This is the second course of Operations Research. I think several pieces of knowledge are useful according to my experience.
Learned Things
About Algorithm
It explains what algorithms are used to solve linear programming, integer programming and nonlinear programming.
A simplex method is a method by the matrix operations to find the optimal solution on the extreme point or boundary with high efficiency instead of using the figure to solve linear programming. Because it is easy to implement it on the computer.
A branch and bound method is to solve integer programming. The idea is like the chart. Each circle is solved by the simplex method as same as linear programming.
It uses linear regression to solve the problem first to check whether the solutions are all integers or not. If it is not, it sets new constraints to the integer according to the solutions then keep trying to find the answer. It is called a branch.
The bound is the current best objective value by integer solutions in one branch. If another branch is already worse than the current best with no integer solutions, then no need to branch this node further. It is called the node is bounded.
The gradient descent and Newton’s method are to search the solution for nonlinear programming by the differential equation including first order differential equation and second order differential equation which are called Gradient and Hessians also.
About Model Implement
It mentioned the important concept of model-data decoupling. It’s a necessary design when you need to deal with practical problems in industry. It means the model is an abstraction. We can use the same model to solve different instances easily by changing the data only without changing our model code. The method is to use symbols to substitute the numbers in the model.
About Algorithm Performance
It explained how to evaluate the performance of your solution when the optimal solution can’t be obtained within a limited time. It usually used a relaxation model, a linear programming, to get the objective value. It’s also can be applied to the heuristic algorithms. The equation below can used to evaluate your algorithm quickly. Z^LR can be obtained by the simplex method.
About Gurobi Installation
Because it’s a technical part, I’ll use another post to explain this. The link. It’s an important part of solving the assessment problems in the course. Because you can’t use Excel to solve the problems anymore.
Summary
You can know what algorithm is used behind the method; therefore, you can consider the properties of these methods when you formulate your mathematical model. So, you will solve your problem more practically. If you want to take the course, you can check the course link.
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