Discrete optimization

Discrete optimization is a fun way to solve problems by picking the best choice from a list of options. It mixes ideas from applied mathematics and computer science. Instead of looking for answers that can change smoothly, like temperature, it finds answers that are whole numbers or picked from a short list.

One big difference between discrete optimization and continuous optimization is that discrete optimization works with whole numbers. This helps us solve many real-world problems. For example, it can help make school schedules, design tiny parts in computers, and plan the best routes for delivery trucks.

Discrete optimization has three main parts. The first is combinatorial optimization, which works with graphs and other special structures. The second is integer programming, and the third is constraint programming. These parts work together. For example, finding the shortest path between two places can be a problem in combinatorial optimization and also in integer programming.