Discrete Optimization (Coursera) week2 - 1.5 问题的建模，A toy example

Take 1-D knapsack problem as an example:

How to model an optimization problem

• Choose some decision variables
• Express the problem constraints in terms of these variables
• Express the objective function

In 1-D knapsack

The difficulty comes from the exponential growth of search space:

Suppose there are 50 items to pick, then we have $2^{50}$250 choices. If we use 1 milisecond to check if a solution is valid, it needs 1,285,273,866 centuries.

So We have to somehow narrow the search space …