Advantages of Branch and Bound Algorithm

• We don’t explore all the nodes in a branch and bound algorithm. Due to this, the branch and the bound algorithm have a lower time complexity than other algorithms.
• Whenever the problem is small and the branching can be completed in a reasonable amount of time, the algorithm finds an optimal solution.
• By using the branch and bound algorithm, the optimal solution is reached in a minimal amount of time. When exploring a tree, it does not repeat nodes.

Branch and bound algorithms are used to find the optimal solution for combinatory, discrete, and general mathematical optimization problems.

A branch and bound algorithm provide an optimal solution to an NP-Hard problem by exploring the entire search space. Through the exploration of the entire search space, a branch and bound algorithm identify possible candidates for solutions step-by-step.

There are many optimization problems in computer science, many of which have a finite number of the feasible shortest path in a graph or minimum spanning tree that can be solved in polynomial time. Typically, these problems require a worst-case scenario of all possible permutations. The branch and bound algorithm create branches and bounds for the best solution.

In this tutorial, we’ll discuss the branch and bound method in detail.

Different search techniques in branch and bound:

The Branch  algorithms incorporate different search techniques to traverse a state space tree. Different search techniques used in B&B are listed below:

1. LC search
2. BFS
3. DFS

1. LC search (Least Cost Search):

It uses a heuristic cost function to compute the bound values at each node. Nodes are added to the list of live nodes as soon as they get generated.
The node with the least value of a cost function selected as a next E-node.

2.BFS(Breadth First Search):
It is also known as a FIFO search.
It maintains the list of live nodes in first-in-first-out order i.e, in a queue, The live nodes are searched in the FIFO order to make them next E-nodes.

3. DFS (Depth First Search):
It is also known as a LIFO search.
It maintains the list of live nodes in last-in-first-out order i.e. in a stack.

The live nodes are searched in the LIFO order to make them next E-nodes.