A Novel LP-based Local Search Technique -Fast and Quite Good-

• Main Author: Avdil, Alaubek
• Format: Others
• Language: English; en
• Published: 2009
• Online Access: https://tuprints.ulb.tu-darmstadt.de/1914/1/thesis_avdil.pdf; Avdil, Alaubek <http://tuprints.ulb.tu-darmstadt.de/view/person/Avdil=3AAlaubek=3A=3A.html> (2009): A Novel LP-based Local Search Technique -Fast and Quite Good-.Darmstadt, Technische Universität, [Ph.D. Thesis]

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 the modification of the underlying problem. Generally speaking, we will look at the non-linear formulations of the problems and apply small modifications to transform the non-linear ingredients into linear ones. It is a requirement of our technique to work that the optimal basis solutions of the LP are feasible to the primary optimization problem. We consider four optimization problems: the directed Max-Cut problem with a source and a sink, and three variations of the Max-k-SAT problem with k=2, k=3 and k=4. In each case, we define the modification such that the vertices of the LP are integral, and that the simplex method will not end up at infinity. To compare our technique, we run local search repeatedly with random start solutions. Our technique produces consistently final solutions whose objective values are nearly identical to 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. Furthermore, an implementation of our technique to the Longest Directed Path problem with a source and a sink (in which we obtain an LP by incorporating flow-consistency inequalities) strongly supports our empirical findings. On the other hand, the run time of our technique is rather small, so the technique is very efficient and seemingly quite accurate.