Solving Multiple Traveling Salesman Problem with MATLAB

The Multiple Traveling Salesman Problem (MTSP) is an extension of the classic Traveling Salesman Problem, involving multiple salesmen visiting a set of cities and returning to their starting point. It is commonly applied in route planning, logistics distribution, and similar scenarios. MATLAB, with its powerful matrix computation capabilities and optimization toolbox, can efficiently solve such combinatorial optimization problems.

The core approach to solving MTSP using MATLAB typically includes: Problem Modeling: Convert city coordinates into a distance matrix, define objective functions (e.g., minimize total path length) and constraints (e.g., each city visited exactly once). MATLAB's matrix operations enable rapid processing of large-scale distance calculations using functions like `pdist2` for Euclidean distance computation. Algorithm Selection: Implement metaheuristic algorithms such as Genetic Algorithm (`ga`), Simulated Annealing, or Ant Colony Optimization. MATLAB's Global Optimization Toolbox provides built-in functions like `ga`, which can directly handle constrained MTSP by defining custom fitness functions and constraint matrices. Result Visualization: Use MATLAB's plotting functions (`plot`, `scatter`) to visualize multiple salesmen's routes, clearly displaying city assignments and path connections with different colors or markers.

Key Advantages: Matrix Computation: MATLAB's vectorized operations efficiently handle distance matrix calculations and path evaluation through array operations without loops. Flexible Extension: Supports customization of objective functions (e.g., balancing workloads among salesmen) and dynamic constraints using anonymous functions or external function files.

Extension Directions: Integrate `k-means` clustering for preliminary city allocation to reduce problem complexity using MATLAB's Statistics and Machine Learning Toolbox (`kmeans` function). Utilize Parallel Computing Toolbox (`parfor` loops) to accelerate solution processes for large-scale MTSP instances through multi-core processing.