Answer :
Final answer:
The branch and bound algorithm used by Solver branches or divides the problem into smaller subsets and explores these subsets in a systematic way using a decision tree. This approach helps limit the search to a feasible set of solutions, efficiently identifying the optimal solution.
Explanation:
The branch and bound algorithm that Solver uses to solve integer optimization models utilizes a variety of strategies for efficient problem solving. The branching part of the algorithm specifically refers to the process wherein it uses a decision tree to systematically explore subsets of solutions in order to find the optimal solution. This systematic exploration helps limit the search to a more feasible set of integer solutions rather than exploring all possibilities, which would be very time-consuming and relatively impractical.
To better understand, you can think of the whole set of potential solutions as a tree structure. The 'branching' is like starting at the root of the tree and then moving towards the branches, dividing the problem into smaller subsets (or sub-problems) along the way. At each step, the algorithm checks if the 'branch' or sub-problem can possibly lead to a better solution than the best one identified so far (also known as the incumbent solution). If not, that branch is 'bounded' or pruned, and its sub-problems are not explored. This procedure continues until the best solution is found or all subsets are pruned.
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