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MIPs

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by

Sharlee Climer

on 30 April 2018

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Transcript of MIPs

MIPs
Mixed Integer Programs (MIPs)
Can be used to represent many diverse problems
Generic solvers can be used to solve to optimality
How can we model the TSP?
Given a set of cities and the cost of travel between pairs of cities
Find the minimum-cost tour that visits each city and returns to the start city

Most are NP-hard
NP: non-deterministic polynomial time
Combinatorial explosion of number of feasible solutions

Traveling Salesman Problem (TSP)
Extensively researched
Produced search strategies for more general problems

MIPs in Biological Data Science
24,978-city TSP (Sweden)
85,900-city TSP (integrated circuit)
How many feasible solutions?
(
n
- 1) !
Approximate solution for 100,000-city TSP
$1000 award for finding a better solution
49-city TSP
1954
532-city TSP
1987
What do you think are the largest TSPs that have been solved to optimality?
Sequence alignment problem:
Shortest Common Superstring
MIPs in Biological Data Science
Clustering
k
-Means
Newman's Modularity
cGWAS
Michael's research
Other possibilities
Protein folding
Protein docking
Many other possibilities
This can be cast as a TSP!
Use DNA nucleotides in sequencing reads to map a genome
Computing costs continue to decline
Even if Moore's Law slows, still increasingly affordable to have more processors working in parallel
Optimally solving NP-Hard problems may become more commonplace in the near future
Full transcript