It is possible to obtain the porosity and permeability of filter cakes formed during cake filtration by fitting power law type relationships to experimental data. Specifically, local filtration data of the form of pressure and concentration profiles can be used to determine the constitutive relationships. However, when applied to data on the filtration of suspensions encountered in the pulp and paper industry, methods of minimization such as the Levenberg-Marquardt (LM) method fail to produce unique sets of model parameters representing the constitutive relationships. Recourse to more sophisticated methods such as simulated annealing (SA) has to be made in order to obtain suitable global minima for describing wide ranging experimental data. In this paper, we chose experimental filtration data of pulp mill lime muds (essentially CaCO3 particulate suspensions) reported by 'Sep. Technol. 5 (1995) 165' to study the best means of obtaining robust parameter sets for use in the permeability and compressibility relationships. The efficacy of a heuristic algorithm based on SA over a straightforward LM algorithm as applied to the filtration of lime muds and papermaking pulps is demonstrated. A second example of constant pressure filtration of papermaking pulps reported by 'TAPPI 35 (1952) 439' was also chosen. The parameters in the permeability relationship for pulp mats consist of the specific surface area (hydrodynamic) and the specific volume of the papermaking fibers. By using the SA method, it is shown that these two parameters as well as the compressibility parameters could be determined directly. (C) 2002 Elsevier Science B.V. All rights reserved.