CSE4002 Artificial Intelligence Fundamentals Report Sample

CSE4002 Artificial Intelligence Fundamentals

Assignment Details

Problem Description

Farmer, Wolf, Goat and Cabbage Problem

A farmer has a wolf, a goat, and a cabbage on the east side of a river. He wants to move them to the west side of the river. He has a boat in which he and only one other thing may fit. The wolf will eat the goat if they are left together unattended. The goat will eat the cabbage if they are left together unattended. Generate a plan for the farmer to safely move all items including himself to the west side of the river.

Requirements

The problem must be solved using state space search algorithms implemented in the Python programming language.

Two state space search algorithms: (1) a blind (Depth-First) search and (2) a heuristic (A*) search algorithms must be included to complete the assignment.
The completion of the assignment consists of two steps as listed below.

Step 1 Problem Analysis and Design

Before writing the python code, students are required to perform an analysis in order to determine the best design to solve the problem. This includes

(1) The representation of the state

(2) The representation of the state space (at least 8 levels)

(3) The design of the heuristic evaluation function in the A* algorithm

(4) The strategy to avoid any unsafe states which have been identified in the Problem Description. The problem analysis and design should be documented in the analysis and design document.

Step 2 Coding

Write the Python program to implement the design created in Step 1

The program must implement both Depth-First Search and A* Search algorithms. When running the program, it should output

(1) The state space with each unsafe state marked and made a dead end.

(2) The action plan (the path from the initial state to the goal state) generated by the Depth-first search algorithm.

(3) The action plan generated by the A* algorithm.

Marking Scheme

The assignment will be marked based on the following criteria:

• Quality of the analysis and design document

o Design of the state representation

o Selection of the heuristic function and the effectiveness of the function

o Strategies to avoid unsafe states

o Program Structure design (classes, functions, parameters and output etc.)

Solution

1. Introduction

A well-known puzzle in artificial intelligence and puzzle solving is "Wolf, Goat, and Cabbage". A farmer has to move a wolf, a goat, and some cabbage from the west bank to the east bank of a river in the situation shown in the puzzle. The farmer confronts two major obstacles: the wolf will devour the goat if he leaves it alone on either bank, and his boat can only hold one item at a time. The goat will eat the cabbage if they are left alone on either bank, in a similar manner. The puzzle's goal is to figure out the order in which the three things can be safely transported to the east bank by boat (Tang, G. et al, 2021).

We'll investigate two distinct search algorithms—Depth-First Search (DFS) and the A* algorithm—to tackle this problem. In the case of A* search, both approaches entail creating a heuristic evaluation function, handling safe and unsafe states, and describing the state space.

The organisation of our analysis and design document presents a synopsis of the essential components needed to solve the "Wolf, Goat, and Cabbage" puzzle:

1.1 Status of State Representation:

We define a state in the context of this puzzle as a tuple or list that includes the locations of the items (farmer, wolf, goat, and cabbage) on the east and west sides of the river, together with the riverside where the boat is situated. A state can be written, for instance, as (["W", "G", "C"], [], "west"), which shows the original arrangement with the boat, wolf, goat, and cabbage on the west side.

1.2 State Space Representation:

The state space is shown as a graph, with edges signifying legal acts (such as boat voyages) and nodes representing potential states. We take care to produce child states from parent states in a way that guarantees no repeating states occur in order to prevent cycles in the state space. There are a minimum of eight depth levels in the state space graph.

The heuristic evaluation function (A algorithm) is designed as follows:**

We create a heuristic evaluation function for the A* algorithm that calculates the approximate cost of moving from a current state to the desired state. Our heuristic function for this puzzle is straightforward yet efficient: it counts the number of things that are still on the west side. This heuristic function is OK as long as it never exceeds the true cost (Baswana, S., et al, 2019).

1.3 Preventing dangerous conditions:

Particular dangerous conditions that need to be avoided are listed in the problem description. We carefully incorporate safeguards to keep the puzzle out of these dangerous situations. To make sure that no new states result in dangerous circumstances, these checks are incorporated into the state generation algorithm MBA assignment expert.

We give a thorough rundown of our strategy for applying DFS and the A* algorithm to solve the "Wolf, Goat, and Cabbage" conundrum in this analysis and design document. By elucidating our methods for representing states, designing the state space, developing a heuristic function, and guaranteeing the avoidance of unsafe states, our study aims to set the groundwork for the implementation that follows.

Representation of the State

The "Wolf, Goat, and Cabbage" puzzle requires a strong state representation to be solved. The state includes the arrangement of the objects (farmer, wolf, goat, and cabbage) on the east and west banks of the river, as well as the boat's present position. This form makes it easier to keep track of the puzzle's progress and make sure that every state complies with the problem's limits and rules.

According to our representation, a state is a tuple (or list) made up of the following components:

2.1 Locations of Farmer, Wolf, Goat, and Cabbage:

Lists or sets indicating the items' locations on the corresponding riverbanks are kept on the east and west sides. An initial state, for instance, is expressed as:
["F", "W", "G", "C"] is the west. (On the west side: Farmer, Wolf, Goat, and Cabbage).
east: [] (East side has nothing).

2.2 Boat's Location:

The boat's location is shown as a string with the words "west" or "east" to denote which side it is currently on. The boat is on the west side in its basic state:
location of boat: "west"

Accurate recording of the items' current configuration is ensured by this state representation. The objects will be moved from the west to the east, or vice versa, as you solve the puzzle, and the boat's location will adjust appropriately.

Both the A* algorithm and depth-first search (DFS) rely on the state representation. It provides the foundation for producing child states, evaluating goal circumstances, and guaranteeing a proper and regulated progression of the problem (Khan, 2019).

The following acronyms are used by us for uniformity and clarity:

F: Farmer

W: Wolf

G: Goat

C: Cabbage

With this representation in place, we can efficiently carry out the selected search algorithms and explore the state space.

2. The Representation of the State Space

The whole spectrum of potential states that could arise when solving the "Wolf, Goat, and Cabbage" puzzle is referred to as the state space. Every state denotes a different arrangement of the objects (farmer, wolf, goat, and cabbage) on either side of the river, as well as the position of the boat.

Making ensuring the state space is large enough to accommodate all potential configurations while adhering to the puzzle's rules is an important part of the design process. It becomes critical to properly design in order to control computational complexity as the state space grows quickly (Tang, G. et al, 2021).

To create a structured state space, we define the following elements:

3.1 State Generation:

Transitional objects (farmer, wolf, goat, cabbage) between the east and west banks of the river create states. That means that the position of the boat also shifts. The principle that no dangerous configurations take place during the transition is adhered to in every state transition. Situations in which the goat is left alone with the wolf or the cabbage are considered unsafe states. We guarantee that there are never any dangerous states in the state space by constantly adhering to these guidelines.

3.2 Safe State Identification:

Dead endpoints are denoted with the identification of unsafe states. These are the states that, in our illustration, have the wolf and cabbage on one side and the goat on the other. These states are indicated as dangerous since it would be against the rules to leave the goat alone with the wolf or the cabbage.

3.3 Depth-First Search State Space:

We create a multi-level state space for the Depth-First Search (DFS) algorithm. We build child states iteratively, moving objects across the river while ensuring safety, starting from the initial state (all items on the west side). The search is carried out depth-first, delving as far as feasible before turning around.

3.4 A Algorithm State Space:*

The state space of the A* algorithm is intended to intelligently direct the search. A heuristic evaluation function and the depth are included in the cost assigned to each state. The number of objects that are still on the west side is a common way to gauge the heuristic's distance between the current and objective states. This aids in putting states closer to the objective first when it comes to state exploration.

We preserve control over the puzzle-solving process by guaranteeing the organised form of the state space and designating dangerous states as dead ends. This strategy guarantees that we systematically investigate different state transitions for the DFS algorithm while averting hazardous scenarios. The organised state space and the heuristic evaluation are used in the A* algorithm to direct the search for effective solutions (Liu, C., et al, 2019).

A crucial part of issue analysis is designing the state space, which has an immediate effect on how well the selected algorithms perform in solving the "Wolf, Goat, and Cabbage" challenge.

3. Design of the Heuristic Evaluation Function in the A Algorithm*

Because the A* algorithm can produce optimal solutions by effectively exploring the state space, it is a favoured option for resolving the "Wolf, Goat, and Cabbage" issue. The development of a strong heuristic evaluation function is essential to the A* algorithm's performance. The algorithm can prioritise state exploration and choose the most promising paths by using this function, which calculates the cost to attain the goal from a given state.

We incorporate a heuristic assessment function in our design that considers the following factors:

4.1 Remaining Items on the West Side:

Our heuristic function's major focus is the quantity of things that are still on the west side of the river. All of the items—farmer, wolf, goat, and cabbage—must be on the east side in order to reach the objective state. As a result, the function calculates how many steps are needed to move every item to the east side (Raschka, S., et al, 2020).

4.2 Balancing Complexity and Efficiency:

Although counting the number of things on the west side would be the easiest heuristic, it might not be the most effective one. Rather, we seek a heuristic that strikes a compromise between accuracy and simplicity. Without overly complicating the review process, the number of objects left on the west side offers a clear and useful indicator of progress towards the objective.

4.3 Admissibility and Consistency:

Admissibility and consistency are upheld via the heuristic evaluation function. It makes sure the A* algorithm chooses the best answer by never overestimating the actual cost of achieving the goal. Furthermore, the function is consistent, meaning that the true cost between the current state and the neighbouring state is never less than the estimated cost from the current state to the goal + the heuristic cost from the goal to a neighbouring state.
 
4.4 Integration with State Space Design:

There is close integration between the structured state space design and the heuristic assessment mechanism. It functions under the presumption that dangerous regions have previously been identified as dead ends. As a result, using safe state transitions to estimate the cost is free.

We give a dependable and simple measure of objective progress to the A* algorithm by using the number of items left on the west side as the primary heuristic evaluation. We want to balance efficiency and complexity, and the function's simplicity fits that goal. Furthermore, we ensure that the algorithm will identify optimal solutions by following the consistency and admissibility rules.

One crucial element of the A* algorithm that improves its effectiveness in resolving the "Wolf, Goat, and Cabbage" puzzle is the design of the heuristic evaluation function. It helps the algorithm find the best answer by helping it navigate the state space intelligently and spot potential routes.

4. Strategy to Avoid Unsafe States

In order to solve the "Wolf, Goat, and Cabbage" puzzle, it is essential to guarantee the security and legitimacy of state transitions. This section describes the tactics and factors we take into account to keep ourselves safe when solving puzzles.

5.1 Marking Unsafe States as Dead Ends:

Recognising and marking unsafe states as dead ends in the state space is one of the basic tactics for preventing them. We discover particular state configurations that are deemed dangerous due to their violation of the puzzle's limitations. Among these dangerous conditions are situations in which:

On the same side of the river, the goat and the wolf are abandoned.

On the same side of the river, the cabbage and the goat are abandoned.

We build a technique to identify these unsafe states during the state space exploration so that the algorithm is prevented from traversing them. Upon encountering an unsafe state, the algorithm promptly identifies it as a dead end and stops exploring (Gorjao et al, 2022).

5.2 Validation During State Generation:

We thoroughly validate each freshly created state to make sure the puzzle's requirements are respected throughout the state generation process. To be more precise, prior to including a state in the list of potential transitions, we verify the following conditions:

The unsupervised farmer's presence alongside the wolf or goat.

The unsupervised farmer's presence next to the goat or cabbage.

Any state that deviates from these requirements is seen as dangerous and is not accepted as a legitimate transition. This verification procedure is carried out in the Depth-First Search (DFS) and A* algorithms during the child state creation phase.

5.3 Consistency Across Algorithms:

Both the DFS and A* algorithms use the same approach to prevent dangerous conditions. The same set of dangerous state conditions are identified in both situations, and in order to discourage additional investigation, these states are handled as dead ends. Because of consistency, neither algorithm will explore dangerous states or entertain them as viable solutions.

5.4 Efficient Search and Heuristic-Based Safety:

The A* method uses a heuristic evaluation function, whereas the DFS algorithm searches the state space exhaustively. The A* algorithm is guided by the heuristic, which was described in a previous section, and takes into account the quantity of things that are still on the west side of the river. This method guarantees that the safety component is considered in the heuristic-based state evaluation even in the A* algorithm.

Conclusion

We have successfully created and implemented two efficient algorithms, DFS and A*, to solve the "Wolf, Goat, and Cabbage" puzzle in this succinct analysis. These algorithms produce ideal answers by deftly navigating the state space and making sure that dangerous states are avoided. Our research highlights the usefulness of AI techniques in a variety of real-world contexts by showcasing their capacity to tackle complicated issues successfully. 

Graph for DFS Algo and A* Algo. The cost is same across the nodes. 

References

Tang, G., Tang, C., Zhou, H., Claramunt, C. and Men, S., 2021. R-DFS: A coverage path planning approach based on region optimal decomposition. Remote Sensing, 13(8), p.1525.

Baswana, S., Chaudhury, S.R., Choudhary, K. and Khan, S., 2019. Dynamic DFS in undirected graphs: Breaking the o(m) barrier. SIAM Journal on Computing, 48(4), pp.1335-1363.

Khan, S., 2019. Near optimal parallel algorithms for dynamic DFS in undirected graphs. ACM Transactions on Parallel Computing (TOPC), 6(3), pp.1-33.

Tang, G., Tang, C., Claramunt, C., Hu, X. and Zhou, P., 2021. Geometric A-star algorithm: An improved A-star algorithm for AGV path planning in a port environment. IEEE access, 9, pp.59196-59210.

Liu, C., Mao, Q., Chu, X. and Xie, S., 2019. An improved A-star algorithm considering water current, traffic separation and berthing for vessel path planning. Applied Sciences, 9(6), p.1057.

Raschka, S., Patterson, J. and Nolet, C., 2020. Machine learning in python: Main developments and technology trends in data science, machine learning, and artificial intelligence. Information, 11(4), p.193.

Gorjao, L.R., Hassan, G., Kurths, J. and Witthaut, D., 2022. MFDFA: Efficient multifractal detrended fluctuation analysis in python. Computer Physics Communications, 273, p.108254.