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What is Combinatorial Optimization?
Demonstrating the true power of combinatorial explosions and how they affect simple problems.
What is Combinatorial Optimization?
Imagine you are a Data Scientist working for an airline and are told to find the optimal flight schedule for the week to maximize the number of flights subject to constraints such as fuel and airspace.
How would you do this?
Well, you could try every possible solution, this is called brute-force search, however what if I told you we were going to do 500 flights? The number of different combinations you would need to try would be on a scale of ~500! which is roughly equal to 1.22 x 10¹¹³⁴. This number is unimaginably huge and makes brute-force search intractable.
So, how do you solve this problem?
Combinatorial Optimization!
Combinatorial optimization deals with finding an optimal solution from finite objects where the problem is intractable. This sounds very much like our problem above!
In fact, combinatorial optimization is used in sundry fields:
- Logistics and supply chain
- Manufacturing
