection. Extensive experiments demonstrate the algorithm's effectiveness in achieving new best-known results on benchmark instances.

Structure:

1. Introduction to Minmax mTSP
2. Previous Studies on Minmax mTSP
3. Proposed Learning-Guided Iterated Local Search Algorithm
4. Experimental Evaluation and Comparison with Reference Algorithms
5. Additional Experiments:
   • Rationale behind the local search procedure
   • Rationale behind the Multi-Armed Bandit (MAB) algorithm
   • Convergence analysis of MILS algorithm

Statistieken

"Extensive experiments on 77 commonly used benchmark instances show that our algorithm achieves excellent results in terms of solution quality and running time."
"The proposed multi-armed bandit guided iterated local search (MILS) consists of several complementary search components."

Citaten

"The proposed multi-armed bandit guided iterated local search (MILS) consists of several complementary search components."
"Extensive experiments on 77 commonly used benchmark instances show that our algorithm achieves excellent results in terms of solution quality and running time."

Belangrijkste Inzichten Gedestilleerd Uit

Learning-guided iterated local search for the minmax multiple traveling salesman problem

by Pengfei He,J... om arxiv.org 03-20-2024

https://arxiv.org/pdf/2403.12389.pdf

Diepere vragen

How can dynamic radius search improve the computational efficiency of the local search component

Dynamic radius search can improve the computational efficiency of the local search component by dynamically adjusting the search radius based on the problem instance's characteristics. By adapting the neighborhood exploration range according to specific features of the problem, such as density or distribution of cities, dynamic radius search can focus on relevant areas and avoid unnecessary computations in less promising regions. This targeted approach reduces the number of unnecessary evaluations and allows for more efficient exploration of potential solutions. Additionally, dynamic radius search can help in avoiding getting stuck in local optima by intelligently expanding or contracting the search space based on current progress, leading to faster convergence towards high-quality solutions.

What are potential applications of the multi-armed bandit algorithm combined with various operators beyond the minmax mTSP

The multi-armed bandit algorithm combined with various operators has applications beyond just solving minmax mTSP. One potential application is in other combinatorial optimization problems like vehicle routing problems (VRP), where selecting appropriate operators dynamically during a metaheuristic algorithm's execution can lead to improved performance and better solution quality. In VRP scenarios, different neighborhoods or perturbation strategies could be selected using a multi-armed bandit approach to escape local optima efficiently and explore diverse regions of the solution space. Furthermore, this combination could be beneficial in resource allocation problems, scheduling tasks with multiple objectives, portfolio optimization in finance, and even reinforcement learning settings where adaptive decision-making is crucial.

Why are efficient exact algorithms still lacking for the minmax mTSP, and how can research address this gap

Efficient exact algorithms are still lacking for minmax mTSP due to its inherent complexity and NP-hard nature. The challenge lies in finding optimal solutions within reasonable time frames for large-scale instances while guaranteeing optimality without compromising computational resources extensively. Research efforts aimed at addressing this gap could focus on developing hybrid approaches that combine exact methods with heuristic techniques to handle both small-scale instances optimally and larger instances efficiently through approximation methods or intelligent branching strategies within branch-and-bound frameworks. Moreover, advancements in mathematical modeling techniques tailored specifically for minmax objectives may offer new insights into formulating tighter relaxations or cutting planes that enhance exact algorithms' performance when solving complex instances of minmax mTSP.