Constraint Selection and Deterministic Annealing

  • Authors:

  • Alistair I. Mees;Cameron Tovey

  • Affiliations:

  • Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, NT, Hong Kong (E-mail: alistair@cado.uwa.edu.au)/ Centre for Applied Dyn ...;Centre for Applied Dynamics and Optimization, The University of Western Australia, Perth, Western Australia

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2003

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Abstract

The deterministic annealing optimization method is related to homotopy methods of optimization, but is oriented towards global optimization: specifically, it tries to tune a penalty parameter, thought of as ``temperature'', in such a way as to reach a global optimum. Optimization by deterministic annealing is based on thermodynamics, in the same sense that simulated annealing is based on statistical mechanics. It is claimed to be very fast and effective, and is popular in significant engineering applications. The language used to describe it is usually that of statistical physics and there has been relatively little attention paid by the optimization community; this paper in part attempts to overcome this barrier by describing deterministic annealing in more familiar terms.The main contribution of this paper is to show explicitly that that constraints can be handled in the context of deterministic annealing by using constraint selection functions, a generalization of penalty and barrier functions. Constraint selection allows embedding of discrete problems into (non-convex) continuous problems.We also show how an idealized version of deterministic annealing can be understood in terms of bifurcation theory, which clarifies limitations of its convergence properties.