MILP Optimization - Minimizing Travel Route Optimization

• Goal: To construct a path that has the shortest distance.
  Here I implemented Pyomo framework to solve the Mixed-Integer Linear Programming(MILP) optimization problem, and make comparison with Greedy Algorithm.
  

Directed Diagram:

Steps:

1. Define Parameters, Variables, and Sets. (see notebook)
2. Mathematical formulation: Define object function and constraints.(see notebook)
3. Optimization programming.

The solution by Pyomo framework with total distance 20.

The solution by Greedy Heuristic Algorithm with total distance 25.

Conclusion:

1. With Pyomo framework, we got the optimal solution 20.
2. Through Greedy Heuristic Algorithm, we got the optimal solution 25, which demonstrates there is no algorithms that always provides the best solution. It depends on the problem statement and objective.