How does an agent formulate a problem?

In artificial intelligence (AI) and machine learning, an agent is an entity that perceives its environment, processes information and acts upon that environment to achieve specific goals. The process by which an agent formulates a problem is critical, as it lays the foundation for the agent's decision-making and problem-solving capabilities.

This article explores the steps and considerations involved in problem formulation by an intelligent agent.

Understanding Problem Formulation

Problem formulation is the process by which an agent defines the task it needs to solve. This involves specifying the initial state, goal state, actions, constraints, and the criteria for evaluating solutions. Effective problem formulation is crucial for the success of the agent in finding optimal or satisfactory solutions.

Steps in Problem Formulation

1. Define the Initial State: The initial state is the starting point of the agent. It includes all the relevant information about the environment that the agent can perceive and use to begin the problem-solving process.
   • Example: In a navigation problem, the initial state could be the agent's starting location on a map.
2. Specify the Goal State: The goal state defines the desired outcome that the agent aims to achieve. It represents the condition or set of conditions that signify the completion of the task.
   • Example: For the navigation problem, the goal state is the destination location.
3. Determine the Actions: Actions are the set of operations or moves that the agent can perform to transition from one state to another. Each action should be well-defined and feasible within the given environment.
   • Example: In a robot navigation scenario, actions could include moving forward, turning left, or turning right.
4. Establish the Transition Model: The transition model describes how the environment changes in response to the agent's actions. It defines the rules that govern state transitions.
   • Example: In a game, the transition model would include the rules that specify how the game state changes based on the player's moves.
5. Set Constraints and Conditions: Constraints are the limitations or restrictions within which the agent must operate. These can include physical limitations, resource constraints, and safety requirements.
   • Example: For a delivery drone, constraints might include battery life, weight capacity, and no-fly zones.
6. Define the Cost Function (if applicable): The cost function evaluates the cost associated with different actions or paths. It helps the agent to optimize its strategy by minimizing or maximizing this cost.
   • Example: In route planning, the cost function could represent the distance traveled, time taken, or energy consumed.
7. Criteria for Success: The criteria for success determine how the agent evaluates its progress and final solution. This includes metrics for measuring the effectiveness and efficiency of the solution.
   • Example: For a puzzle-solving agent, success criteria could be the completion of the puzzle within the shortest time or the fewest moves.

Example: Problem Formulation for a Package Delivery by an Autonomous Drone

We will demonstrate how to formulate the problem of package delivery by an autonomous drone, implementing the concepts in Python code. The drone needs to navigate from an initial location to a customer's location while avoiding no-fly zones and managing its battery life.

Step 1: Define the Initial State

The initial state includes the drone's starting location and its battery level.

We create a Drone class with an initializer (__init__ method) that sets the initial location, battery level, no-fly zones, and goal location.

class Drone:
    def __init__(self, initial_location, battery):
        self.location = initial_location
        self.battery = battery
        self.no_fly_zones = [(2, 3), (3, 3)]
        self.goal_location = (5, 5)  # Changed to coordinates for consistency

Step 2: Define Actions and Transition Model

The drone can take various actions such as taking off, landing, and moving in different directions. The transition model updates the drone's state based on the action taken.

The takeoff, land, and move methods define how the drone's state changes with each action. The transition_model method uses these actions to update the drone's state.

def takeoff(self):
    if self.battery > 20:
        self.location = 'airborne'
        self.battery -= 1

def land(self):
    self.location = 'ground'
    self.battery -= 1

def move(self, direction):
    if self.battery <= 20:
        return  # Battery constraint
    if self.location == 'airborne':  # Ensure the drone is airborne before moving
        x, y = self.location
        if direction == "up":
            new_location = (x, y + 1)
        elif direction == "down":
            new_location = (x, y - 1)
        elif direction == "left":
            new_location = (x - 1, y)
        elif direction == "right":
            new_location = (x + 1, y)
        
        if new_location not in self.no_fly_zones:
            self.location = new_location
            self.battery -= 1

def transition_model(self, action):
    if action == "takeoff":
        self.takeoff()
    elif action == "land":
        self.land()
    else:
        self.move(action)

Step 3: Define the Goal State and Objective Function

The goal state is the customer's location. The objective function evaluates the drone's performance based on whether it reaches the goal and the remaining battery life.

The objective_function method returns a high score if the drone reaches the goal and otherwise returns the remaining battery level.

def objective_function(self):
    if self.location == self.goal_location:
        return 100  # High score for reaching the goal
    return self.battery  # Otherwise, prefer states with more battery remaining

Complete Implementation

Now let's put the problem formulation for a package delivery by an autonomous drone into practice:

We instantiate a Drone, execute a sequence of actions, and print the final location, battery level, and objective function score.

class Drone:
    def __init__(self, initial_location, battery):
        self.location = initial_location
        self.battery = battery
        self.no_fly_zones = [(2, 3), (3, 3)]
        self.goal_location = 'customer_location'

    def takeoff(self):
        if self.battery > 20:
            self.location = 'airborne'
            self.battery -= 1

    def land(self):
        self.location = 'ground'
        self.battery -= 1

    def move(self, direction):
        if self.battery <= 20:
            return  # Battery constraint
        if direction == "up":
            self.location = (self.location[0], self.location[1] + 1)
        elif direction == "down":
            self.location = (self.location[0], self.location[1] - 1)
        elif direction == "left":
            self.location = (self.location[0] - 1, self.location[1])
        elif direction == "right":
            self.location = (self.location[0] + 1, self.location[1])
        self.battery -= 1

    def transition_model(self, action):
        if action == "takeoff":
            self.takeoff()
        elif action == "land":
            self.land()
        else:
            self.move(action)

    def objective_function(self):
        if self.location == self.goal_location:
            return 100  # High score for reaching the goal
        return self.battery  # Otherwise, prefer states with more battery remaining

# Example usage
drone = Drone(initial_location=(0, 0), battery=100)
actions = ["takeoff", "move_up", "move_right", "move_up", "land"]

for action in actions:
    drone.transition_model(action)

print(f"Final Location: {drone.location}, Battery: {drone.battery}")
print(f"Objective Function Score: {drone.objective_function()}")

Output:

Final Location: ground, Battery: 95
Objective Function Score: 95

Importance of Problem Formulation

Effective problem formulation is essential because:

• Clarity: It provides a clear understanding of the problem, making it easier to devise a solution.
• Efficiency: Proper formulation can significantly reduce the computational resources required to solve the problem.
• Optimal Solutions: It helps in finding the most optimal or satisfactory solution by accurately defining the goals and constraints.

Challenges in Problem Formulation

• Incomplete Information: The agent may not have access to all the necessary information about the environment.
• Dynamic Environments: The environment may change unpredictably, requiring the agent to adapt its problem formulation.
• Complex Constraints: Managing and incorporating complex constraints can be challenging.

Conclusion

A key step in artificial intelligence is problem formulation, which has a big influence on how well an agent completes its duties. An agent may efficiently traverse its environment and accomplish desired results by providing precise definitions for the starting state, actions, target state, restrictions, transition model, and objective function. By using a structured approach, the agent is guaranteed to be able to tackle complicated issues methodically and make well-informed judgments that result in effective and efficient solutions. The examples given show how issue formulation is used in a variety of contexts, underscoring its adaptability and significance in the area of artificial intelligence. Problem formulation techniques will continue to be essential to creating intelligent agents that can solve an ever-expanding array of problems as AI develops.