Travelling Salesman Problem PDF
Preview Travelling Salesman Problem
Optimizing Autonomous Drone Delivery Application of the Travelling Salesman Problem to an emerging Issue ABHINAV SINHA Why Address Drone delivery? • It is an upcoming sector in the consumer industry with a lot of potential • There are real world constraints that make it a challenging application to scale • Delivery Drones are expensive to acquire, requiring optimal usage • Payload parameters are defined, adding limitations • Total flight time is limited, reducing the total number of “Home Trips” Problem Statement • Application: Autonomous Drones • Constraints: • Travel Distance • Payload • Flight time/Battery Capacity * Note: Payload and Flight time are inversely related DJI S900 • Acquisition Cost: $1400 • Max Payload: 18-pound payload • Max Flight Time at full payload: 10 minutes full payload • Notable Design Features: 900 cm wing span Pros/Cons: Required frequent charging for longer trips FreeFly Alta 6 • Acquisition Cost: $12000 • Max Payload: 20-pound payload • Max Flight Time @ full payload: 18 minutes full payload • Notable Design Features: Compact design • Pro: State of the art • Con: Not scalable What is the Travelling Salesman Problem (TSP) • A Common optimization model of a salesman who must visit ‘X’ cities while minimizing total distance travelled. • Applications range from straightforward (1 salesman) to computationally intense (Multiple Agents and constraints) • Also referred to as travelling purchaser problem and the vehicle routing problem. Basic TSP Model • N cities, 1 salesman • Problem is considered NP- Hard • Naïve solution – find all (n-1)! Routes • Calculate cost and return minimum cost • Works for one agent Approach to problem • Implement a basic TSP model, one agent (Drone) multiples nodes • Add constraints one at a time • Test model on a small scale • Add agents (Drones) as the model gets bigger • Add nodes (Destinations) and test optimal paths • Create a visualization/simulation of model. • Use the Austin street data to plot the networks Objectives and Constraints • Objectives: • Constraints: • Minimize cost of Delivery • Weight of Payload • Complete all deliveries • Flight time • Minimal recharges • Proximity to Charge station • Number of delivery agents available • Expected time to delivery General tsp Model • Constraint 1, 2 – each node has only one entering and exiting edge • Constraint 3, 4 – Number of drones leaving is the number entering
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