We introduce a meta-heuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima. It makes large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We have tested this meta-heuristic for the traveling salesman and graph partitioning problems. Tests on instances from public libraries and random ensembles quantify the power of the method. Our algorithm is able to solve large instances to optimality, improving upon state of the art local search methods very significantly. For the traveling salesman problem with randomly distributed cities in a square, the procedure improves on 3-opt by 1.6%, and on Lin-Kernighan local search by 1.3%. For the partitioni...

Many large-scale engineering and scientific calculations involve repeated updating of variables on an unstructured mesh. To do these types of computations on distributed memory parallel computers, it is necessary to partition the mesh among the processors so that the load balance is maximized and inter-processor communication time is minimized. This can be approximated by the problem of partitioning a graph so as to obtain a minimum cut, a well-studied combinatorial optimization problem. Graph partitioning is NP complete, so for real world applications, one resorts to heuristics, i.e., algorithms that give good but not necessarily optimum solutions. These algorithms include recursive spectral bisection, local search methods such as Kernighan-Lin, and more general purpose methods such as simulated annealing. We show that a general procedure enables us to combine simulating annealing with Kernighan-Lin. The resulting algorithm is both very fast and extremely effective. 1 Introduction Co...

We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by “local” algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given the distribution of cut sizes associated with each heuristic, we provide a ranking procedure which takes into account both the quality of the solutions and the speed of the algorithms. This procedure is demonstrated for a selection of local graph bisection heuristics.

This paper proposes a method for partitioning the vertex set of an undirected simple weighted graph into two subsets so as to minimise the difference of vertex-weight sums between the two subsets and the total weight of edges cut (i.e., edges with one end in each subset). The proposed heuristic algorithm works in a divide-and-conquer fashion and is a modification of an algorithm suggested in the literature. The algorithm has the same time complexity as the previous one but is extended to work on weighted graphs. 1 Introduction While graph partitioning problems, in particular the minimal-cut graph bisectioning problem, have been studied in [3, 10, 12], they have been concerned with unweighted graphs. These studies have thus concentrated mostly on minimising the number of edges cut while partitions are constrained to containing equal numbers of vertices (or a difference of one for graphs with odd numbers of vertices). The minimal-cut problem has seen applications in memory segmentation ...

In this thesis we show a need for a new ASIC IC design methodology that produces more regular IC layout masks by construction otherwise it will be impossible or prohibitively expensive to manufacture or, even, verify manufacturability of IC designs at technology nodes of 65nm and below Regularity- definition by Oxford English Dictionary: 1.Arranged or recurring in a constant or definite pattern, especially with the same space between individual instances. 2.Doing the same thing often or at uniform intervals. 3.Done or happening frequently. 4.Conforming to or governed by an accepted standard of procedure or convention.