CS 286P Introduction to Optimization

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CS 286P Introduction to Optimization

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Course Overview

This version of the course will focus on Discrete (Combinatorial) Optimization. Let's learn more about the programme. Combinatorial optimization is a branch of mathematics related to operations research and computational complexity.

The process of selecting the best object or combination of objects from a limited number of options is known as combinatorial optimization. Many of these problems are unsolvable by exhaustive search because the set is finite but cannot be identified. Common problems include the travelling salesman problem, the minimum spanning tree problem, and the knapsack problem. Real-world applications include airline operations, supply chain management, logistics, finance, healthcare, and environmental science and engineering.

Discrete optimization was the most powerful topic in the broader discipline of Operations Research prior to WWII (the official dates appear to be 1939-1945). The initial impetus was ballistics (in general).

Many technology companies have large optimization and operations research departments (Amazon, Uber, Didi). Smaller ones (Apple, Dell, Intel, and so on) may or may not be related to supply chain management.


The final grade will be determined by four individual homework assignments (40 per cent of the grade) and five group projects (50 per cent of the grade) (40 per cent for the first 4 and 20 per cent for the final project).

There will be no final exam at the conclusion of the course. The final assignment is due on December 10th, the day before the final exam. In case, you do not get the desirable output/result then we can help you in this too. You just need to ask us to take my online exam for me and we give you a guarantee of high grades.

Evaluation of Assignments

Group homework will be completed in groups of 2-4 students, with the majority of groups consisting of three students. However, in this course, you must form your own groups, or ask the TAs or Professor Regan for assistance if you are having difficulty finding a group.

In addition, latex should be used for written assignments (most students will use Overleaf). It is critical to remember that both the final individual homework assignment and the final project must be completed on time. However, in some cases, late homework is acceptable. However, we can help you with your assignments, we offer services like do my homework or do my assignment and assure you to boost your grades. Even you can ask us for hist 1302 united states history ii online coursework help.

References and Readings

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Coding and Optimization Solver Guidelines

Homework should be completed in Python or Matlab using Gurobi. If you are unable to write assignments in python or Matlab, you can seek assistance from our experts. They will assist you in the best way possible and will also assist you in gaining some additional knowledge.

This is the web link where you must register with the Gurobi for the work done.


Course Schedule- Subject to minor changes as the course progresses


Week 1: Introduction to Optimization as a field, Introduction to current business application

  • Reading: Chapters 1 and 2 of Optimization by GRASP.
  • Homework: Take the survey on Monday of week 1 if you can, but no later than before class on Wednesday.
  • Install both the Cplex and Gurobi solvers, or investigate both and install the one you want to start with.

Week 2: Introduction to Classical Problems in Discrete Optimization

  • Knapsack problem
  • Cutting stock problem
  • Traveling salesman problem
  • Vehicle routing problem
  • Introduction to matrix formulation of problems
  • Reading: A Tutorial on Integer Programming, Gerard Cornuejols, Michael
  • J. Trick, Matthew J. Saltzman – you can focus on the problems listed
  • above.
  • Reading: What Healthcare is learning from Transportation and Manufac[1]turing https://hcs.us.com/workflow-control/
  • Homework (individual): A set of problems will be provided. Write the mathematical formulations with clean descriptions and notation

Week 3: Tricks for formulating Integer Programming Problems

  • Reading: TBD
  • Homework: TBD

 Week 4

Formulating Some Real Problems + Branch and Bound

  • Monday – A case study in class – Ecotricity
  • Wednesday – Branch and Bound
  • Homework – Solve the Ecotricity problem using Gurobi
  • Homework – other formulations to be added after class on Wednesday
  • (short additional assignment).
  • Reading – Look over the Mixed integer programming formulations for sin[1]gle machine scheduling problems, by Keha, Khowala and Fowler – no need to read every word – the idea is to see how a problem can be formulated many different ways.
  • Reading – The chapter on duality

Week 5

More about solving integer linear programs via Branch and Bound

  • Guest Lectures 
  • Branch and Bound with an LP Solver
  • Heuristic Approach using greedy (depth-first)
  • Basic Simplex Algorithm
  • Homework (Week 4): Foundations and Formulations
  • Homework (Group Project): Implement a Branch and Bound solver in MATLAB or Python and integrate with the Gurobi or Cplex Solver. Write this code in a clean manner with com[1]ments. The problems will be announced on Monday of Week 5.

Week 6: Extended vs Compact Formulations

  • Guest Lecture
  • Compact formulation of the cutting stock problem – see where this goes wrong
  • The expanded form of the cutting stock problem.
  • Branching only helps a little in the compact formulation
  • How many columns are needed?
  • Examine cases where the expanded formulation is weak.
  • Homework (Group Project): Code the weak LP relaxation and code the strong LP relaxation. Fully enumerate all columns for strong relaxation. Note how many branches are required for the weak formulation. Also, note how many columns are required for the strong formulation as the problem size grows.

Week 7: Column Generation: Basic

  • Guest Lecture
  • Primal and Dual formulation of a linear program.
  • Column generation
  • Pricing using a dynamic program.
  • The Lagrangian bound.
  • Rounding the solution to the ILP solver on a subset of the
  • columns
  • Homework (Group Project): Implement column generation on bin packing problem. Use different LP solvers and note the difference in convergence.

Week 8: Column Generation: Dual Stabilization

  • Guest Lecture 
  • Degeneracy
  • Classic dual optimal inequalities for cutting stock problems
  • Box step method.
  • Various smoothing methods
  • Homework (Group Project): Implement the box step method or a smoothing method for the single-source capacitated facility location problem.

Weeks 9 and 10: Metaheuristics Revisited

  • Genetic Algorithms, Tabu Search, GRASP (revisited), Harmony Search
  • Reading: TBD
  • Final Project (Group Project) – select an optimization problem from a set that will be provided – solve this problem with the metaheuristic of your choice.
  • Submit Your Final Project by the end of the Day on December 10th.

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