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Localized Men on Mission Strategy

This strategy attempted to improve on the Men on Mission player from last year and was successful in doing so in a variety of game configurations. The strategy takes advantage of the fact that robots are more effective at creating rectangles close to their current position rather than drawing ones farther away. This notion led to a localized rectangle searching algorithm that is much more focused and efficient than a randomized search or a brute force search.

I. Basic Algorithm and Analysis

Here is some pseudocode explaining the algorithm:

Compute: maxDelta = n * RISKINESS
For each robot r with position p, perform:

1. If the robot is already building a rectangle R, continue building it, unless its associated score S(R) (explained below) drops down to zero.
2. Otherwise, iterate over all rectangles with one vertex at p, such that the rectangle's length and width is at least three, and the perimeter does not lie on filled cells, and the length and width are both bounded by maxDelta.
   • For each rectangle found matching the above criteria, count the number of unfilled cells on the interior. This count will be the score S(R) for that rectangle.
   • Save the coordinates of the rectangle R with the highest score.
     • If the highest scoring rectangle has a score of at least one, build a state machine for the robot, instructing it to move to the opposite corner of the rectangle, since p is already one of the corners.
     • Else, if the highest score is 0, do not draw the rectangle. Just keep moving.

Round 5	Round 27	Round 113

• The robots are able to build more quickly since no movement is required to get into the starting position.
• If a robot has no unfilled cells around it, it will move around the perimeter of the board until it finds unfilled cells. This means that the robots will systematically search for free space. At the same time they will act as guards against the opponent drawing a rectangle around the entire perimeter, an important defense in a 2 player game.
• The parameterization of the RISKINESS factor makes it easy to adjust how agressive the player should be. For a more agressive player this value can be set to 0.5. For a more conservative player, this value should be less than 2.5.
• Since the robots go for rectangles that are near rectangles they have already constructed, they are more likely to reuse existing rectangle borders in building new rectangles. This means that much of the time, the robot will only have to one or two edges before the rectangle is completed. Since the score of the rectangle is checked every time in Step 1, we will stop drawing the rectangle as soon as it is either complete or no longer viable.
• This strategy is also good at finding the last few free areas in the later stages of the game. When faced with this considerable advantage, Group 1 decided to incorporate it into their own player in order to complement their main strategy. As a result, Group 1 performed as well or better than our player in many games.

One major problem with this approach is that unless an opening is used where a lot of territory in the middle is taken up, it will be difficult for the robots to find and claim free space that is not in their immediate vicinity. Similarly, the algorithm does not guarantee that the robots will choose the optimal rectangles to draw at any given time. To address these problems, we began developing a modification to the player to make it more flexible.

II. Improving the Basic Algorithm

1. At the start of every turn, sample random locations on the board and check if those locations are in an area of free space. Give each location a score based on the number of unfilled cells that are nearby.
2. For each robot:
   • If the highest scoring rectangle at our location has score zero, check the list of board samples.
   • Assuming the list is not empty, take the sampled location with the highest score.
   • Build a state machine to instruct the robot to move to that location.
   • Once relocated, the robot should continue with the Basic Algorithm.

This procedure will effectively for robots in highly filled locations to move to locations that are more open. Unfortunately, the robots can be stuck at local minima in terms of rectangle score, preventing them from taking this alternative route. Secondly, if the robots do not move along the perimeter, then the player is danger of losing to the naive shoot-the-moon strategy.

III. Pseudo-cooperative Behaviour

Although the framework we used allows for the creation of teams of robots employing different strategies, we chose not concentrate on that aspect for this particular player. Instead this player was meant to demonstrate our most effective yet stable offensive strategy. Taking advantage of more complex cooperative or adaptive behaviour, is discussed in the Strategies Switching section.

However, we did make some modifications to the player so that it would appear as if the robots cooperated in groups of two. To achieve this, we initialized the robots in pairs. Each pair acted as a team such that the first robot would build a rectangle by moving east/west and then north/south, while the second robot would build in the opposite order. The effect of this is that the robots would build rectangles simultaneously as long as they we in the same location. This strategy was useful in the beginning when fast expansion is critical.

IV. Tournament Results and Future Work

Rank	Number of Robots	Number of Players	Board Size	Comments
1st	2	4	40
1st	5	6	50
2nd	3	6	50
2nd	2	6	50
3rd*	10	2	40	Highest ranking non-chaser
3rd	3	2	50

The results show that our player was particularly effective in games with fewer robots per player and many players. Aside from the two players that employed a chasing strategy (our newest anti-chasing implementation was not complete in time for the tournament) our player was also the best in the more standard 10-robot, 2-player scenario (*).

We expect that our player's performance in games with many robots will improve with better cooperation among the robots. Some key features that are missing include:

• Improved logic for cooperative rectangle tracing
• Optimal rectangle tracing
• Rectangle size vs. risk calculation
• More intelligent anti-chasing algorithm that monitors the length of its trail. If the length of the trail doesn't change for several consecutive moves, the robot should stop and wait until the chaser goes away.