Branch And Bound Techniques

Branch and Bound Algorithm

Branch and Bound is an optimization technique used to find the most optimal solution by systematically exploring the solution space while eliminating suboptimal paths.

Key Characteristics

• Used to find the most optimal solution in search and optimization problems.
• Each solution path has a cost associated with it, and the algorithm aims to minimize or maximize this cost.
• The technique keeps track of solutions and their costs, continuing the search only if a better solution is possible.
• Unlike heuristic-based methods, Branch and Bound searches the entire solution space but eliminates unnecessary explorations.
• Each path (not just the node) has a cost, and the cost increases with path length.
• The algorithm prunes paths that have an estimated cost higher than the best solution found so far, avoiding unnecessary computations.

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function BranchAndBound(problem):
    best_solution = None
    best_cost = ∞  # Initialize best cost as infinity
    queue = PriorityQueue()  # Use a priority queue for exploring the search space
    queue.insert(problem.initial_state, cost=0)

    while queue is not empty:
        current_state, current_cost = queue.pop()  # Remove state with the least cost

        if current_cost ≥ best_cost:
            continue  # Prune this branch as it cannot yield a better solution

        if problem.is_goal(current_state):
            best_solution = current_state
            best_cost = current_cost
            continue

        for child, cost in problem.expand(current_state):
            total_cost = current_cost + cost
            if total_cost < best_cost:
                queue.insert(child, total_cost)  # Add to queue if it can be a better solution

    return best_solution, best_cost