Local Search is one of the fundamental approaches to combinatorial optimization and it used throughout AI. Several local search algorithms are based on searching k-exchange neighborhood. This set solutions that can be obtained from current solution by exchanging at most k elements. As a rule thumb, larger is, better chances finding an improved solution. However, for inputs size n, naive brute-f...

In this paper, statistical counting is introduced in the context of stochastic local search. From a sample of trajectories by independent local search computations, it is shown that interesting statistical information can be actually extracted about the search space, most notably an unbiased estimate of the number of solutions. Computational results for random #SAT instances are provided.

Most tracking-by-detection methods employ a local search window around the predicted object location in the current frame assuming the previous location is accurate, the trajectory is smooth, and the computational capacity permits a search radius that can accommodate the maximum speed yet small enough to reduce mismatches. These, however, may not be valid always, in particular for fast and irre...

In this paper we propose a form of the DIRECT algorithm that is strongly biased toward local search. This form should do well for small problems with a single global minimizer and only a few local minimizers. We motivate our formulation with some results on how the original formulation of the DIRECT algorithm clusters its search near a global minimizer. We report on the performance of our algor...

Streamlined constrained reasoning powerfully boosts the performance of backtrack search methods for finding hard combinatorial objects. We use so-called spatially balanced Latin squares to show how streamlining can also be very effective for local search: Our approach is much faster and generates considerably larger spatially balanced Latin squares than previously reported approaches (up to ord...

The Genomic Median Problem is an optimization problem inspired by a biological issue: it aims at finding the genome organization of the common ancestor to multiple living species. It is formulated as the search for a genome that minimizes some distance measure among given genomes. Several attempts have been made at solving the problem. These range from simple heuristic methods to a stochastic l...

We describe a general method for deriving new inequalities for integer programming formulations of combinatorial optimization problems. The inequalities, motivated by local search algorithms, are valid for all optimal solutions but not necessarily for all feasible solutions. These local search inequalities can help in either pruning the search tree at some nodes or in improving the bound of the...