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A Multiobjective Optimization of a Room Configuration

Designing a good room configuration is not a simple task. Even deciding whether one is better than another is often very difficult! This Demonstration is an example of a multiobjective optimization of a very simple building layout with two apartments (red and green), each having only two rooms (red: 1, 2; green: 3, 4) and a corridor. The layouts are ranked according to three criteria:
1) The size of the corridor (the blue grid)
2) The distance of room 3 from the southernmost edge of the layout
3) The geometrical complexity
For the rooms, the geometrical complexity is the total number of unique coordinates of all the corners of each room. If two rooms share a corner, it is counted only once; for the corridor, the geometrical complexity is the number of unshared vertices.
These three values are normalized, weighted, and combined into the aggregate objective function (AOF). You can change the weights to alter the importance of a given parameter; for example, "It is very important that room 3 (for the green apartment) is on the south AND that the corridor (of the whole layout) is as small as possible". The values of these parameters are shown for each layout. There are 247 different room configurations, but only the 12 best (according to a given AOF) are shown.

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Related Curriculum Standards

US Common Core State Standards, Mathematics

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