Understanding Depth-First Branch and Bound implementation to StarCraft 2

Question

The problem is that I'm finding it difficult to understand how DFBB works, what the parameters and output should be for this case.

I'm working on creating an AI for the game StarCraft 2 that will handle the build order in the game (for team Terran). I was planning to follow the approach described in the link (see below) which followed a very similar thing that I was going for. To summarize what I'm planning to do:

A list of different type of buildings that need to be built will be given to me. Buildings cost minerals and gas (this is the currency in the game), some buildings have prerequisites (meaning other buildings need to be built before it's possible to build it) and they take a certain amount of time to build.

In the article they used Depth-First Branch and Bound to figure out the optimal build order, meaning the fastest way possible to build the buildings in that list. This was their pseudocode:

Where the state S is represented by S = (current game time, resources available, actions in progress but not completed, worker income data). How S´ is derived is described article and it is done through three functions so that bit I understand.

As mentioned earlier I'm struggling to understand what the starting status S, goal G, time limit t and bound b should be represented by in the pseudocode that they are describing.

I only know three things for sure: the list of buildings that needs to be built, what consumables I have at the moment (minerals and gas), resources (that is buildings I already have in the game). This should then be applied to the algorithm somehow, but it is unclear what the input should be to the function. The output should be a list sorted in the right order so if I where to building the buildings in the order they come in then it should all work out and it should be the optimal possible time it can be done in.

For example should I iterate through the list buildings and run DFBB on every element with the goal then being seeing if the building can be built. But what should the time limit be set too and what does bound mean in this case? Is it simply the cost?

Please explain how this function should be run on the list in order to find the optimal path of building it. The article is fairly easy to read, but I need some help understanding how it is meant to work and how I can apply it to my problem.

Link to article: https://ai.dmi.unibas.ch/research/reading_group/churchill-buro-aiide2011.pdf

Answer 1

Starting Status S is the initial state at the start of the game. I believe you have 100 minearls and Command center and 12? SCVs, so that's your start.

The Goal here is the list of building you want to have. The satisfies condition is are all building in goal also in S.

The time limit is the amount of time you are willing to spend to get the result. If yous set it to 5 seconds it will probably give you a sub-optimal solution, but it will do it in 5 seconds. If the algorithm finishes the search it will return earlier. If you don't care leave it out, but make sure you write solutions to a file in case something happens.

Bound b is the in-game time limit for building everything. You initially set it to infinite or some obvious value (like 10 minutes?). When you find a solution the b gets updated so every new solution you find MUST be faster (in-game) than the previous one.

A few notes. Make sure that the possible action (children in step 9) includes doing nothing (wait for more resources) and building an SCV.

Another thing that might be missing is a correct modelling of SCV movement speed. The units need to move to a place to build something and it also takes time for them to get back to mining.