Question 1: Starcraft 2 Build Order Optimizer [200]
![Question 1: Starcraft 2 Build Order Optimizer [200]](/img2/240/torch2012.webp)
The Operations Research Challenge 2012 Team Number: Question 1: Starcraft 2 Build Order Optimizer [200] In the game of Starcraft, you are given control over an alien race and must lead them to victory against an opposing player’s aliens. You will be given control of the Protoss race and must make the best decisions to beat your opponent. There are three fundamental aspects you can develop in the game of Starcraft: economy, army and technology. However, you are limited in how quickly you can develop the three aspects since improving any one of these three areas requires resources. The resources you have are food, minerals and gas. For this problem, you must decide what to build and when to build it in order to reach a milestone in the fastest time. Table 1 shows the buildings available to you, the cost of making the building, the time required to complete construction, and the building you already need to have constructed in order to build this building. Building Nexus Pylon Assimilator Gateway Cybernetics Core Robotics Facility Minerals 600 150 110 225 225 300 Gas 0 0 0 0 0 150 Time (s) 100 25 30 65 50 65 Pre-requisite None None None Pylon Gateway Cybernetics Core Table 1: Buildings you have access to and their requirements Table 2 shows the units you can build, their cost, time to build and the building that must be used to build the unit. When building a unit, the building will be busy and cannot do anything else or build any other units. For example, if you are building a zealot from the gateway, you cannot build any other unit (zealot, stalker or sentry) from that gateway until the zealot is completed. In order for you to build two zealots, stalkers, sentries or a combination of any of these two at the same time, you must have already completed building two gateways. 1
The Operations Research Challenge 2012 Team Number: Furthermore, each unit requires food. If your army does not have a sufficient amount of food, you cannot start building the unit. Food is crucial in keeping your army strong and alive. Details on how food works will be provided later. For now, it is sufficient to understand that each unit requires a different amount of food specified in Table 2 below. Unit Probe Zealot Stalker Sentry Immortal Minerals 75 150 175 75 400 Gas 0 0 75 150 150 Time(s) 17 38 42 37 50 Building Nexus Gateway Gateway* Gateway* Robotics Facility Food Req. 1 2 2 2 4 Table 2: Units you have access to and their requirements *Stalkers and Sentries can’t be built from a Gateway until a Cybernetics Core is built. You start the game with 1 Nexus, 6 probes, and 75 minerals. You can make use of probes to mine for minerals at a rate of 1 mineral/second. Thus, when you start the game, your six probes will give you 6 minerals/second. You can continue to build probes from your Nexus to improve your economy. However, a single Nexus can only support a maximum of 24 probes mining minerals. If there is a 25th probe trying to mine extra minerals, that probe becomes useless. If you wish to mine for minerals with more than 25 probes, you must build a second Nexus to support these extra probes. In order for you to obtain gas, you must build an Assimilator. Once you have an Assimilator built, you can start to mine gas at a rate of 1 gas/second. However, the Assimilator can only support a maximum of 3 probes. Furthermore, you can only build a maximum of 2 Assimilators for each Nexus you own. That is, if you have 1 Nexus, you can have 2 Assimilators. If you have 2 Nexus, you can have 4 Assimilators. The probes mining gas will not affect the maximum of 24 probes mining minerals on a Nexus. Therefore, each Nexus can support a maximum of 30 probes – 24 mining minerals and 6 mining gas (2 Assimilators). When an Assimilator is completed, make sure to state how many probes you want to assign the task of mining gas. If none is stated, it will be assumed that you do not get any gas. During the course of the game, you will also want to make sure that you are not focusing too much on economy (mining minerals and gas). You will have to ensure that you have enough of an army to fend off any attacks your opponent may make. The zealot, stalker, sentry and immortal units are your army units. These units can fight for you when the enemy comes to attack your base. Specific milestones are stated below: you must ensure that you have a sufficient army for potential attacks at specific times. How we know if your army is sufficiently large is based on the food requirements. Therefore, if the size requirement is 4, you must have at least two of any of the following units – zealots, stalkers and sentries. You can also meet the 2
The Operations Research Challenge 2012 Team Number: 4-army size requirement by having just an immortal. Any mixture of units will be sufficient, as long as the food requirements are greater than or equal to the size requirements. Note that probes do not count towards your army size. Army Size Constraints (You must have:) 4 food worth of army at 270 seconds 10 food worth of army at 500 seconds Food requirements also have another property that must be considered. As mentioned earlier, your units require various proportions of food to function. If you do not have the sufficient amount of food, you cannot build that unit. A Nexus is a source of food and can support a total of 10 food. A pylon also supplies food for your units and can support a total of 8 food. Since you start with a Nexus, you can have up to 10 food worth of units before you must either build another Nexus or pylon. Since you start with 6 probes (a total of 6 food requirements), you can build at most another 4 probes (6 4 10) before you must build a new Nexus or pylon to continue building units. The final aspect of the game is technology. We can increase our economy by building probes, Nexus and Assimilators. Army can grow by building fighting units. Technology will give you access to stronger and better units. The immortal is considered a “tech” unit since it is much stronger than the zealot, sentry and stalker. However, to obtain an immortal, we must spend more time getting the advanced building, the Robotics Facility. A common tactic in Starcraft is to use a timing push. A timing push occurs when a player obtains a specific technology and sufficient army size to attack their opponent. In our case, the technology we want is in the immortal unit and once we have this new technology, we know our army is much stronger. Of course, we will need an army to help strengthen our immortal further as well. The main goal of this problem is to build 2 Immortals, 4 sentries, 6 stalkers and 8 Zealots in the fastest possible time. Once we have these units, we can attack the enemy. However, time is very important. The longer we delay, the more time we give our opponent to build up his own army to defend our attack. The points you obtain will be based on how fast you can get the army required for this attack. The faster you are able to get these units, the more points you will get. However, you must ensure that you meet the Army Size Requirements. If you are not able to meet the size requirements, your time will be incremented by 30 seconds/food deficit. Therefore, if at 500 seconds you only have 6 food worth of army, 120 seconds will be added to your final time. When answering this question, it is best for you to make a point form list of what you will do and at what time. 3
The Operations Research Challenge 2012 Team Number: Therefore, an example answer can be @ start, time 0 @ time 0, build a probe @ time 17, probe completes @ time 50, build a pylon @ time 75, pylon completes @ time 100, build a gateway @ time 100, build a probe @ time 117, probe completes @ time 165, build a zealot @ time 167, build a Nexus @ time 203, zealot completes . Minerals: 75 Minerals: 0 Minerals: 102 Minerals: 183 Minerals: 358 Minerals: 308 Minerals: 233 Minerals: 352 Minerals: 586 Minerals: 2 Minerals: 306 Gas: 0 Gas: 0 Gas: 0 Gas: 0 Gas: 0 Gas: 0 Gas: 0 Gas: 0 Gas: 0 Gas: 0 Gas: 0 Food: 6/10 Food: 7/10 Food: 7/10 Food: 7/10 Food: 7/18 Food: 7/18 Food 8/18 Food 8/18 Food 10/18 Food 10/18 Food 10/18 Make sure that you have enough resources to build what you want at the time you have specified. If you do not have sufficient resources, you will be penalized. 4
The Operations Research Challenge 2012 Team Number: Question 2: London Olympics [40] The London Olympics start on 2012-7-27. In order to represent your country, you must solve the following puzzle: O 2 L L 0 Y O 1 M N 2 P D 7 I O 2 C N 7 Each letter represents a single digit number between 0-9, inclusive. The digits assigned to the letters have to all be different. For example, assigning 7 to both M and Y is not allowed. Please help our national athletes by informing them whether this puzzle a. Has only one solution (if so, please state the solution). b. Has multiple solutions (if so, please state at least two solutions). c. Does not have a solution (if so, please provide an explanation of why there can be no solution). 5
The Operations Research Challenge 2012 Team Number: Question 3: Planning a Picnic [60] Having participated in TORCH 2012, you have been assigned the task of making five picnic tables for an upcoming family get-together. Each picnic table has four legs (at 3 ft. high), requires five support beams (at 4 ft. long), and has a table top made of six, 5 ft. long boards. You can purchase only wood planks that are 14 ft. long. All table components have to be one continuous piece. One solution is to buy 30 wood planks and to cut each with a pattern as shown in Table 3. The pattern indicates that each wood plank is cut into one piece of 3 ft., one piece of 4 ft, one piece of 5 ft., and with 2 ft. left over. Having 30 wood planks cut with the pattern in Table 3, you will have 30 legs, 30 supports and 30 long boards. Therefore, you have enough legs, supports and long boards to make five picnic tables. However, as an expert in Operations Research, you need to find the minimum number of wood planks in order to make five tables. You also need to state the pattern(s) used to cut each plank. Cutting Pattern 3 ft. 1 4 ft. 1 5 ft. 1 Table 3: A cutting pattern 6
The Operations Research Challenge 2012 Team Number: Question 4: A Winning TORCH Strategy [100] It is the night before the third annual TORCH contest, and as team captain you want to maximize your chances of winning the next day. To do so, you will need to decide how you should prepare beforehand, what you should bring and the strategy your team should use during the day. You will have two other team members to direct, and you must provide a description of what all three teammates should do. Each student on the team can bring either a set of reference books with them, or any two of the following (two of the same item is allowed): A calculator Pencils for everyone Paper for the team to use A can of Red Bull to stay awake As well as bringing items, each student can also choose how to prepare for the quiz the night before by doing only ONE of the following: Reading reference books Reading Wikipedia Sleeping During the quiz there are two phases: morning and afternoon. For a particular phase, you must decide what each of the three members will do (they can only do one per phase): Sleep Ask questions Answer questions When making your choices as team captain, there are a number of rules you must follow to select what a member should do to prepare, bring and do for the contest. These are the rules you must follow: Each person can bring no more than two items. If they bring reference books then they cannot bring anything else. At least one person needs to bring pencils. At least one person needs to bring paper. Each person can do only one of the three preparations. A member can use reference books only if they studied reference books the night before, but the person using the books does not have to be the one to bring them. Only one person can use a set of reference books at a time. 7
The Operations Research Challenge 2012 Team Number: A member can do only one action in each phase (morning and afternoon). Only one member can use a can of Red Bull, but a team may bring (and use) multiple cans. If a member sleeps (either the night before or during the contest) then they are considered rested for the remainder of the contest. They are also considered rested if they drink a Red Bull. Drinking a can does not require an action, but occurs at the start of a phase and only lasts for the phase it is used in. For example, Person #2 drinking a can in the morning phase means they are rested for the morning phase, but not rested in the afternoon phase. A member can answer questions only if they are rested. The success of a team is measured by their TORCH Points (TPs). How does a team get TPs? By preparing and competing as efficiently as possible, of course. Specifically, these are the ways to gain TPs for a team: (5 TP) Awarded for every calculator a team has. (15 TP) Awarded for asking questions (20 TP) Awarded for answering questions without a reference book (22 TP) Awarded for asking questions with wiki knowledge (25 TP) Awarded for answering questions with a reference book Format for your answer: For this question, you must provide a plan for the three team members, including: how they should prepare, what they should bring and what they will do in the morning / afternoon phases. An example solution: Member # : Preparation / Bringing / Morning Action / Afternoon Action 1: Sleep / Calculator, Red Bull / Answer / Answer 2: Sleep / Pencils, Paper / Answer / Answer 3: Read Wiki / Calculator, Calculator / Ask / (drink) Answer Score (Answer without books * 5) (Calculators * 3) (Ask with wiki * 1) Score (20 * 5) (5 * 3) (22 * 1) Score 137TP 8
The Operations Research Challenge 2012 Team Number: Question 5: March Madness - Sweet Sixteen [200] March Madness is the top US college basketball competition where more than 60 top teams around the nation compete for National glory. After two rounds of the competition, sixteen teams are left in the tournament. The remaining sixteen teams, known as the Sweet Sixteen, are placed in a draw (see attached) where only the winner can advance and the losers go home. NCAA, the organizers of March Madness, would like you to help their ticket department for the remaining games. Given the demand for tickets to the games, the March Madness organizers want you to design a ticket package to maximize their profits. There are two types of tickets: Team Pass tickets and Individual Game tickets. The holder of the Team Pass ticket may attend all games played by a specific team. However, the Team Pass tickets must be purchased before the start of Sweet Sixteen. In comparison, the Individual Game tickets are sold before each game and they are valid for that game only. The prices of the Team Pass ticket for each team are listed below in Table 4. The prices of the Individual Game tickets are listed in the attached “2012 March Madness Tournament Bracket”. Michigan State Louisville Missouri Marquette Syracuse Wisconsin Ohio State Florida State West 40 20 20 40 East 50 30 40 30 Game 1 Kentucky Indiana Duke Baylor Game 2 Game 5 North Carolina Michigan Kansas Georgetown Game 6 South 60 50 80 20 Mid-West 70 20 60 20 Game 3 Game 4 Game 7 Game 8 Table 4: Team Pass ticket prices The capacity for each game is 10,000 and individual tickets are sold only if capacity is not met. If the number of Team Pass tickets sold to the two competing teams exceeds the capacity, a refund must be paid to all holders of the Team Pass tickets who cannot attend the game due to capacity. The refund is twice the price of the Individual Game ticket. The holders of the Team Pass ticket are still eligible for the next game if their team has advanced. Your job is to determine: The number of Team Pass tickets to be sold for each team in the Sweet Sixteen in order to maximize profit. Furthermore, you may ask an expert for a prediction of the outcome of three specific games. The expert will inform you about the teams playing in the game and the outcome. The expert’s prediction is 100% correct. 9
Game #:1 Michigan State 10 Game #:1 Louisville Game #: 9 20 Game #: 13 Game #:2 Missouri Game #:2 Marquette Game #:3 Kentucky 10 Game #: 9 30 10 Game #:3 Indiana Game #: 15 Game #: 10 20 Game #: 13 Game #:4 Duke 10 Game #: 10 Game #:4 Baylor Game #:5 Syracuse 40 10 Game #:5 Wisconsin Game #: 11 20 Game #:6 Ohio State 10 Game #: 14 Game #: 11 Game #:6 Florida State 30 Game #:7 North Carolina 10 Game #:7 Michigan Game #: 12 20 Game #: 14 Game #:8 Kansas 10 Game #: 12 Game #:8 Georgetown 2012 March Madness Tournament Bracket Game #: 15
The Operations Research Challenge 2012 Team Number: Question 6 (a): Finding a Cure [100] Meningitis Ischemia Syndrome (MIS) is a disease where an inflation of the brain is caused by deficiency of blood supply. A group of scientists have identified one hundred core chemicals that may help cure MIS, a highly contagious disease. The scientists have collectively discovered that the cause for MIS is through the infection of a chemical solution. The solution, known as the MIS-Composition or MISC, is composed of one or more core chemicals. MISC has the following properties: 1. The MISC will turn healthy living cells into infected cells. 2. The combination of MISC with other core chemicals will also turn a healthy cell into an infected cell. 3. Any combination of core chemicals that does not include the entire MISC chemicals will instantly kill a living cell. 4. The number of chemicals in MISC is at least two and at most ten. The scientists hypothesized that once the composition of MISC is known, a cure may be found. The objective of the scientists is to determine the core chemicals in MISC by making chemical solutions and testing them on cells. But first, they need your help to determine the minimum number of living cells required to fully identify MISC. Your job is to figure out that number. Please also describe your testing strategy. 10
The Operations Research Challenge 2012 Team Number: Question 6 (b): Transporting the Cure [100] Once the composition of MISC is known, the cure is created and stored in cells for transportation. We are given a container with a fixed-size grid of cells. Each position of the grid contains a cell in one of two possible states, alive or dead. Every cell interacts with the neighbours around it. At each step in time, the following transitions occur: 1. Any live cell with fewer than two live neighbours dies, as if caused by under-population. 2. Any live cell with two or three live neighbours lives on to the next generation. 3. Any live cell with more than three live neighbours dies, as if by overcrowding. 4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction. Given the grid below and the set of rules above, the problem is how to place the maximum number of live cells on the grid container so that this number will not change over time (no cell dies or is created - the cell grid remains static). Here is an example of a smaller container that worked in the previous transportation, where each live cell is indicated by an “X”: X X X X 11
The Operations Research Challenge 2012 Team Number: Question 7: London Tube [200] You are staying at The Savoy hotel in London for 14 days during the Olympics. You want to see 28 sports (i.e., all sports specified in Table 5 below). Being an operations research specialist, it should be no problem for you to save time by travelling between different event venues by subway. The sports you want to see are located in seven different venues, each of which can be reached by subway from your hotel. The hotel is located at the Charing Cross station. The closest station(s) to each venue are indicated in Table 5. If there are two stations indicated, either of them can be used to reach the venue. One visit to a particular venue allows you to view one sport (even if it is a venue for multiple sports). Every venue can be visited at most once per day. For example, you cannot see both boxing and fencing at the ExCeL centre on the same day. You are allowed to see at most two events per day. All events at a given venue start and end on the days specified in the Table 5 below. This means that you can view the sports in that venue only between the given start day and end day, inclusive. For example, football can be viewed on days 1, 2, 3, 4, 5, 6, 7 only. A map of the London Tube (subway), which indicates the locations of the seven venues is attached. You want to minimize the total travel time subject to the above constraints. The time of traveling between two stations on the same subway line is 1 minute, and the required time for switching subway lines is 3 minutes. The travel time between two venues located at the same subway station is 0. You need to return to the hotel, whose location is also indicated on the map, at the end of each day. Therefore, you need to indicate the subway path you take each day, the venues you visit, the sports you watch on each visit, the total travel time for each day and the total travel time over the 14 days. The attached map has a legend indicating the names of the subway lines. Circles on the map indicate interchange stations. For example, Charing Cross is an interchange station between Bakerloo Line and Northern Line, while the Embankment station is an interchange station between Northern, Bakerloo, Circle and District Lines. Non-interchange stations are indicated by small rectangles, see, for example, the Temple station just to the right of Embankment. Temple is a non-interchange station on the Circle Line and also a non-interchange station on the District Line. In writing your answers, please indicate the name of the subway line if there is any ambiguity (e.g., if the station is an interchange station or if there are two stations with the same name on different lines). 12
The Operations Research Challenge 2012 Team Number: Example of time calculations based on the subway map: Suppose you want to get to Baker Street station on the Metropolitan Line from your hotel at Charing Cross. One way to do so is to go through 4 stations (Piccadilly Circus, Oxford Circus, Regent’s Park, Baker Street on Bakerloo Line) and then switch stations to get to Baker Street station on Metropolitan Line. The total travel time is the 4 minutes on the Bakerloo Line plus 3 minutes for switching lines at the end, so 7 minutes. If you then want to get to West Hampstead on the Jubilee Line, you could travel from Baker Street to Finchley Road on the Metropolitan Line (1 minute), switch to Jubilee Line (3 minutes) and then travel to West Hampstead on the Jubilee Line (1 minute). Thus, the total travel time from Baker Street on the Metropolitan Line to West Hampstead on the Jubilee Line is 5 minutes. The total travel time from your hotel to West Hampstead using this route is 12. Format for your answer: Day 1: subway path: Charing Cross, Piccadilly Circus, Oxford Circus, Regent’s Park, Baker Street on Bakerloo Line, Baker Street on Jubilee Line, St. John’s Wood total travel time 8 minutes venue visited: Lord’s Cricket Ground sports watched: Archery subway path back to hotel: St. John’s Wood, Baker Street on Jubilee Line, Bond Street on Jubilee Line, Green Park on Jubilee Line, Green Park on Piccadilly Line, Piccadilly Circus on Piccadilly Line, Piccadilly Circus on Bakerloo Line, Charing Cross on Bakerloo Line total travel time 11 minutes Day 1 total travel time 19 minutes Day 2: . 13
The Operations Research Challenge 2012 Venue VeloPark Wembley Stadium, Wembley Arena Greenwich Park Basketball Arena Aquatics Centre ExCeL Earl’s Court Team Number: Closest station(s) Start (subway line names) day Stratford 1 (Central/Jubilee/DLR/ National Rail/ London Overground), West Ham (Jubilee/ District/ Hammersmith & City) End day Sports 3 Cycling – BMX, Cycling – Track Wembley Park (Metropolitan/Jubile e Line) Greenwich (DLR/National Rail), Cutty Sark (DLR) 1 7 Football, Rhythmic Gymnastics 1 8 Stratford 3 (Central/Jubilee/DLR/ National Rail/ London Overground), West Ham (Jubilee/ District/ Hammersmith & City) Stratford 5 (Central/Jubilee/ DLR/National Rail/ London Overground), West Ham (Jubilee/ District/Hammersmit h & City) Prince Regent (DLR), 3 Custom House (DLR) 5 Equestrian – Jumping, Equestrian – Dressage, Equestrian – Eventing, Paralympic Equestrian, Modern Pentathlon Basketball, Paralympic Basketball, Handball Earl’s Court (District/Piccadilly) 11 9 14 Diving, Swimming, Synchronised Swimming, Modern Pentathlon – Swimming, Paralympic Swimming, Water Polo 14 Boxing, Fencing, Judo, Table Tennis, Taekwondo, Weightlifting, Wrestling, Paralympic Table Tennis, Paralympic Judo Volleyball Table 5: Venues, subway stations and time windows for different sports. 14
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Question 1: Starcraft 2 Build Order Optimizer [200] In the game of Starcraft, you are given control over an alien race and must lead them to victory . The main goal of this problem is to build 2 Immortals, 4 sentries, 6 stalkers and 8 Zealots in the fastest possible time. Once we have these units, we can attack the enemy. However, time is .
Why should you read this Thesis? I Gives the formal basis for implementing Build Order planner for StarCraft Brood War. I Formalism can also be used in other RTS. For example StarCraft 2. I The description will allow to judge whether the formalism works with a other RTS. I The concepts used to simplify the search space could also be useful in real life temporal planning.
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starcraft ii barcraft event strategy guide tips and tactics for running a successful starcraft ii viewing party (v.0.2) contents 1.0 introduction 1 2.0 first steps 1 2.1 scout out existing events 1 2.2 the research phase 2 2.3 identify an epic event 2 2.4 find a venue 2 3.0 planning your event 3 4.0 how to promote your event 3
function of the distribution of opening build orders, so that maps with similar winning percentages exhibit similar distributions of build orders. 2 Approach Starcraft allows players to record replays of games for future viewing. To compare the win rate and the build order distribution, we collected approximately
others in this guide. First, StarCraft 2 and all other property belonging to it is the work of Blizzard Entertainment. Second, this guide does contain original work from me, but most of this guide is the original . Game Elements, Hotkeys, Build Orders, Map Notes, Advanced Unit Tricks Section B - Five Fundamentals Macro, Economy, Micro .
Chapter 1 Question 1-1: Question 1-2: Question 1-3: Question 1-4: Question 1-5: Question 1-6: Question 1-7: Question 1-8: Question 1-9: Question 1-10: . QDRO take them into account? . 33 How may the participant’s retirement benefit be div
avanzados de Alfredo López Austin, Leonardo López Lujan, Guilhem Olivier, Carlos Felipe Barrera y Elsa Argelia Guerrero con la intención de mostrar si existió ó no el sacrificio humano entre los aztecas y si los hubo con qué frecuencia y crueldad. Por otra parte, he de mencionar que la elaboración de este trabajo ha sido una ardua tarea de síntesis de diferentes fuentes sobre la .
