Multiobjective Optimal Waste Load Allocation Models for Rivers Using Nondominated Sorting Genetic Algorithm-II S. R. Murty Yandamuri 1 ; K. Srinivasan 2 ; and S. Murty Bhallamudi 3 Abstract: A multiobjective optimization framework for optimal waste load allocation in rivers is proposed, considering 1 the total treatment cost, 2 the equity among the waste dischargers, and 3 a comprehensive performance measure that reflects the dissolved oxygen DO violation characteristics. This framework consists of an embedded river water quality simulator that has a gradually varied flow module and a pollutant transport module, which simulates the transport process including reaction kinetics in terms of biochemical oxygen demand-DO. The outer shell of the framework consists of the two nonseasonal, deterministic, multiobjective waste load alloca- tion planning models, namely, cost-performance model and cost-equity-performance model. These models are solved using a powerful and recently developed multiobjective genetic algorithm technique known as the Nondominated Sorting Genetic Algorithm-II. The practical utility of the multiobjective framework in decision-making is illustrated through a realistic example of the Willamette River in the state of Oregon. DOI: 10.1061/ASCE0733-94962006132:3133 CE Database subject headings: Wasteload allocation; Rivers; Dissolved oxygen; Oregon; Water pollution. Introduction Water quality protection along rivers involves water quality moni- toring and assessment, establishing water quality goals, and con- trolling pollutant discharges, so that an acceptable level of water quality is maintained. The control of water quality in any river/ stream at various locations, requires the determination of the op- timal pollutant removal levels at a number of point and nonpoint source locations along the river that would yield a satisfactory water quality response in a cost-effective, equitable, and efficient manner Burn 1987; Burn and Yulianti 2001. This is known as “optimal waste load allocation.” Typical multiobjective optimal waste load allocation problems address minimization of the total treatment cost and minimization of the inequity among the pollutant dischargers, subject to con- straints on satisfaction of a specified dissolved oxygen DO stan- dard at all the check points located along the river Brill et al. 1984; Srigiriraju 2000; Burn and Yulianti 2001. Performance measures such as number of DO violations, magnitude of maxi- mum DO violation, and total magnitude of DO violations at the checkpoints can be expressed either as additional objectives or as constraints in the optimization model. Burn and Lence 1992 proposed four different optimization formulations of a general waste load allocation model to evaluate efficient management solutions. Two of these formulations were based on maximum deviations from a specified DO standard and the other two on total deviations from the same. Cardwell and Ellis 1993 pro- posed a series of optimization models with the aim to minimize the control cost and either the number of water quality standard violations or some measure of the magnitude of violations. These multiobjective models can be used to generate trade-offs between cost and either frequency or magnitude of water quality standard violations. Recently Burn and Yulianti 2001 have formulated two planning models with treatment cost as one of the objectives, and either total magnitude of DO violations or equity as the other objective. The number of objective functions to be handled will increase to five if all three previously mentioned performance measures are to be included in the cost-equity based optimal waste load allocation model as separate objective functions, in order to en- sure complete representation of the system. Obtaining the Pareto- optimal solutions would become very difficult in such a case. Also, analysis of the trade-off relationships among the various objectives would become complicated. Therefore, it is useful to derive a comprehensive performance measure that would include 1 the number of DO violations, 2 the magnitude of maximum DO violation, and 3 the total magnitude of DO violations. Also, cost-equity formulations do not offer flexibility to the decision maker in terms of allowing some prespecified violations if strict adherence to a DO standard is included as a constraint in the formulation. At times, the decision maker may wish to find out if there are reasonable cost-equity trade-off solutions for a given system, for a desired performance level that may be less than 100%. To the writers’ knowledge, no studies addressing the above-mentioned issues have been reported in the literature. The classical constraint method of multiobjective program- ming Cohon 1978 is used to solve the optimal waste load allo- 1 Formerly, Research Scholar, Environmental and Water Resources Engineering Division, Dept. of Civil Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India. 2 Professor, Environmental and Water Resources Engineering Division, Dept. of Civil Engineering, Indian Institute of Technology, Madras, Chennai, 600 036, India. 3 Professor, Environmental and Water Resources Engineering Division, Dept. of Civil Engineering, Indian Institute of Technology, Madras, Chennai, 600 036, India. Note. Discussion open until October 1, 2006. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and pos- sible publication on June 4, 2004; approved on October 19, 2005. This paper is part of the Journal of Water Resources Planning and Manage- ment, Vol. 132, No. 3, May 1, 2006. ©ASCE, ISSN 0733-9496/2006/3- 133–143/$25.00. JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT © ASCE / MAY/JUNE 2006 / 133