Local search starting from an LP solution: Fast and quite good

We present and evaluate a specific way to generate good start solutions for local search. The start solution is computed from a certain LP, which is related to the underlying problem. We consider three optimization problems: the directed MAX-CUT problem with a source and a sink and two variations of the MAX-k-SAT problem with k = 2 and k = 3. To compare our technique, we run local search repeatedly with random start solutions. Our technique produces, consistently, final solutions whose objective values are not too far from the best solutions from repeated random starts. The surprising degree of stability and uniformity of this result throughout all of our experiments on various classes of instances strongly suggests that we have consistently achieved nearly optimal solutions. On the other hand, the runtime of our technique is rather small, so the technique is very efficient and probably quite accurate.

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