Path De-Crossing After Solving TSP Problems with Ant Colony Optimization

Ant Colony Optimization (ACO) is an intelligent optimization algorithm that simulates ant foraging behavior, commonly used for solving Traveling Salesman Problems (TSP). In TSP problems, the objective is to find the shortest path that visits all cities exactly once. The ATT48 dataset serves as a standard benchmark for TSP, containing coordinate information for 48 cities.

After solving TSP using Ant Colony Algorithm, the resulting path might still contain crossovers - situations where path segments intersect, potentially leading to suboptimal total length. De-crossing serves as a post-processing optimization technique designed to detect and eliminate path crossovers, thereby further reducing the total path length.

The implementation of de-crossing typically involves two main steps: Crossover Detection: Iterate through all path segments to check for intersections. A common implementation approach uses geometric calculations to determine segment intersections, often employing the cross product method or line equation comparisons in code. Crossover Correction: When crossovers are detected, swap the order of subpaths to eliminate intersections. For example, if the path crosses between segments A→B and C→D, the path can be adjusted from A→B→…→C→D to A→C→…→B→D. This can be implemented using array manipulation functions to reverse subarray segments between crossover points.

This optimization method significantly enhances path quality beyond the basic Ant Colony Algorithm solution, particularly effective for medium-scale TSP problems like ATT48, where it can achieve better solutions within reasonable computational time frames.