Heuristic Algorithm for Route Optimization

delivery location. Your task is to design a heuristic algorithm to help optimize the delivery routes for each truck, considering the following constraints:

Each truck has a maximum capacity, and the total weight of deliveries for a truck cannot exceed its capacity.

Each delivery has a specified location with $x$ and $y$ coordinates.

The trucks must start and end at a central warehouse $($location: $(0,0)).$

The goal is to minimize the total distance traveled by each truck during its delivery route.

Delivery locations cannot be visited more than once by the same truck.

total distance traveled.

Task

Design a heuristic algorithm to determine the optimal delivery routes for each truck.

Describe the heuristic you used and explain why it is suitable for this problem.

Implement a Python function that receives a list of trucks $($with their capacities$)$ and a list of deliveries $($with their weights and coordinates$)$ and returns the optimal delivery routes for each truck.

Use the following example data to test your algorithm:

Trucks:

Truck $1$: capacity $1000kg$

Truck $2$: capacity $1500kg$

Deliveries:

Delivery $1$: weight $200kg,$ location $(5,10)$

Delivery $2$: weight $300kg,$ location $(10,5)$

Delivery $3$ : weight $500kg,$ location $(15,10)$

Delivery $4$: weight $700kg,$ location $(20,20)$

Delivery $5$ : weight $400kg,$ location $(25,5)$

Considerations

To find the best heuristic, consider common methods like the "nearest neighbor" heuristic or clustering techniques to group deliveries in a way that reduces travel distance.

Evaluate the algorithm's efficiency and any trade$-$offs it might involve.

Explain the solution's limitations and possible improvements or alternative approaches.