Which of the following best describes the technique for solving optimization problems where making the locally optimal choice at each step leads to a globally optimal solution"

The correct answer is Option 3) Greedy method.

Key Points

• The Greedy Method is an algorithmic paradigm that solves optimization problems by making a sequence of choices, each of which looks best at the moment (locally optimal).
• The key assumption is that these locally optimal choices will lead to a globally optimal solution.
• Common examples where greedy algorithms work effectively:
  • Activity Selection Problem
  • Fractional Knapsack Problem
  • Dijkstra’s Shortest Path Algorithm (non-negative weights)
  • Prim’s Minimum Spanning Tree Algorithm

Additional Information

• Option 1 – Branch and Bound: Used for solving combinatorial problems like TSP, Knapsack (0/1), but explores the entire state space with bounding to eliminate unpromising options.
• Option 2 – Backtracking: Explores all possibilities recursively and backtracks upon reaching a dead end. More exhaustive than greedy.
• Option 4 – Dynamic Programming: Solves problems by combining the solutions of overlapping subproblems. Suitable for problems with optimal substructure and overlapping subproblems, not just local choices.

Conclusion: Greedy Method solves optimization problems by making locally optimal choices at each step with the hope of reaching a global optimum.