Dynamic Programming vs Branch and Bound

Dynamic Programming vs Branch and Bound is discussed in this blog post. Both methods are used for solving optimization problems. Optimization methods find the best solution out of a pool of feasible solutions. The aim of optimization methods is to minimize or maximize the given cost function.

Branch and Bound is a method for solving discrete and combinatorial optimization issues as well as mathematical optimization problems. The collection of candidate solutions is viewed as forming a rooted tree with the entire set at the root in a branch-and-bound method, which uses state-space search to systematically enumerate them. The method investigates the tree’s branches, which are subsets of the solution set. Before enumerating a branch’s candidate solutions, it’s tested against upper and lower estimated bounds on the optimal solution, and it’s eliminated if it can’t generate a better solution than the algorithm’s best so far.

Dynamic programming is a computer programming approach as well as a mathematical optimization tool. Richard Bellman invented the approach in the 1950s, and it has since been used in a variety of industries. It refers to breaking down a big problem into simpler sub-problems in a recursive way in both situations. While certain choice issues cannot be deconstructed in this manner, decisions that span many points in time are frequently dismantled in this manner. In computer science, a problem is said to have optimum substructure if it can be solved optimally by breaking it down into sub-problems and then recursively finding the best solutions to the sub-problems.

Dynamic Programming vs Branch and Bound

Dynamic Programming vs Branch and Bound

Dynamic Programing Branch and Bound
Constructs the solution in form of a table. Constructs the solution in form of a tree.
Solves all possible instances of problem of size n. Only solves promising instances from the set of instances at any given point.
Does not require a bounding function. Needs to compute and apply a bounding function at each node.
After constructing the table, it needs to be traced back to find the solution sequence. The solution sequence is implicit, a leaf node of the tree is the final solution.
Applications:
Binomial Coefficient
Making a change
Knapsack problem
Multistage graph
optimal Binary Search Tree
Matrix Chain Multiplication
Longest Common Subsequence
Bellman-Ford (SSSP) Algorithm
Assembly Line Scheduling
Traveling Salesman Problem
Flow Shop Scheduling
Applications:
Traveling salesman problem
Knapsack problem
Job Sequencing Problem

Additional Reading: Read More

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