Algorithmic efficiency of simulated annealing for heat exchanger network design

Abstract Heat exchanger network synthesis by simulated annealing, a new multivariable optimization method based on the mathematical theory of Markov chains, has recently been reported by Dolan et al. ( Foundations of Computer- Aided Process Operations , CACHE, Elsevier, New York, 1987; AIChE Jl 35 , 725, 1989). Two aspects of the algorithm strongly affect computation time: the evaluation of the change in cost between different randomly generated states and the annealing temperature schedule. This paper describes a new implementation of the simulated annealing algorithm that efficiently treats the first aspect through the use of a linked-list data structure to calculate changes in cost directly, resulting in a speed increase of two orders of magnitude over earlier implementations of the algorithm. The second aspect is addressed through the use of the annealing schedule of Aarts and van Laarhoven ( Philips J. Res. 40 , 193, 1985). This new implementation of the algorithm is used to generate a new low-cost solution to the 7SP4 problem (Papoulias and Grossmann, Comput. Chem. Engng 7 , 707, 1983; Floudas et al. , AIChE Jl 32 , 276, 1986).

[1]  P.J.M. van Laarhoven,et al.  Theoretical and Computational Aspects of Simulated Annealing. , 1990 .

[2]  Ignacio E. Grossmann,et al.  A structural optimization approach in process synthesis—I: Utility systems , 1983 .

[3]  A. Dress,et al.  Parsimonious phylogenetic trees in metric spaces and simulated annealing , 1987 .

[4]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[5]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[6]  Arthur W. Westerberg,et al.  A modified least squares algorithm for solving sparse n × n sets of nonlinear equations , 1978 .

[7]  Ralph H. J. M. Otten.  Layout Compiler-Annealing Applied to Floorplan Design , 1988 .

[8]  D. Balmer.  Theoretical and Computational Aspects of Simulated Annealing , 1991 .

[9]  Ehl Emile Aarts,et al.  Statistical cooling : a general approach to combinatorial optimization problems , 1985 .

[10]  Ignacio E. Grossmann,et al.  Optimum design of heat exchanger networks , 1978 .

[11]  Peter T. Cummings,et al.  Process optimization via simulated annealing: Application to network design , 1989 .

[12]  G. B. Smith,et al.  Preface to S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images” , 1987 .

[13]  B. Linnhoff,et al.  The pinch design method for heat exchanger networks , 1983 .

[14]  Moshe J. Augenstein,et al.  Data Structures Using Pascal , 1981 .

[15]  Ignacio E. Grossmann,et al.  A structural optimization approach in process synthesis. II: Heat recovery networks , 1983 .

[16]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[17]  Christodoulos A. Floudas,et al.  Automatic synthesis of optimum heat exchanger network configurations , 1986 .

[18]  John R. Flower,et al.  Synthesis of heat exchanger networks: II. Evolutionary generation of networks with various criteria of optimality , 1978 .

[19]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  John R. Doyle,et al.  Classification by ordering a (sparse) matrix: a “simulated annealing” approach , 1988 .

[21]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .