Bounded Implicit Enumeration for Wastewater‐Treatment Systems
Publication: Journal of Environmental Engineering
Volume 116, Issue 5
Abstract
A wastewater‐treatment system can be represented by a multistage configuration consisting of a variety of unit processes from various stages. The number of treatment combinations may be very large when the number of unit processes in a stage and the number of stages in a system increase. Enumeration techniques, e.g., total enumeration and implicit enumeration, have been used to eliminate infeasible treatment combinations and to identify the least‐cost treatment system. A bounded implicit enumeration approach is proposed to make the implicit enumeration more efficient. A lower bound is calculated at each stage and added to the up‐to‐date objective function value to eliminate more combinations before reaching the final stage. The results for two wastewater‐treatment‐system‐synthesis models indicate that the bounded implicit enumeration is consistently more efficient than the total and implicit enumeration approaches in identifying least‐cost and feasible treatment alternatives.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Adams, B. J., and Panagiotakopoulos, D. (1977). “Network approach to optimal wastewater treatment design system.” J. Water Pollution Control Federation, 49(4), 623–632.
2.
Balas, E. (1965). “An additive algorithm for solving linear programs with zero‐one variables.” Operations Res., 13(4), 517–546.
3.
Berthouex, P. M., and Polkowski, L. B. (1970). “Optimum waste treatment plant design under uncertainty.” J. Water Pollution Control Federation, 42(9), 1589–1612.
4.
Bowden, K., Gale, R. S., and Wright, D. E. (1976). “Evaluation of the CIRIA prototype model for the design of sewage treatment works.” Water Pollution Control, 75(2), 192–205.
5.
Bowden, K., and Wright, D. E. (1978). “CIRIA model for cost‐effective wastewater treatment.” Mathematical models in water pollution control, A. James, ed., John Wiley and Sons Ltd., London, U.K.
6.
Bush, M. J., and Silveston, P. L. (1978). “Opitmal synthesis of waste treatment plants.” Computer and Chemical Engrg., 2(2), 153–159.
7.
Chang, S. Y., and Liaw, S. L. (1985). “Generating designs for wastewater systems.” J. Envir. Engrg., ASCE, 111(5), 665–679.
8.
Chen, G. K., Fan, L. T., and Erickson, L. E. (1972). “Computer software for waste‐water treatment plant design.” J. Water Pollution Control Federation, 44(5), 746–762.
9.
Churchman, C. W. (1968). The systems approach. Dell Publishing Co., Inc., New York, N.Y.
10.
“Computer‐assisted procedure for the design and evaluation of wastewater treatment systems: Users Guide.” (1980). EM 1110‐2‐501, Part III, U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss.
11.
“Computer‐assisted procedure for the design and evaluation of wastewater treatment systems: Program user's guide.” (1981). PB81‐220964, NTIS, U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss.
12.
“Computer‐assisted procedure for the design and evaluation of wastewater treatment systems: Programmer's reference manual.” (1983). PB83‐173138, NTIS, U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss.
13.
Craig, E. W., Meredith, D. D., and Middleton, A. C. (1978). “Algorithm for optimal activated sludge design.” J. Envir. Engrg. Div., ASCE, 104(6), 1101–1117.
14.
Ecker, J. G., and McNamara, J. R. (1971). “Geometric programming and the preliminary design of industrial waste treatment plants.” Water Resources Res., 7(1), 18–22.
15.
Eilers, R. G., and Smith, R. (1978). “The role of computer programs in preliminary design.” Proc., Applications of computer programs in the preliminary design of wastewater treatment facilities, Section I, Workshop Lectures. EPA‐600/2‐78‐185A, Environmental Protection Agency, Washington, D.C.
16.
Eilers, R. G., et al. (1978). “Applications of computer programs in the preliminary design of wastewater treatment facilities, Section II.” EPA‐600/2‐78‐185B, Environmental Protection Agency, Washington, D.C.
17.
Evenson, D. E., Orlob, G. T., and Monser, J. R. (1969). “Preliminary Section of Waste Treatment Systems.” J. Water Pollution Control Federation, 41(11), 1845–1858.
18.
Fan, L. T., et al. (1973). “Synthesis of bioengineering systems.” AIChE Symp. Series, 69(132), 123–133.
19.
Gillett, B. E. (1976). Introduction to operations research: A computer oriented algorithmic approach. McGraw‐Hill, Inc., New York, N.Y.
20.
Grady, C. P. L., Jr. (1977). “Simplified optimization of activated sludge process.” J. Engrg. Div., ASCE, 103, 413–429.
21.
Ignall, E., and Schrage, L. (1965). “Application of the branch and bound technique to some flowshop problems.” Operations Res., 13(3), 400–412.
22.
Keinath, T. M., and Wanielista, M. (1975). Mathematical modeling for water pollution control process. Ann Arbor Science Publisher Inc., Ann Arbor, Mich.
23.
Liaw, S. L. (1986). “Use of optimization models in the design of wastewater treatment systems,” thesis presented to the University of Missouri, at Rolla, Mo., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
24.
Lynn, W. R., Logan, J. A., and Charnes, A. (1962). “Systems analysis for planning wastewater treatment plants.” J. Water Pollution Control Federation, 34(6), 565–579.
25.
McGhee, T. J., Mojgani, P., and Vicidomina, F. (1983). “Use of EPA's CAPDET program for evaluation of wastewater treatment alternatives.” J. Water Pollution Control Federation, 55(1), 35–43.
26.
Middleton, A. C., and Lawrence, A. W. (1974). “Cost optimization of activated sludge systems.” Biotech. Bioengrg., 16(6), 807–826.
27.
Middleton, A. C., and Lawrence, A. W. (1976). “Least cost design of activated sludge systems.” J. Water Pollution Control Federation, 48(5), 889–905.
28.
Mishra, P. N., Fan, L. T., and Erickson, L. E. (1974a). “Optimal capacity expansion of a secondary treatment system.” J. Water Pollution Control Federation, 46(12), 2704–2716.
29.
Mishra, P. N., Fan, L. T., and Erickson, L. E. (1974b). “Application of mathematical optimization techniques in computer aided design of wastewater treatment systems.” Water‐1974: II. Municipal Waste Treatment, AIChE Symp. Series, 71(145), 136–153.
30.
Morin, T. L., and Marsten, R. E. (1976). “Branch‐and‐bound strategies for dynamic programming.” Operations Res., 24(4), 611–627.
31.
Panwalkar, S. S., and Khan, A. W. (1976). “An improved branch and bound procedure for nxm flowshop problems.” Naval Res. Logistics Quarterly, 22(4), 787–790.
32.
Parkin, G. F., and Dague, P. R. (1972). “Optimal design of wastewater treatment systems by enumeration.” J. Sanit. Engrg. Div., ASCE, 98(6), 833–851.
33.
Piper, C. J., and Zoltners, A. A. (1976). “Implicit enumeration based algorithms for postoptimizing zero‐one programs.” Naval Res. Logistics Quarterly, 22(4), 791–809.
34.
Rossman, L. A. (1979). “Computer‐aided synthesis of wastewater treatment and sludge disposal systems.” EPA‐600/2‐79‐158, Environmental Protection Agency, Washington, D.C.
35.
Rossman, L. A. (1980a). “Synthesis of waste treatment systems by implicit enumeration.” J. Water Pollution Control Federation, 52(2), 148–160.
36.
Rossman, L. A. (1980b). “EXEC/OP reference manual: Version 1.2.” Wastewater Res. Div., Municipal Environmental Res. Lab., Environmental Protection Agency, Washington, D.C.
37.
Roodman, G. M. (1974). “Postoptimality analysis in integer programming by implicit enumeration; The mixed integer case.” Naval Res. Logistics Quarterly, 21(4), 595–607.
38.
Rountree, S. L. K. (1979). “Parametric integer linear programming: A synthesis of branch and bound with cutting planes,” thesis presented to the University of Missouri, at Rolla, Mo., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
39.
Scherfig, J., Schinzinger, R., and Morgan, T. W. (1970). “Waste treatment optimization by geometric programming.” Advances in Water Pollution Research, Proc. 5th Int. Conf. 2, II‐22/11‐II‐22/18, Int. Assoc. on Water Pollution Res., San Francisco, Calif.
40.
Shih, C. S., and Krishman, P. (1969). “Dynamic optimization for industrial waste treatment design.” J. Water Pollution Control Federation, 41(10), 1787–1802.
41.
Shih, C. S., and Defilippi, J. A. (1970). “System optimization of waste treatment plant process design.” J. Sanit. Engrg. Div., ASCE, 96(2), 409–421.
42.
Smith, D. W. (1970). “Computer design of CMAS systems.” J. Sanit. Engrg. Div., ASCE, 96(4), 977–990.
43.
Sterling, R. A. (1976). “Computerized algorithms simplify meeting federal effluent standards.” Water and Sewage Works, 123(10), 68–72.
44.
Suidan, M. T., et al. (1983). “Wastewater treatment: Sensitivity analysis.” J. Envir. Engrg., ASCE, 109(1), 120–138.
45.
Tang, C. C., Brill, E. D., Jr., and Pfeffer, J. T. (1987a). “Optimization techniques for secondary wastewater treatment system.” J. Envir. Engrg., ASCE, 133(5), 935–951.
46.
Tang, C. C., Brill, E. D., Jr., and Pfeffer, J. T. (1987b). “Comprehensive model of activated sludge wastewater treatment system.” J. Envir. Engrg., ASCE, 133(5), 952–969.
47.
Tyteca, D., Smeers, Y., and Nyns, E. D. (1977). “Mathematical modeling and economic optimization of wastewater treatment plants.” CRC Crit. Rev. Environ. Control, 8(1), 1–89.
48.
Tyteca, D. (1981). “Nonlinear programming model of wastewater treatment plant.” J. Envir. Engrg. Div., ASCE, 107(4), 747–765.
49.
Tyteca, D., and Smeers, Y. (1981). “Nonlinear programming design of wastewater treatment plant.” J. Envir. Engrg. Div., ASCE, 107(4), 766–779.
Information & Authors
Information
Published In
Copyright
Copyright © 1990 ASCE.
History
Published online: Sep 1, 1990
Published in print: Sep 1990
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.