Simulated annealing is a multivariable optimization technique based on the Monte Carlo method used in statistical mechanical studies of condensed systems and follows by drawing an analogy between energy minimization in physical systems and costs minimization in design applications. In this paper, simulated annealing is introduced and reviewed. The utility of the method for optimization of chemical processes is illustrated by applying it to the design of pressure relief header networks and heat exchanger networks.
IntroductionComputer-aided chemical process design and optimization increasingly play an important role in reducing the time lag between process innovation and commercial implementation, in ensuring the efficiency and flexibility of new chemical plants, and in improving the operating efficiencies of existing plants.This paper applies the simulated annealing algorithm to design problems in chemical engineering. Simulated annealing is a general method for treating a broad class of large, multivariable optimization problems. It has found wide application in the physical sciences and engineering, but evidently not previously to problems in chemical engineering.The simulated annealing algorithm was proposed by Kirkpatrick et al.(1 983), who drew an analogy between the cooling of a fluid and the optimization of a complex system. In order for a pure substance to be 'frozen' into a perfect or nearly perfect crystal, it must be annealed by first melting and then cooling very slowly. If the substance is cooled too quickly, a crystal with many defects or a glass will be formed; the resulting structure will be far from the highly ordered, minimum energy, crystalline state. To illustrate the effectiveness of simulated annealing, Kirkpatrick et al. (1983) applied the method to two combinatorially large optimization problems: the traveling salesman problem and the layout of very-large-scale integrated (VLSI) circuit computer chips. For the latter, the placement and wiring of several thousand discrete circuit elements are principal concerns. In general, the shorter the connections are between the elements, the more optimal is the design; however, the circuit elements cannot be placed too close together since they can interfere with each other. Simulated annealing has now become a standard technique for designing VLSI chips. In particular, it is often used to assess whether designs obtained by other, perhaps heuristic, methods can be improved upon by starting the anneal-
W. B. Dolan P. T. Cummings
M. D. LeVanDepartment of Chemical Engineering University of Virginia Charlottesville, VA 22901 ing a t relatively low temperature using the proposed design as the initial configuration.Simulated annealing is based on the theory of Markov chains, as described below. It accepts and rejects randomly generated 'moves' on the basis of a probability related to an 'annealing temperature'. It can accept moves which change the value of an objective function in the direction opposite to that of the desired long-term trend. Thus, for a gl...