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BFS vs A*, Help Mario 👨⚠‼ Save the princess 👸

Prerequisites:

  • Conda 4.9.2
  • JetBrains IDE
  • If you don't have conda, then maybe you will need to install flask

Installation

  • Open a terminal in the folder named "a-star-mario-dussan"
  • Write the following command: "python app.py"
  • Click on the URL or open your localhost

Project Description

This is a basic web application where you can build your own board which includes pipelines 🏁, walls 🟥 and of course Mario 👨! The main objective of this application is to find the path to the closest pipe and mark the path using BFS and A *, make some comparisons, find the effective effective branch factor and calculate the number of states.

This web application has two basic interfaces:

  1. Menú:
  2. Board:
  • You can load maps with different difficulties
  • You can create your own board with the dimensions that you want and play with the application options 😉:

Agent:

  • Formulation of the objective: Find the closest pipeline using BFS and A*
  • Problem formulation:
    • Initial state: The initial state is a board without any value marked
      • Description of the actions:
        • UP = Move up from the current position ⬆
        • DOWN = Move down from the current position ⬇
        • LEFT = Move left from the current position ⬅
        • RIGHT = Move right from the current position ➡
    • Transitional model:
      • UP: move("up", state.row, state.col) -> state: (row, col + 1)
      • DOWN: move("down", state.row, state.col) -> state: (row, col - 1)
      • LEFT: move("left", state.row, state.col) -> state: (row - 1, col)
      • RIGHT: move("right", state.row, state.col) -> state: (row - 1, col)
    • Target test:
      • Find a pipeline

Heuristic functions used:

  • The heuristics used are based on the dimensions of the board. We could say that this heuristics are admissible because they are based on the board dimensions. However, perhaps with more experiment we could have better heuristics
  • Rect line: if the successor's grandfather, successor father and successor share the same column or row, then the heuristic is lower
  • Near borders 🧱: if the successor is in the border of the boar, then the heuristic is lower
  • Radar 🔍:
    • A fast search is made from mario's position until a pipe it's found, in other words, the context it's found(this search is only made at the beginning or when F cost is high)
    • Once we know the position of the closest pipe, that position is classified that position as:
      • right: In the same row, at right
      • left: In the same row, at left
      • up: In the same col, at up
      • down: In the same col, at down
      • upper_right: upper_right quadrant
      • upper_left: upper_left quadrant
      • down_right: down_right quadrant
      • down_left: down_left quadrant
    • Then a parse is made in order to get a cost from each classification
      • Lower heuristic: right, left, up and down
      • Higher heuristic: upper_right, upper_left, down_right and down_left

Observations 👀:

  • After several experiments, we got the following conclusions:
    • A*, using Radar heuristic, is the one that opens fewer states. However, the A* function is also the one that takes more time to find the solution(In comparisson of the other heuristics). This heuristic has a much better performance when there is not obstacles
    • A*, using Rect line and Near borders Heuristic, have almost the same results in all the cases.
    • BFS, takes less time and more states in almost all the cases (more states are expanded)
    • The difference between A* and BFS are less, when the map has mane obstacles