Intro
As a passionate player of settlers of catan I’ve always been intrigued in figuring out a winning strategy. But it seems that every time I play there is a sneaker player that outsmarts me with a better strategy. Is it luck? is my non-poker face revealing all my plans? Or is my initial strategy just not good enough? Soon we will find out.
And you ask why is a computational designer / architect interested in such a nerdy endeavour? Well, we just implemented a multiple objective optimization engine in KOPE, and we believe it is capable of simplifying many computational challenges encountered in modern methods of construction. So, for now, just for fun, lets step outside of the world of industrialized construction and push the limits of what this engine can solve.
Catan
I’m guessing that if you decided to read this blogpost you likely know how to play Settlers of Catan, but just as a quick recap. Settlers of Catan is a game of resource collection, where players create settlements next to different resource tiles. Whenever the dice outcome matches the number on the tile these resources are collected and then used to accomplish different objectives such as building roads, cities, armies, etc. These objectives grant you points, the first player to get ten points wins.
So basically…
The game starts with a hexagonal grid imitating an island full of resources. Both resource tiles and numbers are placed differently every game. Since every element you build on the map has a unique building cost every settlement you build directly influences your chance of getting a resource and expanding your empire.
Will leave some other rules and details out just for the sake of this demonstration.
Strategy
So, how come this apparently simple game nurture such devotion and rivalry? It all comes down to setting strategies to outcompete other players for resources, and since there are multiple ways to win, there are multiple objectives a player may pursue (foreshadowing future use of multiple objective optimization) There is also the added complexity of power relations /psychology and trade. So, a straightforward computer calculation will not get you to win. You need to analyse possible opportunities and be clever at adapting your game to fulfil these opportunities.
We will now explore placement strategies for the beginning of the game. Then of doing a little bit of google research I’ve narrowed the list of recommendations to these 6:
1. Focus on the odds
2. Get a good distribution of numbers
3. Diversify your resources
4. Build plenty of roads
5. Get development cards
6. Monopolize a resource
With a little help from statistics, we can easily evaluate settlement positions to a certain criterion. Let’s take for example recommendation number1 (focus on the odds). By using double dice probability, we can score and compare each position.
Focusing only on this criterion can be restrictive, as you are not aware of other implications; is a resource monopolized by another player? Will you be able to build roads? etc.
This is where a multiple objective optimization engine may come in handy, allowing you to compare and optimize multiple nonrelated criteria. So, for now I took the 6 recommendations described above and the dice probability chart to rate different first placement positions for a fake 4thred player.
Option 1:
Option 2
You can compare both options and decide what strategies to consider, if you are interested in monopolizing a material you may go with option 1, or if you decide to focus on roadbuilding, you may choose option 2.
Let’s use KOPE’s multiple objective optimization engine to generate different solutions. We are going to place settlement 1 and settlement2 at various parts of the board and analyse their scores. (This takes just a couple of seconds)
You can sort and filter solutions based on desired criteria:
Or you can use the advanced chart filter to explore multiple solutions at once:
Exposure vs Automation
If you have read something on AI and gaming, you probably know that there are currently far more advanced deep learning techniques to automate a game strategy. So why and when is multiple objective optimization valuable? As you have seen above multiple objective optimization solutions are quite comprehensible. Their procedure is transparent, so you can take an active involvement in deciding a final solution. Multiple objective optimizations are also ideal for small-simple-interconnected optimization problems, and these are abundant in the MMC world.
Going back to Modern Methods of Construction
Since we are not in the Catan winning business, but in the AEC business we have been applying multiple objective optimizations to offsite construction with great success. Barton Malow for example, required a study in prefab slab design, where cost, floor plate efficiency, framing tonnage, etc. were considered in optimizing a slab fabrication system. You can see a study below:
