Divide-and-Conquer Optimization Algorithm: Difference between revisions

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(Created page with "A Divide-and-Conquer Optimization Algorithm is an optimization algorithm (to solve computational tasks) that systematically breaks down complex problems into smaller subproblems (that can be solved independently and combined). * <B>AKA:</B> Divide and Conquer Approach, D&C Algorithm. * <B>Context:</B> ** It can transform Complex Problem into multiple subproblems through problem decomposition. ** It can apply Core Strategy throu...")
 
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** [[Linear Algorithm]]s, which process [[input data]] sequentially without recursion.
** [[Linear Algorithm]]s, which process [[input data]] sequentially without recursion.
* <B>See:</B> [[Algorithm Design Pattern]], [[Recursive Algorithm]], [[Problem Decomposition Strategy]], [[Algorithmic Complexity]], [[Parallel Algorithm]], [[Recursive Partitioning Algorithm]].
* <B>See:</B> [[Algorithm Design Pattern]], [[Recursive Algorithm]], [[Problem Decomposition Strategy]], [[Algorithmic Complexity]], [[Parallel Algorithm]], [[Recursive Partitioning Algorithm]].
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== References ==
=== 2025-01 ===
* LLM
<code>
Algorithm: OPTIMIZE(problem, constraints)
Input: Optimization problem and constraints
Output: Best solution found
1. If IS_SMALL_ENOUGH(problem) Then
    Return SOLVE_DIRECTLY(problem)
2. // Divide
  subproblems = SPLIT_PROBLEM(problem)
  solutions = []
 
3. // Conquer
  For each sub in subproblems:
      If IS_FEASIBLE(sub, constraints):
          solution = OPTIMIZE(sub, constraints)
          solutions.append(solution)
4. // Combine
  result = MERGE_SOLUTIONS(solutions)
5. Return LOCAL_OPTIMIZE(result)
SPLIT_PROBLEM(problem):
    // Divide into smaller subproblems
    mid = problem.size / 2
    return [problem[0:mid], problem[mid:end]]
MERGE_SOLUTIONS(solutions):
    // Combine subsolutions into complete solution
    result = INITIALIZE_SOLUTION()
    For each s in solutions:
        result = MERGE(result, s)
    Return result
LOCAL_OPTIMIZE(solution):
    // Improve combined solution
    current = solution
    While CAN_IMPROVE(current):
        current = IMPROVE_SOLUTION(current)
    Return current
</code><


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Latest revision as of 22:22, 29 January 2025

A Divide-and-Conquer Optimization Algorithm is an optimization algorithm (to solve computational tasks) that systematically breaks down complex problems into smaller subproblems (that can be solved independently and combined).



References

2025-01

  • LLM

Algorithm: OPTIMIZE(problem, constraints)
Input: Optimization problem and constraints
Output: Best solution found

1. If IS_SMALL_ENOUGH(problem) Then
   Return SOLVE_DIRECTLY(problem)

2. // Divide
  subproblems = SPLIT_PROBLEM(problem)
  solutions = []
 
3. // Conquer
  For each sub in subproblems:
      If IS_FEASIBLE(sub, constraints):
          solution = OPTIMIZE(sub, constraints)
          solutions.append(solution)

4. // Combine
  result = MERGE_SOLUTIONS(solutions)

5. Return LOCAL_OPTIMIZE(result)
SPLIT_PROBLEM(problem):
   // Divide into smaller subproblems
   mid = problem.size / 2
   return [problem[0:mid], problem[mid:end]]
MERGE_SOLUTIONS(solutions):
   // Combine subsolutions into complete solution
   result = INITIALIZE_SOLUTION()
   For each s in solutions:
       result = MERGE(result, s)
   Return result
LOCAL_OPTIMIZE(solution):
   // Improve combined solution
   current = solution
   While CAN_IMPROVE(current):
       current = IMPROVE_SOLUTION(current)
   Return current

<