A genetic programming approach for evolving highly-competitive general algorithms for envelope reduction in sparse matrices

  • Authors:

  • Behrooz Koohestani;Riccardo Poli

  • Affiliations:

  • School of Computer Science and Electronic Engineering, University of Essex, UK;School of Computer Science and Electronic Engineering, University of Essex, UK

  • Venue:
  • PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part II
  • Year:
  • 2012

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Abstract

Sparse matrices emerge in a number of problems in science and engineering. Typically the efficiency of solvers for such problems depends crucially on the distances between the first non-zero element in each row and the main diagonal of the problem's matrix -- a property assessed by a quantity called the size of the envelope of the matrix. This depends on the ordering of the variables (i.e., the order of the rows and columns in the matrix). So, some permutations of the variables may reduce the envelope size which in turn makes a problem easier to solve. However, finding the permutation that minimises the envelope size is an NP-complete problem. In this paper, we introduce a hyper-heuristic approach based on genetic programming for evolving envelope reduction algorithms. We evaluate the best of such evolved algorithms on a large set of standard benchmarks against two state-of-the-art algorithms from the literature and the best algorithm produced by a modified version of a previous hyper-heuristic introduced for a related problem. The new algorithm outperforms these methods by a wide margin, and it is also extremely efficient.