In this paper we describe the advantadges and disadvantages of local search and exact methods of solving NP-hard problems and see why combining the two approaches is highly desirable. We review some of the papers existent in the literature that create new algorithms from such combinations. In this paper we focus on local search approaches that are strengthened by the use of exact algorithms.

For efficiency reasons, neighbourhoods in local search are often shrunk by only considering moves modifying variables that actually contribute to the overall penalty. These are known as conflicting variables. We propose a new definition for measuring the conflict of a variable in a model and apply it to the set variables of models expressed in existential second-order logic extended with counti...

This work presents a local search approach to the High School Timetabling Problem. The addressed timetabling model is the one stated in the Third International Timetabling Competition (ITC 2011), which considered many instances from educational institutions around the world and attracted seventeen competitors. Our team, named GOAL (Group of Optimization and Algorithms), developed a solver built...

Using constraint-based local search, we effectively model and efficiently solve the problem of balancing the traffic demands on portions of the European airspace while ensuring that their capacity constraints are satisfied. The traffic demand of a portion of airspace is the hourly number of flights planned to enter it, and its capacity is the upper bound on this number under which air-traffic c...

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In this paper, we examine the eeects of noise on both local search and genetic search. Understanding the potential eeects of noise on a search space may explain why some search techniques fail and why others succeed in the presence of noise. We discuss two eeects that are the result of adding noise to a search space: the annealing of peaks in the search space and the introduction of false local...

An Iterated Local Search method for the constrained two-dimensional non-guillotine cutting problem is presented. This problem consists in cutting pieces from a large stock rectangle to maximize the total value of pieces cut. In this problem, we take into account restrictions on the number of pieces of each size required to be cut. It can be classified as 2D-SLOPP (two dimensional single large o...

A number of algorithms have been proposed for the Minimum Vertex Cover problem. However, they are far from satisfactory, especially on hard instances. In this paper, we introduce Edge Weighting Local Search (EWLS), a new local search algorithm for the Minimum Vertex Cover problem. EWLS is based on the idea of extending a partial vertex cover into a vertex cover. A key point of EWLS is to find a...