Planning of Chemical Process Networks via Global Concave Minimization
The problem of selecting processes and planning expansions of a chemical complex to maximize net present value has been traditionally formulated as a multiperiod, mixed-integer linear program. In this paper, the problem is approached using an entirely continuous model. Compared to previous models, the proposed formulation allows for more general objective functions. In solving the continuous model, minimizing its nonconvex objective function poses the major obstacle. We overcome this obstacle by means of a branch-and-bound global optimization algorithm that exploits the concavity and separability of the objective function and the linearity of the constraint set. The algorithm terminates with the exact global optimum in a finite number of iterations. In addition, computational results demonstrate that the proposed algorithm is very efficient as, for a number of problems from the literature, it outperforms OSL, a popular integer programming package. We also develop a procedure for generating test problems of this kind.
KeywordsBipartite Graph Process Network Linear Programming Relaxation Capacity Expansion Convex Envelope
Unable to display preview. Download preview PDF.
- A. Brooke, D. Kendrick and A. Meeraus. GAMS-A User's Guide. The Scientific Press, Redwood City, CA, 1988.Google Scholar
- IBM. Optimization Subroutine Library Guide and Reference Release 2. International Business Machines Corporation, Kingston, NY, third edition, July 1991.Google Scholar
- M. L. Liu and N. V. Sahinidis. Long range planning in the process industries: A projection approach. To appear in Computers é4 operations research, 1995.Google Scholar
- H. S. Ryoo and N. V. Sahinidis. A branch-and-reduce approach to global optimization. Accepted for publication, Journal of Global Optimization, 1995.Google Scholar
- H. S. Ryoo and N. V. Sahinidis. Global optimization of nonconvex nips and minlps with applications in process design. Computers and Chemical Engineering, 19: 551 - 566, 1995.Google Scholar
- N. V. Sahinidis and I. E. Grossmann. Reformulation of the multiperiod milp model for capacity expansion of chemical processes. Operations Research, 40, Supp. No. 1: S127 — S144, 1992.Google Scholar
- J. P. Shectman and N. V. Sahinidis. A finite algorithm for global minimization of separable concave programs. In C. A. Floudas and P. M. Pardalos, editors, Proceedings of State of the Art in Global Optimization: Computational Methods and Applications, Princeton University, April 28-30, 1995, 1995.Google Scholar