Deze videotutorial legt het gebruik van spel-AI in Pac-Man uit.

Hieronder een video met de AI-script die toont hoe de spoken Pac-Man achtervolgen:

De Pac-Man Projects zijn ontwikkeld voor de introductiecursus Kunstmatige Intelligentie aan de Universiteit van Californië, Berkeley. Ze passen een reeks AI-technieken toe op het spelen van Pac-Man. Deze projecten zijn niet gericht op het bouwen van AI voor videospellen. In plaats daarvan leren ze fundamentele AI-concepten, zoals geïnformeerde staat-ruimte zoekalgoritmen, probabilistische inferentie en versterkend leren. Deze concepten vormen de basis voor toepassingsgebieden in de echte wereld, zoals natuurlijke taalverwerking, computervisie en robotica:

We hebben deze projecten ontworpen met drie doelen voor ogen. De projecten stellen studenten in staat om de resultaten van de toegepaste technieken te visualiseren. Ze bevatten ook voorbeeldcode en duidelijke instructies, maar dwingen studenten niet om zich door overmatige hoeveelheden hulpstructuren te worstelen. Tot slot biedt Pac-Man een uitdagende probleemomgeving die creatieve oplossingen vereist; echte AI-problemen zijn uitdagend, en dat geldt ook voor Pac-Man.

In de cursus hebben deze projecten gezorgd voor een toename in inschrijvingen, positieve beoordelingen van het onderwijs en betrokkenheid van studenten. De projecten zijn op Berkeley meerdere semesters lang getest, verfijnd en foutloos gemaakt. Ze zijn nu klaar om ze beschikbaar te stellen aan andere universiteiten voor educatief gebruik.

Het INTERNATIONAL JOURNAL OF CREATIVE RESEARCH THOUGHTS – IJCRT instituut heeft een paper geschreven met analyse van de inzet van AI bij het spel Pac-Man:

This project is about developing pacman game with AI..The Game Pac-Man is a very challengingvideo game that can
be useful in conducting AI(Artificial Intelligence) research. Here, the reason we have implemented various AI algorithms for
pacman game is that it helps us to study AI by using visualizations through which we can understand AI more effectively. The
main aim is to build an intelligent pacman agent which finds optimal paths through the maze to find a particulargoal such as a
particular food position, escaping from ghosts. For that, we have implemented AI search algorithms like Depth first search,
Breadth first search, A*search, Uniform cost search. We have also implemented multi-agents like Reflex agent, Minimax agent,
Alpha-beta agent .Through these multiagent algorithms, we can make pacman to react from its environmental conditions and
escape from ghosts to get high score. We have also done the visualization part of the above AI algorithms by which anyone can
learn and understand AI algorithms easily. For visualisation of algorithms, we have used python libraries matplotlib and
NetworkX(used to draw graphs for the states explored).
Index Terms – Pacman, maze, DFS, BFS, UCS, A*Search, Reflexagent, Minimaxagent, alpha-betapuning, visualization,
Networkx, matplotlib.

I. INTRODUCTION
Pac-man is a maze arcade game developed and published by Namco in 1980. The player supervise Pac-man, who must eat all the
dots inside an surrounded maze while keeping away from the four colored ghosts. Eating huge flashing dots called power pellets
changes the ghosts to turn blue, allowing Pac-Man to consume them for bonus points. Pac-Man was a critical and commercial
victory, and has an commercial and cultural legacy. The game is supreme and influential, and it is often listed as one of the
extraordinary video games of all time.

II. RELATED WORK
Veenus Chhabra et al. [1] expressed the brief explanation of Game theory. through this we showed some characteristics of
game. The algorithm is developed for using smaller indices so that there is less complication for guessing the tack number and
then determining as we follow color indexing through number and assign. Also, we can also execute the game to begin from
initial by not only getting “6” at dice but also with “1”. We can also restrict that to “two” only. As we get continuous “three”
“6”, the turn is altered without any move of token.

César Villacís et al. [2] proposed a system how to optimize an educational video game named Tic-Tac-Toe by means of
semiotics analysis, in order to stimulate logical and spatial reasoning of children. The main issue in this model has been to
design a mathematical model that was implemented with Artificial Intelligence algorithms and a graphical user interface
including Semiotics, applied to an incremental methodology with the aim of producing an enjoyable and interactive
environment., this examination mingle theories about stimulating cognitive growth of children; game design prototypes.
Sebastian Thrun et al. [3] proposed a system called NeuroChess, an approach for learning to play chess from the final
outcomes of games. Firstly, instruction time is bounded. This is particularly the case if only the final outcomes are considered.
Secondly, with each move of TO-learning NeuroChess loses data. It is therefore unclear that a TD- like approach will ever, for
example, develop good chess openings .\ It has been well conceded that the resulting cost in chess is determined by the time it
takes to make a move.
Sergey Karakovskiy et al. [4] proposed a system describes the Mario AI benchmark, a game-based benchmark for
reinforcement learning algorithms and game AI techniques developed by the authors. The researchers and students from round
the world have contributed diverse solutions to try to beat the benchmark. The paper synopsis these contributions, gives an survey
of the state-of-art in Mario-playing AIs, and chronicles the growth of the benchmark.
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Koller et al. [5] proposed a graphical representation for non-cooperative games—multi-agent influence
diagrams (MAIDs). The basic elements in the MAID representation are variables, allowing an explicit representation of
dependence, or relevance, relationships among variables and showed strategic relevance can be used to decompose large games
into a set of interacting smaller games, which can be solved in sequenceand also show that this decomposition can lead to
substantial savings in the computational cost of finding Nash equilibria in these games.
Stone et al. [6] proposed the Distributed artificial intelligence (DAI) has existed as a subfield of artificial intelligence for
less than two decades. DAI deals with systems that consist of multiple independent entities that interact in a domain.
Traditionally, DAI is divided into two sub-disciplines: Distributed Problem Solving (DPS) focuses on the information
management aspects of systems with several components working together towards a common goal.
Shoham e t a l . [ 7 ] e x p l a i n e d t h e Game theory and social choice theory have traditionally been the domain of
economics. With growing interest, computer scientists are increasingly using them as tools. The authors refrain from providing a
limited definition and emphasize the openness and interdisciplinary nature of multi-agent systems.
Elmasry et al.[8] gave, among others, an implementation of breadth-first search (BFS) and depth-first search (DFS) in a
graph on n vertices and m edges, taking \(O(m+n)\) time using O(n) and \( O(n \lg \lg n)\) bits of space, respectively an
improvement of the naive implementation \(O(n \lg n)\)(We use \(\lg \) to denote the logarithm to the base 2.) bits. We continue
this line of work with a focus on space.

III. METHODOLOGY
Algorithms:
The structure include implementation of AI search algorithms and Adversial search(Multiagents).
The following are the search algorithms performed:
1. Depth First Search
2. Breadth First Search
3. Uniform Cost Search
4. A* Search
The following are the adversial search algorithms that are performed:
1. Reflex Agent
2. Minimax Algorithm
3. Alpha-beta Pruning

SEARCH ALGORITHMS:
3.1 Uninformed Search Algorithms:
Uninformed search is a class of common search algorithms which control inbrute force-way. Uninformed search algorithms
do not have added instruction about state orsearch space other than how to move the tree, so it is also called blind search.
3.1.1 DFS:
Depth-first search is a circular algorithm for traversing a tree or graph data structure. It is called the depth-first search because it
begins from the source node and go along with each path to its greatest depth node before operating to the following path. DFS
utilize a stack data structure for its execution. The procedure of the DFS algorithm is related to the BFS algorithm.
Time Complexity: Time complexity of DFS will be similar to the node traversed by the algorithm. It is specifiedby:
T(n)= 1+ n2+ n3 +………+ n
m=O(nm) (1)
Where, m= maximum depth of any node and this can be much big than d (Shallowest solutiondepth).
Space Complexity: DFS algorithm require to reserve only single path from the root node, hence space complexity ofDFS is
equivalent to the size of the fringe set, which is
O(bm). (2)

3.1.2 BFS
Breadth-first search is the most usual search strategy for traversing a tree or graph. This algorithm searches breadth wise in a tree
or graph, so it is called breadth-first search.BFS algorithm begins searching from the source node of the tree and enlarge all
beneficiary node at the present level before moving to nodes of next level. The breadth-first search algorithm is an sample of a
general-graph search algorithm. Breadth-first search is performed using FIFO queue data structure.
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Time Complexity: Time Complexity of BFS algorithm can be acquire by the number of nodes traversed in BFS until the
shallowest Node. Where the d= depth of shallowest solution and b is a node at each position .
T (b) = 1+b2+b3+ + bd= O (bd ) (3)

Space Complexity: Space complexity of BFS algorithm is specified by the Memory size of frontier which is
O(bd). (4)

3.1.3 UNIFORM COST SEARCH:
Uniform-cost search is a searching algorithm used for traversing a weighted tree or graph. This algorithm approach into play
when a dissimilar cost is available for each margin. The primary aim of the uniform-cost search is to discover a path to the aim
node which has the lowest cumulative cost. Uniform-cost search enlarge nodes according to their path costs form the root node.
It can be used to resolve any graph/tree where the optimal cost is in demand. A uniform-cost searchalgorithm is executed by the
priority queue. It offers highest priority to the lowest cumulative cost. Uniform cost search is equal to BFS algorithm if the path
cost of all edges is the identical.
Time Complexity: Let C* is Cost of the optimal solution, and ε is each step to get near to the aim node. Thenthe number of
steps is = C*/ε+1. Here we have taken +1, as we start from begin 0 and end toC*/ε.
Hence, the worst-case time complexity of Uniform-cost search isO(b1 + [C*/ε])/. (5)
Space Complexity: The same logic is for space complexity so, the worst-case space complexity of Uniform-costsearch is
O(b1 + [C*/ε]). (6)
3.2 Informed Search Algorithms

3.2.1 A* SEARCH ALGORITHM:
A* search is the most frequently known form of best-first search. It uses heuristic function h(n), and cost to reach the node n
from the begin state g(n). It has collaborate features of UCS and greedy best-first search, by which it resolve the problem
efficiently. A* search algorithm discover the direct path through the search space using the heuristic function. This search
algorithm enlarge less search tree and provides optimal result quick. A* algorithm is close to UCSexcept that it uses
g(n)+h(n) instead of g(n).
In A* search algorithm, we utilize search heuristic as well as the cost to reach the node. Hence we can merge both costs as
following, and this sum is called as a fitness number. f(n)=g(n)+h(n)
f(n)=estimated cost of the cheapest solution
g(n)=cost to reach node n from start state
h(n)=cost to reach from node n to goal node
At each point in the search space, only those node is enlarge which have the small value of f(n), and the algorithm
terminates when the goal node is found.
Time Complexity: The time complexity of A* search algorithm depends on heuristic function,and the number of nodes
enlarge is exponential to the depth of solution d. So the timecomplexity is O(b^d), where b is the branching factor.
Space Complexity: The space complexity of A* search algorithm is O(b^d) (7)
3.3 Adversial Search Algorithms:

3.3.1 REFLEX AGENT:
We produce here a reflex agent which pick out at its turn a random action from the legal ones. Note that this is non identical
from the random search agent, since a reflex agent does not construct a series of actions, but select one action and performs
it.This reflex agent selects its present action based only on its current perception. The ReflexAgent computes the results of the
states reachable with these steps and choose the states that outcome into the state with the highest score. In case more states have
the highest score, it will select randomly one.

3.3.2 MINIMAX ALGORITHM:
In case the world where the agent plan of action ahead includes other agents which plan against it, adversarial search can be
used. One agent is called MAX and the other one MIN. Utility(s; p) offers the _nal numeric value for a game that close in
terminal state s for participant p. For example, in chess the standards can be +1, 0, ½. The game tree is a tree where the nodes are
game states and the edges are moves. Optimal decisions in games must give the finest move for MAX in the beginning state, then
MAX’s moves in all the states proceed from each possible response by MIN, and so on. Minimax value make sure optimal
strategy for MAX.

3.3.3 ALPHA BETA PRUNING:
In order to limit the number of game states from the game tree, alpha-beta pruning canbe registered, where α = the value of the
best (highest value) choice there is so far at any choice point across thepath for MAX
β = the value of the best (lowest-value) choice there is so far at any choice point across the path for MIN
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Table 1. Comparison of search algorithms for Medium maze
DFS BFS UCS A*
Total Cost 130 68 68 68
Nodes
expanded 144 268 269 221
Score 380 442 442 442
Table 2. Comparison of search algorithms for tiny maze
DFS BFS UCS A*
Total Cost 10 8 8 8
Nodes
expanded 14 16 15 14
Score 500 502 502 502
Table 3. Comparison of search algorithms for big maze
DFS BFS UCS A*
Total Cost 210 210 210 210
Nodes
expanded 390 618 620 549
Score 300 300 300 300
IV. RESULTS

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V. CONCLUSION
We have completed executing search algorithms Depth First Search,Breadth FirstSearch,Uniform Cost Search,A* Search.and also
executed Reflex Agent,MiniMax Agent, AlphaBeta Agent. In search algorithms, DFS doesn’t give the best solution because it does
not provide least cost solutions. BFS provides least cost solutions with respect to effort by the pacman in reaching the food but the
expanded nodes are very large(268) which takes a lot of time to find the solution which is best and when we compare UCS with
BFS and DFS, the time and costs are relatively high which does not give us the best solution. So, A* is the best as it finds out the
sum of cost of reaching nodes and the cost of reaching the goal node from that particular node which is (x+y).We have
compared the performance of the search algorithms in terms of nodes expanded, cost, and time taken

.
REFERENCES
[1] Chhabra, Veenus and Kuldeep Tomar. “Artificial Intelligence : Game Techniques Ludo-A Case Study.” (2015).
[2] Villacis Silva, Cesar & Fuertes, Walter & Santillán Trujillo, Mónica & Aules, Hernán & Tacuri, Ana &
Zambrano, Margarita & Salguero, Edgar. (2016). On the Development of Strategic Games based on a Semiotic
Analysis: A Case Study of an Optimized Tic-Tac-Toe. 425-432. 10.5220/0005772904250432.
[3] Learning To Play the Game of Chess – Sebastian Thrun, University of Bonn, Departmentof Computer Science
III, Romerstr. 164, 0-53117 Bonn, Germany.
[4] S. Karakovskiy and J. Togelius, “The Mario AI Benchmark and Competitions,” in IEEE Transactions on Computational
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[5] D. Koller and B. Milch (2003): Multi-agent influence diagrams for representing and solvinggames.
[6] P. Stone and M. Veloso (2000): Multiagent systems: a survey from a machine learningperspective.
[7] Y. Shoham and K. Leyton-Brown (2008): Multiagent systems: algorithmic, game theoretic,and logical
foundations,Cambridge University Press.
[8] Banerjee, Niranka & Chakraborty, Sankardeep & Raman, Venkatesh. (2016). Improved Space Efficient Algorithms for
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