Chapter 9 - Simulations

Bruce Chittenden

Supercomputers www.top500.org

Foxes and Rabbits

Exercise 9.1

Rabbits thin out where the Foxes are in the Field

Exercise 9.2

When the Rabbit population decreases to below a certain threshold, the Foxes go extinct

As the Rabbit population increases the Fox population increases

Exercise 9.3 (First Run)

Exercise 9.3 (Second Run)

Exercise 9.3 (Third Run)

Exercise 9.3 (Fourth Run)

Exercise 9.3 (Fifth Run)

Exercise 9.3 (Sixth Run)

Exercise 9.3 (Seventh Run)

Exercise 9.3 (Eighth Run)

Exercise 9.3 (Ninth Run)

Exercise 9.3 (Tenth Run)

Exercise 9.3Act Rabbit FoxesSteps Rabbits Foxes Survival Survival

1 679 187 0   6792 219 160 0   2193 199 204 0   1994 441 0 52 441  5 130 2 0   1306 240 274 0   2407 748 0 10 748  8 72 33 0   729 471 119 0   47110 432 0 66 432  

Total 3,631 979 128Average 363.1 540.3 287.1

Exercise 9.4

public class Field extends World{ // Constants representing configuration information for the simulation. // The default width for the grid. private static final int WIDTH = 40; // The default depth of the grid. private static final int HEIGHT = 30; // The probability that a fox will be created in any given grid position (in percent). private static final int FOX_CREATION_PROBABILITY = 2; // The probability that a rabbit will be created in any given grid position (in percent). private static final int RABBIT_CREATION_PROBABILITY = 8;

// The current step of the simulation. private int step = 0;

Height and Width of the Field

Exercise 9.4

public class Field extends World{ // Constants representing configuration information for the simulation. // The default width for the grid. private static final int WIDTH = 80; // The default depth of the grid. private static final int HEIGHT = 60; // The probability that a fox will be created in any given grid position (in percent). private static final int FOX_CREATION_PROBABILITY = 2; // The probability that a rabbit will be created in any given grid position (in percent). private static final int RABBIT_CREATION_PROBABILITY = 8;

// The current step of the simulation. private int step = 0;

Changed the Field to be 80 by 60 or 400% of the Original Size

Exercise 9.4

Ran a Long Time

Exercise 9.4

public class Field extends World{ // Constants representing configuration information for the simulation. // The default width for the grid. private static final int WIDTH = 20; // The default depth of the grid. private static final int HEIGHT = 15; // The probability that a fox will be created in any given grid position (in percent). private static final int FOX_CREATION_PROBABILITY = 2; // The probability that a rabbit will be created in any given grid position (in percent). private static final int RABBIT_CREATION_PROBABILITY = 8;

// The current step of the simulation. private int step = 0;

Changed the Field to be 20 by 15 or 25% of the Original Size

Exercise 9.4

With 25% of the Space the Species Went Extinct Very

Quickly

Exercise 9.5

public class Field extends World{ // Constants representing configuration information for the simulation. // The default width for the grid. private static final int WIDTH = 45; // The default depth of the grid. private static final int HEIGHT = 35; // The probability that a fox will be created in any given grid position (in percent). private static final int FOX_CREATION_PROBABILITY = 2; // The probability that a rabbit will be created in any given grid position (in percent). private static final int RABBIT_CREATION_PROBABILITY = 8;

// The current step of the simulation. private int step = 0;

Increase the Size of the Area from 30 x 40 or 1200 sq units to 35 x 45 or 1575 sq units

Exercise 9.5

Establish a Baseline

Exercise 9.5

public class Rabbit extends Animal{ // Characteristics shared by all rabbits (static fields).

// The age at which a rabbit can start to breed. private static final int BREEDING_AGE = 5; // The age to which a rabbit can live. private static final int MAX_AGE = 50; // The likelihood of a rabbit breeding (in percent). private static final double BREEDING_PROBABILITY = 25; // The maximum number of births. private static final int MAX_LITTER_SIZE = 5;

Double the change of Breeding from 12 to 25

Exercise 9.5

Did not seem to make a lot of difference

Exercise 9.6public class Fox extends Animal{ // Characteristics shared by all foxes (static fields). // The age at which a fox can start to breed. private static final int BREEDING_AGE = 10; // The age to which a fox can live. private static final int MAX_AGE = 150; // The likelihood of a fox breeding (in percent). private static final int BREEDING_PROBABILITY = 8; // The maximum number of births. private static final int MAX_LITTER_SIZE = 3; // The food value of a single rabbit. In effect, this is the // number of steps a fox can go before it has to eat again. private static final int RABBIT_FOOD_VALUE = 6;

Double Rabbit Food Value for 6 to 12

Exercise 9.6

Fox Population Seems to Do Very Well

Exercise 9.7public class Fox extends Animal{ // Characteristics shared by all foxes (static fields). // The age at which a fox can start to breed. private static final int BREEDING_AGE = 20; // The age to which a fox can live. private static final int MAX_AGE = 100; // The likelihood of a fox breeding (in percent). private static final int BREEDING_PROBABILITY = 5; // The maximum number of births. private static final int MAX_LITTER_SIZE = 3; // The food value of a single rabbit. In effect, this is the // number of steps a fox can go before it has to eat again. private static final int RABBIT_FOOD_VALUE = 12;

Changed MAX_AGE from 150 to 100

Changed BREEDING_PROBABLY from 8 to 5

Changed BREEDING_AGEfrom 10 to 20

Exercise 9.7

9.2 Ants

Exercise 9.8

Nothing Happens

Exercise 9.9import greenfoot.*; // (World, Actor, GreenfootImage, and Greenfoot)

/* * An ant that collects food. * * @author Michael Kolling * @version 0.1 */public class Ant extends Creature{ /** * Create an ant with a given home hill. The initial speed is zero (not moving). */ public Ant(AntHill home) { setHomeHill(home); }

/* * Do what an ant's gotta do. */ public void act() { }

}

Nothing in the act Method

Exercise 9.10

Exercise 9.11/* * Act: If there are still ants left inside, see whether one should come out. */public void act(){ if(ants < maxAnts) { if(Greenfoot.getRandomNumber(100) < 10) { getWorld().addObject(new Ant(this), getX(), getY()); ants++; } }}

Ants do not move and 10% of the time when the act Method is called another Ant is created at exactly the location of the Ant Hill up to the Maximum number of ants

Exercise 9.12public class Ant extends Creature{ /* * Create an ant with a given home hill. The initial speed is zero (not moving). */ public Ant(AntHill home) { setHomeHill(home); }

/* * Do what an ant's gotta do. */ public void act() { randomWalk(); }

}

Add the randomWalk Method to the Ants act Method

Exercise 9.12

9.3 Collecting Food

Crumbs with Even Distribution Crumbs with Gaussian Distribution

Exercise 9.13

New subclass Food

Exercise 9.13import greenfoot.*; // (World, Actor, GreenfootImage, Greenfoot and MouseInfo)

/* * Write a description of class Food here. * * @author (your name) * @version (a version number or a date) */public class Food extends Actor{ /* * Act - do whatever the Food wants to do. This method is called whenever * the 'Act' or 'Run' button gets pressed in the environment. */ public void act() { // Add your action code here. } }

Exercise 9.14

public class Food extends Actor{ private int crumbs = 100; // number of bits of food in this pile

/* * Act - do whatever the Food wants to do. This method is called whenever * the 'Act' or 'Run' button gets pressed in the environment. */ public void act() { // Add your action code here. } }

Number of Crumbs initialized to 100

Exercise 9.15/* * Update the image */private void updateImage(){ GreenfootImage image = new GreenfootImage(SIZE, SIZE);

for (int i = 0; i < crumbs; i++) { int x = randomCoord(); int y = randomCoord();

image.setColorAt(x, y, color1); image.setColorAt(x + 1, y, color2); image.setColorAt(x, y + 1, color2); image.setColorAt(x + 1, y + 1, color3); } setImage(image);}

Exercise 9.15/* * Returns a random number relative to the size of the food pile. */private int randomCoord(){ int val = Greenfoot.getRandomNumber(SIZE); if (val < 0) return 0;

if (val > SIZE - 2) return SIZE - 2; else return val;}

Greenfoot.getRandomNumber()

Exercise 9.15

Even Distribution of the Random Number Produces a

Square Food Pile

Exercise 9.16

Exercise 9.16

Exercise 9.17/* * Returns a random number relative to the size of the food pile. */private int randomCoord(){ int val = HALFSIZE + (int) (new Random().nextGaussian() * (HALFSIZE / 2)); if (val < 0) return 0;

if (val > SIZE - 2) return SIZE - 2; else return val;}

Random().nextGaussian()

Exercise 9.17

Normal Distribution (Gaussian Distribution) of the Random Number Produces a Better Looking Food Pile

Random DistributionsIf we need random behavior in our program it is sometime important to think about what type of distribution we need.

Uniform Distribution Greenfoot.getRandomNumber(int range)

Normal Distribution new Random().nextGaussian()

Exercise 9.18/* * Remove some food from this pile of food. */public void takeSome(){ crumbs = crumbs - 3; if (crumbs <= 0) { getWorld().removeObject(this); } else { updateImage(); }}

Exercise 9.18

Interactively Remove Food from the Food Pile Until it is All Gone

Exercise 9.18

Continue Until the Food is All Gone. Then Verify That the Food Pile is

Removed from the World

Exercise 9.18

Ant Behavior

If (carrying food) { walk towards home; check whether we are home;}else{ search for food;}

Exercise 9.19/* * Walk around in search of food. */private void searchForFood(){ randomWalk(); checkFood();}

/* * Is there any food here where we are? If so, take some!. */public void checkFood(){ Food food = (Food) getOneIntersectingObject(Food.class); if (food != null) { Greenfoot.stop(); }}

To Verify This Code is Working Place a Call to the stop() Method if an Ant

Finds a Food Pile

Exercise 9.19

Exercise 9.20/* * Is there any food here where we are? If so, take some!. */public void checkFood(){ Food food = (Food) getOneIntersectingObject(Food.class); if (food != null) { takeFood(food); }}

/* * Take some food from a fool pile. */private void takeFood(Food food){ carryingFood = true; food.takeSome(); setImage("ant-with-food.gif");}

Exercise 9.20

Ants Just Wonder Around Even When

Carrying Food

Exercise 9.21/* * Do what an ant's gotta do. */public void act(){ if (carryingFood) { walkTowardsHome(); } else { searchForFood(); }}

Exercise 9.21

The Ants All Go Home When They Are Carrying Food, But They Never Come Back Out

Exercise 9.22/* * Record that we have collected another bit of food. */public void countFood(){ // if we have no food counter yet (first time) -- create it if(foodCounter == null) { foodCounter = new Counter("Food: "); int x = getX(); int y = getY() + getImage().getWidth()/2 + 8;

getWorld().addObject(foodCounter, x, y); } foodCounter.increment();}

Exercise 9.22

9.4 Setting Up the World

We need to create some initialization code that creates some Ant Hills and food automatically.

Exercise 9.23

/* * Create a new world. It will be initialized with a few ant hills * and food sources */public AntWorld(){ super(SIZE, SIZE, 1); createAntHills(); createFoodPiles();}

Initialize the Ant’s World

Exercise 9.23

/* * Create world contents: two ant hills and food. */public void createAntHills(){ removeObjects(getObjects(null)); // remove all existing objects addObject(new AntHill(40), 546, 356); addObject(new AntHill(40), 95, 267);}

Exercise 9.23

/* * Create some food piles. */public void createFoodPiles(){ addObject(new Food(), 80, 71); addObject(new Food(), 291, 56); addObject(new Food(), 516, 212); addObject(new Food(), 311, 269); addObject(new Food(), 318, 299); addObject(new Food(), 315, 331); addObject(new Food(), 141, 425); addObject(new Food(), 378, 547); addObject(new Food(), 566, 529);}

Exercise 9.23

9.5 Adding Pheromones

Each pheromone object is a small drop of a chemical that the ants leave on the ground. This drop will evaporate fairly quickly and then disappear. Ants drop pheromones while they are walking back home from a food source. When other ants smell the drops on pheromone, they can then turn away from their home hill and walk in the direction toward the food.

Exercise 9.24import greenfoot.*; // (World, Actor, GreenfootImage, Greenfoot and MouseInfo)

/* * Write a description of class Pheromone here. * * @author (your name) * @version (a version number or a date) */public class Pheromone extends Actor{ /* * Act - do whatever the Pheromone wants to do. This method is called whenever * the 'Act' or 'Run' button gets pressed in the environment. */ public void act() { // Add your action code here. } }

Exercise 9.24

Exercise 9.25

/* * Make the image. */private void updateImage(){ GreenfootImage image = new GreenfootImage(65, 65); image.setColor(new Color(255, 255, 255, 60)); image.fillOval(0, 0, 65, 65); image.setColor(Color.DARK_GRAY); image.fillRect(32, 32, 2, 2); // small dot in the middle setImage(image);}

Exercise 9.25

Manually Tested with new Pheromone()

Exercise 9.26/* * Act - do whatever the Pheromone wants to do. This method is called whenever * the 'Act' or 'Run' button gets pressed in the environment. */public void act() { intensity -= 1; if (intensity <= 0) getWorld().removeObject(this); else updateImage();}

Decrease the Intensity on Each Act Cycle and When the Intensity Reaches 0 Remove it from the World

Exercise 9.27/* * Make the image. The size and transparency are proportional to the intensity. */private void updateImage(){ int size = intensity / 3 + 5; GreenfootImage image = new GreenfootImage(size + 1, size + 1); int alpha = intensity / 3; image.setColor(new Color(255, 255, 255, alpha)); image.fillOval(0, 0, size, size); image.setColor(Color.DARK_GRAY); image.fillRect(size / 2, size / 2, 2, 2); // small dot in the middle setImage(image);}

Modify updateImage() so that it Uses Intensity

Exercise 9.28

Manually Added a new Pheromone to the World Every 10 Act Cycles to Verify it was Decreasing in Size and Intensity

Exercise 9.29/* * Do what an ant's gotta do. */public void act(){ if (carryingFood) { walkTowardsHome(); handlePheromoneDrop(); checkHome(); } else { searchForFood(); }}

Exercise 9.29/* * Drop pheromone. */private void handlePheromoneDrop(){ Pheromone ph = new Pheromone(); getWorld().addObject (ph, getX(), getY());}

Exercise 9.29

Dropping Pheromone on Every Act Cycle

Exercise 9.30public class Ant extends Creature{ /** Every how many steps can we place a pheromone drop. */ private static final int MAX_PH_LEVEL = 18;

/** Indicate whether we have any food with us. */ private boolean carryingFood = false;

/** How much pheromone do we have right now. */ private int pheromoneLevel = MAX_PH_LEVEL;

Exercise 9.30/* * Check whether we can drop some pheromone yet. If we can, do it. */private void handlePheromoneDrop(){ if (pheromoneLevel == MAX_PH_LEVEL) { Pheromone ph = new Pheromone(); getWorld().addObject(ph, getX(), getY()); pheromoneLevel = 0; } else { pheromoneLevel++; }}

Drop Pheromone on Every 18th Act Cycle

Exercise 9.30

Pseudo Codeif (we recently found a drop of pheromone){ walk away from home;}else if (we smell pheromone now) { walk toward the center of the pheromone drop; if (we are at the pheromone drop center) { note that we found pheromone; } }else{ walk randomly;}check for food;

Implementation of Pseudo Codeprivate void searchForFood(){ if (foundLastPheromone > 0) // if we can still remember... { foundLastPheromone--; walkAwayFromHome(); } else if (smellPheromone()) { walkTowardsPheromone(); } else { randomWalk(); } checkFood();}

Exercise 9.31

9.6 Path FormingOne interesting aspect of this scenario is that there is no code anywhere in the project that talks about forming paths. The behavior of the individual ants is quite simple

if you have food go home; if you smell pheromones go away; otherwise go around;

However, together the ants display some fairly sophisticated behavior. They form stable paths, refreshing the pheromones as they evaporate, and efficiently transport food back to their ant hill.

Exercise 9.32In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs.This algorithm is a member of ant colony algorithms family, in swarm intelligence methods, and it constitutes some metaheuristic optimizations. Initially proposed by Marco Dorigo in 1992 in his PhD thesis, the first algorithm was aiming to search for an optimal path in a graph, based on the behavior of ants seeking a path between their colony and a source of food. The original idea has since diversified to solve a wider class of numerical problems, and as a result, several problems have emerged, drawing on various aspects of the behavior of ants.

Exercise 9.33/* * Check whether we can drop some pheromone yet. If we can, do it. */private void handlePheromoneDrop(){ if (pheromoneLevel == MAX_PH_LEVEL * 4) { Pheromone ph = new Pheromone(); getWorld().addObject(ph, getX(), getY()); pheromoneLevel = 0; } else { pheromoneLevel++; }}

Reduced by a Quarter, The Time Between Drops is Multiplied by 4

Exercise 9.33

The Trails are Not as Good

Exercise 9.34public class Ant extends Creature{ /** Every how many steps can we place a pheromone drop. */ private static final int MAX_PH_LEVEL = 18;

/** How long do we keep direction after finding pheromones. */ private static final int PH_TIME = 10;

/** Indicate whether we have any food with us. */ private boolean carryingFood = false;

/** How much pheromone do we have right now. */ private int pheromoneLevel = MAX_PH_LEVEL;

/** How well do we remember the last pheromone - larger number: more recent */ private int foundLastPheromone = 0;

Changed from 30 to 10

Exercise 9.34

The Ants Seem to be Confused

9.7 Summary

Simulations are an interesting type of application. Many simulations are used in real life for many purposes, such as weather forecasting, traffic planning, environment impact studies, physics research, and many more.

Concept Summary