The Knapsack Problem is a famous problem that falls in the optimization category.
It derives its name from a scenario where, given a set of items with specific weights and assigned values/profits, the goal is to maximize the value/profit in the knapsack while remaining within the weight constraint.
Since this is the 0/1 version, each item can only be selected once, as we don’t have multiple quantities of any item.
Branch and Bound or B&B is an algorithm design paradigm that solves combinatorial and discrete optimization problems. Many optimization issues, such as crew scheduling, network flow problems, and production planning, cannot be solved in polynomial time. Hence, B&B is a paradigm that is widely used to solve such problems.
This algorithm heavily depends on efficiently estimating the search space’s lower and upper limits of branches. It degenerates to an exhaustive or thoroughgoing search if no limits are found. The branch and bound method solves these complex problems relatively faster. In most discrete optimization problems, the B&B method is a reliable choice to solve the issue.