Relaxation: Start by solving the linear programming (LP) relaxation of the ILP, which allows the decision variables to take on continuous values instead of integers.

Branching: If the solution to the LP relaxation includes non-integer values, create branches by adding constraints to force some variables to take integer values. This splits the problem into smaller subproblems.

Bounding: For each subproblem, solve the LP relaxation again to find a bound on the objective function. If the bound is worse than the best integer solution found so far, prune that branch (discard it from further consideration).

Exploration: Continue branching and bounding until all branches are either pruned or lead to feasible integer solutions. The best integer solution found during the process is the optimal solution to the ILP.