ORIGINAL ARTICLE Optimal water and waste load allocation in reservoir–river systems: a case study Mohammad Reza Nikoo • Reza Kerachian • Akbar Karimi • Ali Asghar Azadnia • Keighobad Jafarzadegan Received: 4 May 2013 / Accepted: 6 September 2013 / Published online: 10 October 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract In this paper, a new methodology is developed for optimization of water and waste load allocation in reservoir–river systems considering the existing uncer- tainties in reservoir inflow, waste loads and water demands. A stochastic dynamic programming (SDP) model is used to optimize reservoir operation considering the inflow uncertainty, and another model called PSO-SA is devel- oped and linked with the SDP model for optimizing water and waste load allocation in downstream river. In the PSO- SA model, a particle swarm optimization technique with a dynamic penalty function for handling the constraints is used to optimize water and waste load allocation policies. Also, a simulated annealing technique is utilized for determining the upper and lower bounds of constraints and objective function considering the existing uncertainties. As the proposed water and waste load allocation model has a considerable run-time, some powerful soft computing techniques, namely, Regression tree Induction (named M5P), fuzzy K-nearest neighbor, Bayesian network, sup- port vector regression and an adaptive neuro-fuzzy infer- ence system, are trained and validated using the results of the proposed methodology to develop real-time water and waste load allocation rules. To examine the efficiency and applicability of the methodology, it is applied to the Dez reservoir–river system in the south-western part of Iran. Keywords Water and waste load allocation  Reservoir–river systems  Particle swarm optimization (PSO)  Simulated annealing (SA)  Nonlinear interval optimization  Operating rules Introduction Increasing pollution loads necessitates the incorporation of water quality issues in water resource planning and man- agement. Nowadays, the integration of water quality and quantity targets in reservoir–river systems planning is receiving more attention by researchers. de Azevedo et al. (2000) investigated multiple strategic planning alternatives for water quality and quantity management in a river basin. They used the MODSIM model for water allocation and a model named QUAL2E-UNCAS for water quality routing considering the parameters uncertainties. In their study, some performance measures such as reliability of water quality standard compliance, spatial and temporal unifor- mity of water quality as well as total reliability, total vul- nerability, and total resiliency for quantitative assessment were used to compare the alternatives. The alternatives include various water release policies and corresponding levels of refinement. M. R. Nikoo (&)  A. Karimi  A. A. Azadnia Department of Civil Engineering, East-Tehran Branch, Islamic Azad University, Tehran, Iran e-mail: nikoo@alumni.ut.ac.ir A. Karimi e-mail: erajkarimi@alum.sharif.ir A. A. Azadnia e-mail: azadnia@alumni.ut.ac.ir R. Kerachian School of Civil Engineering and Center of Excellence for Engineering and Management of Civil Infrastructures, College of Engineering, University of Tehran, Tehran, Iran e-mail: kerachian@ut.ac.ir A. A. Azadnia  K. Jafarzadegan School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran e-mail: jafarzadegan@ut.ac.ir 123 Environ Earth Sci (2014) 71:4127–4142 DOI 10.1007/s12665-013-2801-5