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Why is min conflicts so effective on the n queens problem?

  • A.The constraints are all unary and so trivially satisfied
  • B.The problem can be decomposed into independent subproblems
  • C.The solution density is high and the landscape has few local optima
  • D.The problem has only one solution which is easy to find

Answer: C

For large n solutions are extremely numerous and almost any starting point is within a few repairs of one, so a greedy repair heuristic succeeds almost immediately. Problems with few solutions or rugged landscapes defeat it. Solutions are many rather than unique, the constraints are binary, and no decomposition exists. That an algorithm's success depends on the solution density of the instance, rather than on the problem class, explains why local search performs so unevenly.

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