Implement EV Routing Objective Function

I have been studying the article “Joint Routing and Charging Problem of Multiple Electric Vehicles: A Fast Optimization Algorithm” and now need a clear, well-documented MATLAB function that reproduces the objective function exactly as presented in the paper.

The code should:
• Translate every term in the paper’s mathematical formulation, including routing, charging, and energy-related components.
• Accept generic inputs (matrices or vectors) for vehicle paths, charging-station parameters, battery capacities, and travel distances, so I can plug in real or simulated data later.
• Return the single scalar objective value and, if helpful, a structure breaking down the major cost components for quick debugging.
• Be thoroughly commented, mapping each line to its corresponding equation number or symbol in the publication.
• Include a short driver script that feeds the function with a small, reproducible data set (you may invent reasonable sample numbers) to show it works out of the box.

Acceptance criteria
– The function compiles and runs in MATLAB R2021a or newer without extra toolboxes.
– Recreates the example objective value from the paper (or an internally consistent test case) within numerical tolerance.
– Code is clean, vectorised where practical, and easy to extend for future algorithmic work.