Waste Load Allocation Problem Research Articles

Equilibrium strategy based waste load allocation using simulated annealing optimization algorithm.

This study focuses on development of equilibrium strategy based on simulated annealing (SA) algorithm for balancing economic and environmental concerns in waste load allocation (WLA) problem. To resolve conflicts among various stakeholders, including Iran Department of Environment (DoE) as governmental authority and industrial and municipal dischargers, Stackelberg and Nash bargaining games have been applied in this WLA problem and the results have been compared. SA algorithm has been coupled to QUAL2Kw model to derive optimal WLA program and the environmental penalty tariff (EPT) in Nash bargaining and Stackelberg games. The proposed tools and methodologies were illustrated in a case study of multi-stakeholders WLA problem in Gheshlagh River, Sanandaj, Kordestan, Iran. The results indicate that lower BOD removal rates are allocated to the pollutant dischargers in the Stackelberg game compared to the Nash bargaining game. Furthermore, the EPT assigned by Iran DoE in Stackelberg and Nash bargaining games are 11.25 and 3.6 Rials/(gr/month), respectively. The estimated EPT in the Stackelberg game is close to the current tariff (10 Rials/(gr/month)) specified by Iran DoE on impermissible BOD discharges.

Allocation of unequally-weighted wastewater discharge loads using a simulation-optimization approach

In this study, a new simulation–optimization approach is proposed to solve the multi-pollutant waste load allocation (WLA) problems in surface water systems. The proposed approach simulates the fate and transport of multiple pollutants utilizing the AQUATOX model. Since AQUATOX is an independent model and its integration into the optimization process is computationally not efficient, a multi-pollutant concentration–response matrix (mpCRM) is developed by using the results of the AQUATOX model. This mpCRM is then integrated into an optimization model where a nonlinear generalized reduced gradient (GRG) optimization method is used. Unlike in previously conducted studies, a new optimization formulation is proposed wherein the multiple pollutant loads are allocated among the source locations depending on their pre-assigned load allocation weights. This formulation allows for an equal or variable pollutant load allocation plan among source locations depending on the water management strategy for the watershed. The applicability of the proposed approach is evaluated on a sub-watershed of the Küçük Menderes River Basin (KMRB) in Turkey by considering different load allocation scenarios. Furthermore, a detailed sensitivity analysis is conducted to evaluate the model results for different problem parameters. Identified results suggest that the proposed simulation–optimization approach is an effective way to solve the multi-pollutant WLA problem.

A bi-level multiobjective optimization model for waste load allocation in rivers.

It is often difficult to apply existing waste load allocation (WLA) models to management institutions at all levels of the river basin because the existing WLA models do not consider the principles of fairness and efficiency at each management level of the basin. The implementation of environmental protection tax law has also greatly impacted WLA. This paper proposes the bi-level multiobjective allocation model under an environmental protection tax law to solve the WLA problem for different management levels. The upper allocation targets the minimal environmental Gini coefficient and the minimal unit pollutant emission cost. The impact of the environmental protection tax is also considered. The targets of the lower-level allocation are the maximal industrial output value and the minimal unevenness of reduction rates. The proposed model was applied to the case of the Wei River basin, and the results demonstrated that the bi-level multiobjective allocation model could solve the problem of WLA under an environmental protection tax law. Each level of the bi-level multiobjective allocation model considers the principles of fairness and efficiency to distribute the load in the basin, thereby offering a better reference for decision-makers at both levels.

Multi-objective multi-pollutant waste load allocation model for rivers using coupled archived simulated annealing algorithm with QUAL2Kw

Abstract A simulation-optimization approach is a suitable tool in waste load allocation problems when considering competing objectives and complex pollutant fate and transport processes in water bodies. Here, an archived multi-objective simulated annealing (AMOSA) algorithm is developed to determine various decision variables related to multi-pollutant waste load allocation (MPWLA) problems. The developed AMOSA algorithm has been coupled to QUAL2Kw in order to derive optimal MPWLA programs in Gheshlagh River, Kordestan, Iran. Minimizing wastewater treatment plant (WWTP) costs, improving the EquityMeasure, and enhancing water quality index (WQI) of the river have been considered as objective functions of MPWLA problems. The applied WQI integrates various water quality parameters (biochemical oxygen demand (BOD), dissolved oxygen (DO), NH4-N, NO3-N, PO4-P, total suspended solids (TSS), and Coliform) in monitoring stations along the river. Results show in the scenario with the best EquityMeasure, higher pollutant removal rates have been allocated to Sanandaj WWTP effluent and pollutant point source No. 7 (creek of landfill leachate) due to their greater contributions to Gheshlagh River contamination. Owing to high pollutant load effluents and unsuitable background conditions in Gheshlagh River, more specific studies show that the water quality index may not be improved over 0.22, no matter how much cost is incurred or equity is sacrificed.

Planning for agricultural return flow allocation: application of info-gap decision theory and a nonlinear CVaR-based optimization model.

A new methodology is proposed for sizing the required infrastructures for water and waste load allocation in river systems receiving return flow from agricultural networks. A nonlinear optimization model with a constraint based on conditional value at risk (CVaR) is developed to provide water and waste load allocation policies. The CVaR-based constraint limits the probabilistic losses due to existing uncertainties in available surface water. The deep uncertainties of return flow simulation model parameters, which have significant impacts on the simulated quantity and quality of agricultural return flows, are handled by using the info-gap theory. Total dissolved solid (TDS) is selected as water quality indicator and diverting a fraction of return flows to evaporation ponds is considered to control the TDS load of agricultural waste load dischargers. Quantity and TDS load of agricultural return flows over a 1-year cultivation period are simulated by using a calibrated SWAP agro-hydrological model. The results of many runs of SWAP model for different combinations of important uncertain parameters in their ranges of variations provide some response (impact) matrixes which are used in optimization model. The applicability of the proposed methodology is illustrated by applying it to the PayePol region in the Karkheh River catchment, southwest Iran. The selected strategy for water and waste load allocation in the study area is expected to provide total annual benefit of 48.64 million US dollars, while 7.84 million m3 of total return flow should be diverted to evaporation ponds. The results support the effectiveness of the methodology in incorporating existing deep uncertainties associated with agricultural water and waste load allocation problems.

Integrated waste load allocation for river water pollution control under uncertainty: a case study of Tuojiang River, China.

This paper presents a bi-level optimization waste load allocation programming model under a fuzzy random environment to assist integrated river pollution control. Taking account of the leader-follower decision-making in the water function zones framework, the proposed approach examines the decision making feedback relationships and conflict coordination between the river basin authority and the regional Environmental Protection Agency (EPA) based on the Stackelberg-Nash equilibrium strategy. In the pollution control system, the river basin authority, as the leader, allocates equitable emissions rights to different subareas, and the then subarea EPA, as the followers, reallocates the limited resources to various functional zones to minimize pollution costs. This research also considers the uncertainty in the water pollution management, and the uncertain input information is expressed as fuzzy random variables. The proposed methodological approach is then applied to Tuojiang River in China and the bi-level linear programming model solutions are achieved using the Karush-Kuhn-Tucker condition. Based on the waste load allocation scheme results and various scenario analyses and discussion, some operational policies are proposed to assist decision makers (DMs) cope with waste load allocation problem for integrated river pollution control for the overall benefits.

A decision-making framework for river water quality management under uncertainty: Application of social choice rules

An important issue in river water quality management is taking into account the role played by wastewater dischargers in the decision-making process and in the implementation of any proposed waste load allocation program in a given region. In this study, a new decision-making methodology, called ‘stochastic social choice rules’ (SSCR), was developed for modeling the bargaining process among different wastewater dischargers into shared environments. For this purpose, the costs associated with each treatment strategy were initially calculated as the sum of treatment cost and the fines incurred due to violation of water quality standards. The qualitative simulation model (QUAL2Kw) was then used to determine the penalty function. The uncertainty associated with the implementation of strategies under the economic costs (i.e., the sum of treatment and penalty costs) was dealt with by a Monte-Carlo selection method. This method was coupled with different social choice methods to identify the best solution for the waste load allocation problem. Finally, using the extended trading-ratio system (ETRS), the most preferred treatment strategy was exchanged among dischargers as the initial set of discharge permits aimed at reducing the costs and encouraging dischargers to participate in the river water quality protection scheme. The proposed model was finally applied to the Zarjoub River in Gilan Province, northern Iran, as a case study. Results showed the efficiency of the proposed model in developing waste load allocation strategies for rivers.

Hybrid Nested Particle Swarm Optimization for a Waste Load Allocation Problem in River System

AbstractThe aim of this article is to develop a hybrid nested particle swarm optimization to solve a Pigovian tax-based waste load allocation problem for river systems. The river system at the Tuojiang River basin is the prototype which is then extended to a generalized waste load allocation problem. The responsible environmental protection agency (EPA), as the leader, sets the pollution tax standards at a given checkpoint to resolve the conflict between the dischargers, and each discharger, as the follower, makes biological oxygen demand (BOD) removal decisions to minimize their own pollution costs under the specified pollution and pollution tax standards. A cooperative bilevel multifollower decision-making model is established that takes into account the objectives and constraints. The particular nature of this model requires the development of a nested particle swarm optimization algorithm. Instead of using a traditional particle performance measurement method, an exact algorithm for solving the lower-...

Multi-objectiveWaste LoadAllocation in RiverSystembyMOPSOAlgorithm

This paper explores the capabilities of Multi-objective Particle Swarm Optimization algorithmin a simulation-optimization model for solving waste load allocation problems. The main goals are totaltreatment costs, violation of the water quality standards and equity. In this research, the water qualitysimulation model is coupled with a multi-objective optimization model, MOPSO. In order to derive nondominatedsolutions, two different optimization models are used. The first is referred to as the cost versusquality model and the second one also consider minimizing cost and inequity. For the each case, the trade-offcurve (Pareto front) is derived and the best non-dominated solution on the trade-off could be selected bystakeholders and decision makers. The proposed model has been developed for Haraz River in the northernpart of Iran which represented scenarios considering different interests and answered questions to modifyscenarios according to the decision makers’ideas. Solutions were compared with NSGA-II, and the resultsdemonstrate a suitable convergence and diversity of proposed algorithm.

Waste Load Allocation in Rivers using Fallback Bargaining

In this paper, bargaining process between different stakeholders involved in a waste load allocation problem is simulated using the Fallback Bargaining (FB) concept. The paper considers two main parties in a waste load allocation problem. On the one hand, there are wastewater dischargers intending to minimize their treatment costs and on the other hand, there is an environmental protection agency which monitors the river water quality at a checkpoint downstream of the location of dischargers. In this paper, different alternatives which are combinations of dischargers’ treatment scenarios are defined. A water quality simulation model is utilized to estimate the concentration of the water quality indicator along the river based on a selected alternative. If the concentration of water quality indicator in the selected checkpoint violates the water quality standards, a penalty function is used to calculate the amount of penalty assigned to dischargers. The allocated cost to each discharger is computed considering his treatment scenario as well as the penalty allocated to him. Two kinds of Fallback bargaining procedure termed as Unanimity Fallback Bargaining (UFB) and Fallback bargaining with Impasse (FBI), which both aim at minimizing the maximum dissatisfaction of bargainers in a negotiation problem, are utilized for finding a Compromise Set (CS) of alternatives. In this paper, the best alternative (alternatives) among CS members is (are) selected using a social choice theory namely Condorcet winner. The results of these two approaches are compared and the final alternative is selected which shows the initial Tradable Discharge Permits (TDPs) allocated to dischargers. Finally, in order to decrease the total allocated cost to dischargers, initial allocated TDPs are exchanged between them using the Extended Trading Ratio System (ETRS) developed by Mesbah et al. (Environ Model Software 24:238–246, 2009). The applicability and efficiency of the proposed methodology is investigated by applying it to a case study of the Zarjub River in the northern part of Iran.

General Multiobjective Model and Simulated Annealing Algorithm for Waste-Load Allocation

Waste-load allocation (WLA) is a difficult problem with multiobjective features, which requires models that consider a full range of competing goals to identify good and practical solutions. In this study, a general and multiobjective optimization model was proposed. This model integrates different decision variables related to multiple waste-removal efficiencies and outflow discharges into water bodies. This model also considered an equity measure and limits for the concentration of dissolved oxygen and biochemical oxygen demand. A simulated annealing (SA) algorithm and the enhanced stream water quality simulation model (QUAL2E) were used to solve the WLA problem. This approach was applied to the Santa Maria da Vitória River watershed in the state of Espírito Santo, Brazil. Computational results have demonstrated that the proposed optimization model with the SA metaheuristic and QUAL2E could effectively incorporate the expectations and conflicting objectives, providing various good solutions to support decision makers.

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA) problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max–min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga–Bhadra river system in India.

GENERATING ROBUST SOLUTIONS: A WATER QUALITY MANAGEMENT EXAMPLE

Abstract An approach is presented for.analyzing a water quality management problem that considefs multiple pollutant transport responses within an optimization model formulation. The multiple pollutant transport responses represent different possible scenarios that could occur in the water body. Solutions to the optimization model are obtained that are robust with respect to the actual pollutant transport response. The desirable characteristics of the solutions obtained to this waste load allocation problem are demonstrated through the application of the approach to a case study based on the Willamette River in Oregon.

Stochastic dynamic programming models for water quality management

This paper presents optimization models for waste load allocation from multiple point sources which include both parameter (Type II) and model (Type I) uncertainty. These optimization models employ more sophisticated water quality simulation models, for example, in the case of dissolved oxygen modeling, QUAL2E and WASP4, than is typically the norm in studies on the optimization of waste load allocation. Variability in selected input parameters to the water quality simulation models gives rise to stochastic dynamic programming approaches. Two types of reliability and feasibility attributes are highlighted, associated with the management options that are generated. Several dissolved oxygen simulation models are incorporated into the optimization procedures to explore the effects of Type I uncertainty on control decisions. Information from simultaneous consideration of multiple simulation models is aggregated in the dynamic programming framework through two regret‐based formulations. By accommodating both model and parameter uncertainty in the modeling framework, trade‐offs can be generated between the two so as to assess their influence on control decisions. The models are applied to a waste load allocation problem for the Schuylkill River in Pennsylvania.

A Programming Model for River Quality Management under Transverse Mixing

The objective of river quality management is to achieve a given water quality standard at certain control stations by cutting down the pollutant load in the basin at the lowest cost. Conventional programming models, however, cannot guarantee the satisfaction of the quality standard at each drinking water intake when transverse mixing occurs in the river, because they focus on the average concentration of the cross sections, while the raw water is usually drawn from the sides of the river. In this paper, a programming model is proposed to deal with waste load allocation problems. The effect of transverse dispersion on the quality at drinking water intakes is taken into account by introducing an index which represents the degree of mixing in a river. This has made it possible to link the sewage system planning with the improvement of drinking water quality. The results of model application show that the priority of sewage treatment in a river basin is quite different from those advanced by the conventional models, it is suggested that a change of the traditional strategy of waste load allocation is necessary for better quality of drinking water supply.

Stochastic waste load allocation

This paper considers solving a stochastic waste load allocation model in a chance-constrained format. The model explicitly takes into account the uncertainty of the water quality parameters including their spatial and cross-correlations. Random characteristics of the coefficients in the water quality constraints are obtained by using unconditional simulation. A hypothetical example is used to demonstrate the methodologies and investigate the effects of water quality compliance reliability and correlation structures of the water quality parameters on the optimal solution of the waste load allocation problem.

Bi-objective analysis of waste load allocation using fuzzy linear programming

Because of its complexity from both a legal and economic standpoint, the problem of optimal waste load allocation is multiobjective by nature and should be treated accordingly. To perform this task, an optimization technique known as fuzzy linear programming is utilized in solving a multiple-discharge, two-objective waste load allocation problem. The two objectives considered are: (1) the maximization of waste discharge and (2) the minimization of the largest difference in equity measure between the various dischargers. Results from this study reveal that fuzzy linear programming is a valuable tool for solving the multiple-objective water quality management problems. Moreover, it is shown that the selection of a linear or logistic membership function in providing preference criteria between the two objects, has no effect on the ‘best compromising solution’.