Simulated Annealing with a Temperature Dependent Penalty Function

Abstract

We formulate the problem of permuting a matrix to block angular form as the combinatorial minimization of an objective function. We motivate the use of simulated annealing (SA) as an optimization tool. We then introduce a heuristic temperature dependent penalty function in the simulated annealing cost function, to be used instead of the real objective function being minimized. Finally we show that this temperature dependent penalty function version of simulated annealing consistently outperforms the standard simulated annealing approach, producing, with smaller running times, better solutions. We believe that the use of a temperature dependent penalty function may be useful in developing SA algorithms for other combinatorial problems. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.