I have LP, IP, MIP + classification, clustering coming in exam. Prepare a set of questions to practice from.
Understand the Problem
The question is asking for practice questions related to Linear Programming (LP), Integer Programming (IP), Mixed Integer Programming (MIP), classification, and clustering. This indicates that the user is preparing for an exam in fields related to operations research or machine learning.
Answer
1. Differences between LP, IP, MIP and a scenario where each is best applied. 2. Formulate and solve a MIP problem. 3. Describe k-means vs hierarchical clustering. 4. Choose a clustering technique for a dataset. 5. Implications of different distance measures in clustering.
Here is a set of five practice questions for preparing for LP, IP, MIP, and clustering exams:
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Explain the differences between Linear Programming (LP), Integer Programming (IP), and Mixed-Integer Programming (MIP), and provide examples where each model would be most appropriately applied.
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Formulate a simple mixed-integer programming problem for a real-world scenario (e.g., scheduling, transportation). Solve it using a basic branch-and-bound approach.
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Describe the k-means clustering algorithm. How does it differ from hierarchical clustering?
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Given a dataset, choose an appropriate clustering technique. Justify your choice based on the properties of the data.
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Discuss the implications of using different distance measures in clustering algorithms. Provide examples of scenarios where each measure is particularly effective.
Answer for screen readers
Here is a set of five practice questions for preparing for LP, IP, MIP, and clustering exams:
-
Explain the differences between Linear Programming (LP), Integer Programming (IP), and Mixed-Integer Programming (MIP), and provide examples where each model would be most appropriately applied.
-
Formulate a simple mixed-integer programming problem for a real-world scenario (e.g., scheduling, transportation). Solve it using a basic branch-and-bound approach.
-
Describe the k-means clustering algorithm. How does it differ from hierarchical clustering?
-
Given a dataset, choose an appropriate clustering technique. Justify your choice based on the properties of the data.
-
Discuss the implications of using different distance measures in clustering algorithms. Provide examples of scenarios where each measure is particularly effective.
More Information
Clustering is a fundamental task in unsupervised machine learning used to uncover hidden patterns in unlabeled data. Meanwhile, LP, IP, and MIP models are used extensively in optimization problems across industries, from supply chain to finance.
Tips
A common mistake is confusing the applicability of LP, IP, and MIP models based on variable restrictions. Remember: LP deals with continuous variables, IP with integer variables, and MIP with a mix of both. For clustering, confusing clustering methods like k-means and hierarchical in their applications is common.
Sources
- Clustering Techniques: 40 Questions to Test Data Scientists - analyticsvidhya.com
- When to construct LP, IP, or MIP model - Mathematics Stack Exchange - math.stackexchange.com
- Mixed-Integer Programming (MIP) – A Primer on the Basics - gurobi.com
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