Waste load allocation modeling with fuzzy goals; simulation-optimization approach

Abstract

Presence of various types of uncertainties in water quality management problems has been recognized as one of the major challenges in water quality modeling. Vagueness, lack of adequate data and nonlinearity of cost and/or benefit functions in most of water quality and waste load allocation management problems have reduced the capability of direct inclusion of uncertainty analysis in the management models. This study presents a fuzzy waste load allocation model in which cost function and the water quality standards or the goals of dischargers and pollution control agencies are expressed with appropriate linear and/or nonlinear and nondecreasing and/or nonincreasing membership functions. QUAL2E and Classified Population Genetic Algorithm (CPGA) were coupled to develop the optimum strategy resulting in maximum value of the minimum nonzero membership values, which represent the optimum satisfaction level of the conflicting goals. Number of constraint violations was used to penalize the fitness function in order to eliminate the infeasible solutions at the final results. The model was applied to a hypothetical case example. Results show a very suitable convergence of the proposed algorithm to good of possibility to the near global optima. Effects of linear and nonlinear membership functions are examined and the results are analyzed.

An Indirect Simulation-Optimization Model for Determining Optimal TMDL Allocation under Uncertainty

“…Other than that, the calibration and verification of the BRRT model takes only about 5 min, and finding the optimal solution of the BRRT-EILP model for three scenarios with 16 decision variables takes less than 1 min. Taken together, the total computational time taken to find out the approximate optimal solutions was only about 33 h. In contrast, running a traditional direct SOM framework using a GA approach might require several days (e.g., if a population size of 50 is used and the model is iterated for 300 generations, it takes over 10 days to obtain a solution) [11]. More time would be required to increase the chances of obtaining globally-approximate optimal solutions, because multiple GA runs would need to be executed for the same problem [21,22].…”

“…To increase the financial and technical feasibility of implementation, the U.S. Environmental Protection Agency [1] suggested that process-oriented simulation models could be directly integrated into an optimization framework to develop optimal TMDL allocations at the least cost while risk must be identified. Either traditional nonlinear optimization or modern heuristic global search algorithms can be applied in the direct simulation-optimization model (SOM) framework [6][7][8][9][10][11][12][13]; however, this direct SOM approach is rarely applied in practice, primarily due to the prohibitive computational cost and the neglect of uncertainties in both simulation modeling and the optimization process [7,14].…”

“…Even when many data are available, the computational algorithms for stochastic or fuzzy optimization models, such as nonlinear programming (NP) or modern heuristic global searches, may face complex or nonlinear problems [19,20]. For example, traditional NP algorithms, including both gradient and non-gradient based ones, were limited to local optima upon solving the aforementioned SOM framework [11,21]. Although heuristic global search algorithms, including genetic algorithms, evolutionary algorithms and simulated annealing, are capable of surpassing the local optima limitations, their applications in the optimization of TMDL allocation are still restricted by their extremely high computational cost [18,22].…”

Performance evaluation of optimization models in the determination of wastewater treatment efficiencies inside watersheds

“…Thus, the combined use of water quality models and optimization techniques have received attention from various authors such as Cho et al (2004), Aras, Togan and Berkun (2007), Saadatpour and Afshar (2007) and Carvalho and Kaviski (2009), that deal with the definition of treatment efficiencies for sewage plants located in different watersheds.…”

“…Among the metaheuristics techniques, Genetic Algorithms (GA) have enabled applications in various fields such as urban drainage, sewage collection (TSAI;CHANG, 2001;PENN;FRIEDLER;OSTFELD, 2013), water supply and effluent treatment systems (PARK; KO;LEE, 2007;SAADATPOUR;AFSHAR, 2007;HOLENDA et al, 2007).…”