An artificial intelligence algorithm for a computer game competition organised by Google and University ofWaterloo is presented. It competes with others by reasoning, evaluating of a situation and taking decisions in a war simulation

Kruk, Maciej

Ziółko, Bartosz

Annales Universitatis Mariae Curie-Sklodowska sectio AI – Informatica

English

University of Maria Curie-Skłodowska (UMCS): Scientific e-Journals / Uniwersytet Marii Curie-Skłodowskiej: e-czasopisma naukowe

Annales UMCS Informatica AI XII, 1 (2012) 39–45DOI: 10.2478/v10065-012-0009-zAutomatic reasoning in the Planet Wars gameBartosz Ziółko1∗, Maciej Kruk21Department of Electronics, AGH University of Science and Technology,al. Mickiewicza 30, Kraków, Poland.2Department of Computer Science, AGH University of Science and Technology,al. Mickiewicza 30, Kraków, PolandAbstract – An artificial intelligence algorithm for a computer game competition organised by Googleand University of Waterloo is presented. It competes with others by reasoning, evaluating of a situationand taking decisions in a war simulation.1 IntroductionComputer games are rapidly growing computer science industry all over the worldincluding Poland. It is also a popular field to test and develop several types of AI(artificial intelligence) algorithms [1, 2, 3, 4, 5].The objective of the Google AI Challenge [6], a programming contest organisedby the University of Waterloo Computer Science Club, was to create an autonomouscomputer program that plays the game of Planet Wars as intelligently as possible.Planet Wars is a strategic game set in the outer space based on Galcon. A game takesplace on a map (let (i, j) be discrete coordinates) containing several planets, each ofthem with a specific number of space ships on it, belonging to one of the two players orneutral. In each turn, the player may choose to send fleets of ships from any planet heowns to any other planet on the map. The game includes a certain maximum numberof turns, which is 200. The player with the more ships at the end of the game wins.The Galcon game consists of a map and ships. Planet positions are specified relativeto a common origin in the Euclidean space. The coordinates (i, j) are given as thefloating point numbers. However, to simplify mathematical description, let us see themap as a matrix M [i, j]. Planets never move and are never added or removed as the∗bziolko@agh.edu.plPobrane z czasopisma Annales AI- Informatica http://ai.annales.umcs.plData: 04/08/2020 20:58:10UMCS40 Automatic reasoning in the Planet Wars gamegame progresses. Planets are not allowed to occupy exactly the same position on themap. The integer values mij ofM describe production of (i, j) position of the map.The values mij = 0 represent empty space. Planets are locations fulfilling mij > 0 andthey can either belong to one of the players or are neutral. Matrix M does not changein a particular game and even though it is not mentioned in the rules, it is symetricalin all games to allow equal chances of winning for both sides.In each turn, the player may choose to send fleets of ships from any planet he ownsto another planet on the map. He may send as many fleets as he wishes in a singleturn as long as he has enough ships to supply them. After sending fleets, each planetowned by a player (not owned by neutral) will increase the forces there according to theplanets growth rate mi,j . Different planets have different growth rates. The fleets willthen take a number of turns to reach their destination planets, where they will thenfight any opposing forces and, if they win, take ownership of the planet mij . Fleetscannot be redirected during travel. Players may continue to send more fleets in laterturns even while older fleets are in transit.The growth rate of the planet is the number of ships added to the planet after eachturn. If the planet is currently owned by neutral, the growth rate is not applied.Players can only get new ships through growth. The growth rate of a planet will neverchange. It is given as an integer value. Let us denote A[i, j] and B[i, j] as matricesdescribing the positions and numbers of ships for both players. A and B change theirvalues during all turns. The first type of changes is due to production of new ships onplanets∀i,j aij := aij +mij if mij is controlled by player A∀i,j bij := bij +mij if mij is controlled by player B .(1)The second type are movements. Players can order any movements of their ships aijand bij to any positions (i, j) such that mij > 0 (namely to other plantes). A transfercannot be cancelled once started, however, it will last several turns and ships can belocated on any (i, j) position while moving. The total trip length is given as an integer,representing the total number of turns required to make the trip from the source to thedestination. The remaining turns are also an integer, representing the number of turnsleft from the current turn to arrive at the destination. Trip lengths are determined atthe time of departure by taking the Euclidean distance to the destination (i, j) fromthe source (k, n) and rounding up, w (noted later on by ⌈⌈). Finally, if ships of oppositeplayers aij > 0 and bij > 0 meet on the planet mij > 0, they fight. There is no randomaspect in such fights. If aij > bij , then next turn aij := aij − bij , bij := 0 and A takescontrol of production mij . If bij > aij the other way around.2 Basic algorithmOur solution divided possible changes in a game state (moves) into several groups,based on the history of ownership and location mij > 0 of the targeted planet:(1) DefencePobrane z czasopisma Annales AI- Informatica http://ai.annales.umcs.plData: 04/08/2020 20:58:10UMCSBartosz Ziółko, Maciej Kruk 41(2) Attack(3) Expansion(4) SuppliesBefore these moves, planets, states in the future are evaluated in each turn.Every turn, AI makes a decision, which of these moves is locally the highest gainvalue and performs them. To make the decision process more accurate, it needs a wholerange of data concerning the planets and fleets:(1) General planet specification (location, size) M [i, j],(2) Planet status in each point of time i.e.: ownership (A, B or neutral), numberof ships including incoming fleets (A[i, j] and B[i, j]),(3) Possible ways of attack (distances between mij > 0),(4) Planet location in context of other planets of its owner.At the beginning of each turn, the program calculated all the necessary information.Next it entered a sequence of functions responsible for fleets discharge (defence, at-tack, expansion, supplies) in which it assessed each planet’s value and based on it andsurrounding planets state made local decisions of ships transfers.3 Reasoning and decision takingThe function of predicting the future calculates planet states in the future basedon planet ownership, growth rate and flying fleets. Additionally, the function com-putes how many ships can enemy deliver to each planet in each step (used for attackprevention).Defence of planets under attack and ships surplus calculation is taken by the defencefunction. It ensures that aftermax_distance = maxmij>0,mkn>0⌈√(i− k)2 + (j − n)2⌉(2)turns, as many as possible of its planets will remain under control.For each of its planets, the algorithm calculates the number of ships needed tokeep them from being overtaken by the enemy. Later it sorts them according to theirproduction rate mij , distances to other planets{⌈√(i− k)2 + (j − n)2⌉: mkn > 0}and distances to the enemy{⌈√(i− v)2 + (j − w)2⌉: mvw > 0}and try to defend asmany as possible. If it is impossible to keep the planet during all time, the algorithmtries to retake it, not long after it is overtaken. If the planet still belongs to the AIduring the next (2) turns, it calculates how many ships it can send off from this planetnot losing them.The attack stage consists of two activities. The first one is sniping (see Fig. 1). Thealgorithm tries to attack neutral planets that will be overtaken in the future soon afterthe attack. In this way, the enemy loses his forces to fight the neutral planets and ouralgorithm can overtake a planet with fewer ships.Pobrane z czasopisma Annales AI- Informatica http://ai.annales.umcs.plData: 04/08/2020 20:58:10UMCS42 Automatic reasoning in the Planet Wars gameFig. 1. Sniping is a strategy of waiting for conquering a planet by an enemylosing ships during on its defence. Left planet belongs to b and has 35 ships,right to b with 25 ships, and the central one is neutral. First, the player battacks the central planet using 32 ships. 31 of them are lost in fight withthe neutral forces. Afterwards the player a sends a fleet to fight the onlysurvived ship of b plus what he will manage to produce on the central planet,which is 3 in this example. In the last stage the central planet is in controlof a and what is very important, the player a has more ships, namely 26,on its starting planet and player b, 9. The player b has no chance to win,even though, he starts with more ships than the player aThe second phase is a regular attack. The algorithm browses through all enemyplanets and attacks those it is sure that it can overtake even if the enemy sends all theships to defend it (even for just one turn)mfitnessij := c− btij + 1000mij (3)where btij is the prediction of the value of enemy ships in t turns in the future onmij > 0 and c = 2 000 000 is a constant, large value. Value of t is the distance⌈√(i− k)2 + (j − n)2⌉, where mkn is a planet from which we plan to attack. Thealgorithm avoids attacking the planets further than 0.5max_distance, unless there areno enemy planets closer.The expansion phase consists of neutral planets evaluation (based on their growthrate, number of ships and distance to both players).mfitnessij := mij(⌈√(i− k)2 + (j − n)2⌉−⌈√(i− v)2 + (j − w)2⌉+ 1)− sij (4)where mkn belongs to the enemy and mvw to our AI and sij is the number of neutralships on mij . Positive value of (4) means it will be advantageous to take over mij evenif the opponent will take it over afterwards. If (4) is negative, other arguments aretaken into account.AI expands more aggressively, if the own accumulated growth rate is lower than thatof the enemymfitnessij := mfitnessij +{50mij if winning20mij otherwise(5)Pobrane z czasopisma Annales AI- Informatica http://ai.annales.umcs.plData: 04/08/2020 20:58:10UMCSBartosz Ziółko, Maciej Kruk 43Fig. 2. Safe planets should supply the frontal one with ships. The reason forit is that the planets far away from the oponent are unlikely to be attacked.Even if they are attacked they could be reinforced, between discharging shipsby the enemy and arriving to the target. In contrast, typically there are frontline planets which cannot be reinforced already during the attack becausethe distance from the enemy is smaller then from reinforcing planets. Whatis more supplying scheme is also useful to gather ships for a full attack withas short warning as possibleThe map is always symmetric. AI prefers the planets whose mirrors are overtaken bythe enemy (its mfitnessij is increased by 1 000 000). The algorithm always attacks theplanets it is sure to profit from. If it has enough ships, it will also try to overtake otherplanets, based on their previously calculated value mfitnessij .The front consists mainly of the own planets (sometimes also neutral ones that areattacked) that can not be defended by sending ships on time from other planets incase of enemy attack. At the same time, they are capable of defending any non-frontalplanet of our AI. Storing all own ship reserves on the frontal planets improves ourdefence and attack potentials.Another part of the algorithm is reasoning about supplies (see Fig. 2), which is amovement of surplus ships from the non-frontal planets to the front ones. The numberof ships sent to each planet is proportional to the sum of reciprocals of distances to theenemy planets multiplied by the numer of ships they store. This way it tries to takeinto account enemy ships movements.Pobrane z czasopisma Annales AI- Informatica http://ai.annales.umcs.plData: 04/08/2020 20:58:10UMCS44 Automatic reasoning in the Planet Wars game4 ConclusionsThe described algorithm is ranked as 105 for over 4600 competitors and the sixth inPoland. The most difficult task in such AI is in providing a balance between defence,expension on neutral planets and attacking the enemy. Each game consists of too fewturns to adapt behaviour to a particular enemy, especially that calculations have to bemade in up to 2 seconds per turn. Hard coded rules are often too defensive for someopponents and maps while too aggresive for others.Fig. 3. Example of a game with too little expansion (top) and linear,correlated functions of growing of both opponents (middle). The func-tions summarising another (more typical) game are presented for compari-sion(bottom). Both AIs will keep collecting ships in the case of an attackwhich is never going to happen. An AI which would decide to take a riskand attack a neutral planet to enlarge its production potential is likely tosucced in such a scenario.Pobrane z czasopisma Annales AI- Informatica http://ai.annales.umcs.plData: 04/08/2020 20:58:10UMCSBartosz Ziółko, Maciej Kruk 45Undoubtedly, the hardest part to balance is the expansion phase. Too little or too lateattacks on neutral planets usually mean AI is left behind in terms of ships production(see Fig. 3). Too many or badly chosen expansions can make one vulnerable to enemyattacks, or give away the attacked planet to an enemy.Instead of making local decisions to attack/expand/defend, it would be probablybetter to gather all data about every planet, rate them taking into account their in-terrelations and then decide on the fleets destination. Also instead of finding thesource-destination-ships combination, it would be better to plan the planet populationand then send fleets from the closest planet to achieve it. That should help fight offthe situations when fleets are being sent to defend distant planets.In the case of attacking a planet from a few different sources, instead of attackingit simultaneously, it would be better to take into account their distance to the enemyand dispatch fleets at the last possible moment, so all of them reach their destinationat the same moment.Some enemy movements are easy to predict (e.g. planet sniping, repeated supplies,constant attacks) and hence the should be taken into account when making decisions.Other types of movement can be taken into account by browsing the game tree. It istoo big to analyse thoroughly (the competition gives a calculation time limit for eachturn) but at least the analysis of the potential attack routes should be possible. Themain problem is in including these predictions into the future states analysis.AcknowledgementsSome figures were made by Jakub Gawlik thanks to the organiser and the sponsorof the competition.References[1] Baba N., Jain L. C., Handa H., Advanced Intelligent Paradigms in Computer Games, Springer(2007).[2] Barber H., Kudenko D., Generation of adaptive dilemma-based interactive narratives, IEEETransactions on Computational Intelligence in Games 1(4) (2009): 309.[3] Rabin S. C., AI game programming wisdom, Charles River Media, Inc. (2002).[4] Funge J., Artificial Intelligence for Computer Games: An Introduction, A K Peters, Wellesley,MA. (2004).[5] Millington I., Funge J., Artificial intelligence for games, Elsevier (2009).[6] AI Challenge Ants: http://ai-contest.com/ (12.10.2012).Pobrane z czasopisma Annales AI- Informatica http://ai.annales.umcs.plData: 04/08/2020 20:58:10UMCSPowered by TCPDF (www.tcpdf.org)

Automatic reasoning in the Planet Wars game

Bartosz Ziółko

Maciej Kruk

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An artificial intelligence algorithm for a computer game competition organised by Google and University of Waterloo is presented. It competes with others by reasoning, evaluating of a situation and taking decisions in a war simulation

Ziółko, B.

Kruk, M.

Biblioteka Nauki - repozytorium artykuÅÃ³w

https://journals.umcs.pl/ai/article/download/3339/2533

Automatic reasoning in the Planet Wars game

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University of Maria Curie-Skłodowska (UMCS): Scientific e-Journals / Uniwersytet Marii Curie-Skłodowskiej: e-czasopisma naukowe

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Biblioteka Nauki - repozytorium artykuÅÃ³w

Automatic reasoning in the Planet Wars game

Abstract

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Full text

Available Versions

University of Maria Curie-Skłodowska (UMCS): Scientific e-Journals / Uniwersytet Marii Curie-Skłodowskiej: e-czasopisma naukowe

Crossref

Biblioteka Nauki - repozytorium artykuÅÃ³w

Biblioteka Nauki - repozytorium artykuÅÃ³w