What Route Optimization Algorithm Does TREK Use for Day Planning?

TREK uses a greedy nearest-neighbor heuristic implemented in the optimizeRoute function to reorder day-planning waypoints, running entirely client-side with O(N²) time complexity.

TREK is an open-source travel planning application that includes an interactive day-planning feature for optimizing travel routes. When users click the "Optimize" button to reorder their daily stops, the application executes a lightweight route optimization algorithm that balances computational speed with practical route quality. This algorithm is implemented in the RouteCalculator component and processes waypoint coordinates directly in the browser without requiring external API calls.

How the Nearest-Neighbor Algorithm Works

The day-planning route optimization in client/src/components/Map/RouteCalculator.ts follows a four-step greedy process:

1. Collects all waypoints for the selected day, including places, activities, and hotels.
2. Optionally injects start/end anchors, such as the hotel where the day begins or ends.
3. Runs the nearest-neighbor heuristic:
   • Starts at the start anchor (or the first waypoint if none is specified).
   • Repeatedly selects the closest remaining waypoint using Haversine distance calculations on latitude/longitude coordinates.
   • Appends the selected waypoint to the ordered list and removes it from the pool.
   • Continues until every waypoint is placed.
4. Adds the end anchor (if supplied) after the last waypoint.

Distance Calculation Method

The algorithm uses Haversine distance to determine proximity between waypoints. This method calculates the great-circle distance between two points on a sphere given their latitude and longitude coordinates, providing sufficient accuracy for travel planning without the computational overhead of routing network data.

Implementation in client/src/components/Map/RouteCalculator.ts

The core logic resides in the optimizeRoute function within client/src/components/Map/RouteCalculator.ts. This function accepts an array of waypoints and optional anchor parameters, then returns a reordered array optimized for minimal travel distance between consecutive stops.

// Import the helper
import { optimizeRoute } from '@/components/Map/RouteCalculator';

// Example: a day with three stops, starting/ending at the same hotel
const hotel = { lat: 48.8566, lng: 2.3522 };
const stops = [
  { id: 'museum', lat: 48.8606, lng: 2.3376 },
  { id: 'cafe',   lat: 48.8530, lng: 2.3499 },
  { id: 'park',   lat: 48.8625, lng: 2.2876 },
];

// Optimize, forcing the route to begin and finish at the hotel
const ordered = optimizeRoute(stops, { start: hotel, end: hotel });

console.log(ordered.map(p => p.id));
// → [ 'museum', 'cafe', 'park' ] (example output; actual order depends on distances)

When called without explicit anchors, the algorithm automatically selects the first waypoint as the starting point:

// Using the function without explicit anchors – the algorithm picks the first
// waypoint as the start point.
const ordered = optimizeRoute(stops);
console.log(ordered.map(p => p.id));
// → [ 'cafe', 'museum', 'park' ] (nearest‑neighbor ordering)

Performance and Complexity

The route optimization algorithm runs in O(N²) time complexity, where N represents the number of waypoints. This quadratic performance characteristic makes it suitable for client-side execution even with dozens of stops, ensuring the UI remains responsive during interactive day-planning sessions.

Because the calculation happens entirely in the browser, users receive instant feedback without latency from external routing services. This design prioritizes speed and offline capability over finding the mathematically optimal route.

Algorithm Limitations and Design Trade-offs

TREK does not attempt to solve the full Traveling Salesman Problem (TSP). While a TSP solution would guarantee the absolute shortest possible route, the computational requirements would introduce unacceptable latency for an interactive web application.

Instead, the nearest-neighbor heuristic provides a "good enough" ordering that respects user-specified constraints (start and end points) while maintaining sub-second calculation times. This approach aligns with the application's goal of assisting travel planning rather than solving complex mathematical optimization problems.

Summary

• TREK implements a greedy nearest-neighbor algorithm for day-planning route optimization.
• The optimizeRoute function in client/src/components/Map/RouteCalculator.ts processes waypoint coordinates using Haversine distance calculations.
• Optional start and end anchors allow users to fix specific locations (like hotels) while optimizing intermediate stops.
• The algorithm runs in O(N²) time, making it suitable for client-side execution with instant feedback.
• This approach provides practical route quality without the computational overhead of full TSP solutions.

Frequently Asked Questions

What route optimization algorithm does TREK use for day planning?

TREK uses a nearest-neighbor heuristic implemented in the optimizeRoute function. This greedy algorithm starts at a specified point and repeatedly visits the closest unvisited waypoint until all stops are ordered, providing a fast, client-side solution for travel route planning.

Where is the route optimization logic implemented in the TREK codebase?

The route optimization logic is located in client/src/components/Map/RouteCalculator.ts. This file contains the optimizeRoute function that handles the nearest-neighbor calculations and distance computations using the Haversine formula. Additional test coverage exists in client/src/components/Map/RouteCalculator.test.ts and client/tests/integration/hooks/useRouteCalculation.test.ts.

Does TREK solve the Traveling Salesman Problem for route optimization?

No, TREK does not implement a full Traveling Salesman Problem (TSP) solution. While TSP algorithms guarantee the optimal route, they are computationally expensive. TREK's nearest-neighbor approach provides a near-optimal solution that calculates instantly in the browser, which is more appropriate for interactive travel planning.

Can I specify custom start and end points when optimizing a day plan?

Yes, the optimizeRoute function accepts optional start and end anchor parameters. When provided, the algorithm fixes these locations as the beginning and end of the route, then optimizes the ordering of intermediate waypoints between them. If no anchors are specified, the algorithm uses the first waypoint as the starting point.

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