How do you learn integer programming?

1 Basics of integer programming

Before you dive into integer programming, you need to understand some basic concepts and terminology. Integer programming is a type of linear programming, which means that the objective function and the constraints are linear expressions of the decision variables. However, unlike linear programming, some or all of the decision variables are restricted to take only integer values. This makes the problem harder to solve, as there may be many feasible solutions and no obvious way to find the optimal one. To solve integer programming problems, you need to use special algorithms and software tools, such as branch-and-bound, cutting planes, or heuristics.

2 Modeling with integer programming

One of the most important skills for learning integer programming is how to model real-world situations using mathematical equations and logical statements. Modeling is the process of translating the problem description, the objectives, the constraints, and the data into a formal representation that can be solved by a computer. To model with integer programming, you need to identify the decision variables, the objective function, and the constraints, and then express them using linear and integer expressions. You also need to choose the appropriate type of integer programming, such as binary, mixed-integer, or zero-one.

3 Solving with integer programming

Once you have a model of your problem, you need to solve it using an integer programming solver. A solver is a software tool that applies algorithms and techniques to find the optimal solution or a near-optimal solution to your problem. There are many solvers available, such as CPLEX, Gurobi, or GLPK, that can handle different types of integer programming problems and offer different features and options. To use a solver, you need to input your model in a specific format, such as LP, MPS, or AMPL, and then specify the parameters and settings that affect the performance and quality of the solution. You also need to interpret the output and analyze the results.

4 Learning resources for integer programming

To learn more about integer programming, you can use various resources, such as books, courses, tutorials, or blogs. Some of the recommended books are Introduction to Linear Optimization by Bertsimas and Tsitsiklis, Integer Programming by Wolsey, and Modeling with Integer Programming by Williams. Some of the online courses are Linear and Integer Programming by Coursera, Optimization Methods for Business Analytics by edX, and Integer Programming and Combinatorial Optimization by NPTEL. Some of the useful tutorials are Integer Programming in Python by PuLP, Solving Integer Programs in R by ompr, and Integer Programming in MATLAB by YALMIP. Some of the interesting blogs are OR in an OB World by Paul Rubin, Yet Another Math Programming Consultant by Erwin Kalvelagen, and Thoughts on Operations Research by Austin Buchanan.

5 Tips and tricks for integer programming

Finally, here are some tips and tricks that can help you learn integer programming better and faster. First, practice as much as you can with different types of problems and datasets, and compare your solutions with others. Second, use a modeling language or framework, such as AMPL, Pyomo, or JuMP, that can simplify the formulation and communication of your model and allow you to switch between different solvers. Third, learn how to tune and customize your solver to improve the speed and accuracy of your solution, and how to use advanced features, such as callbacks, lazy constraints, or user cuts. Fourth, learn how to deal with common challenges, such as infeasibility, unboundedness, nonlinearity, or uncertainty, and how to apply appropriate techniques, such as relaxation, reformulation, decomposition, or robust optimization. Fifth, keep yourself updated with the latest developments and trends in integer programming, such as new algorithms, software, or applications, and join the online community of integer programming enthusiasts and experts.

6 Here’s what else to consider

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