A Game Theoretic Model for Trading Pollution Discharge Permits in River Systems

Nikoo, Mohammad Reza; Kerachian, Reza; Niksokhan, Mohammad Hossein; Beiglou, Pouyan Hatami Bahman

doi:10.7763/ijesd.2011.v2.116

Cited by 14 publications

(6 citation statements)

References 17 publications

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“…Next, the ‘fitness function’ was assigned. In this research, the fit of the model was evaluated by the error between the output provided by the model and the desired actual output (Nikoo et al ., ). The fit, f i , of an individual chromosome i was measured with the following expression:

f_{i} = true {truefalse\sum}_{j = 1}^{C_{t}} ((), M - (||, C_{(i, j)} - T_{j})),

where M is the range of selection, C ( i , j ) is the value returned by the individual chromosome i for its fit to j (out of C t cases of fit) and T j is the target value for the fit of j .…”

Section: Discussionmentioning

confidence: 97%

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Estimation of saturated hydraulic conductivity from double‐ring infiltrometer measurements

Fatehnia

Tawfiq

2016

European J Soil Science

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This research aims to determine soil vertical saturated hydraulic conductivity (K s ) in situ from the measured steady infiltration rate (I), initial soil properties and double-ring infiltrometer (DRI) test data. Characterizing the effects of these variables on the measured steady infiltration rate will enable more accurate prediction of K s . We measured the effects of the ring diameter, head of ponding, ring depth, initial effective saturation and soil macroscopic capillary length on measured steady infiltration rates. We did this by simulating 864 DRI tests with the finite element program HYDRUS-2D and by conducting 39 full-scale in situ DRI tests, 30 Mini-Disk infiltrometer experiments and four Guelph Permeameter tests. The M5 ′ model trees and genetic programming (GP) methods were applied to the data to establish formulae to predict the K s of sandy to sandy-clay soils. The nine field DRI tests were used to verify the computer models. We determined the accuracy of the methods with 30% of the simulated DRI data to compare I/K S values of the finite element models with estimates from the suggested formulae. We also used the suggested formulae to predict the K s values of 30 field DRI experiments and compared them with values measured by Guelph Permeameter tests. Compared with the GP method, the M5 ′ model was better at predicting K S , with a correlation coefficient of 0.862 and root mean square error (RMSE) of 0.282 cm s −1 . In addition, the latter method estimated K s values of the field experiments more accurately, with an RMSE of 0.00346 cm s −1 . Highlights• Effects of initial soil properties and DRI test data on steady infiltration rate are studied. • M5 ′ model algorithm and genetic programming method are applied on the data to formulate the equations.• Compared to the GP method, the M5 ′ model was better at predicting K s . • The equation from M5 ′ tree model is robust for estimating in situ K s with the DRI.

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f_{i} = true {truefalse\sum}_{j = 1}^{C_{t}} ((), M - (||, C_{(i, j)} - T_{j})),

where M is the range of selection, C ( i , j ) is the value returned by the individual chromosome i for its fit to j (out of C t cases of fit) and T j is the target value for the fit of j .…”

Section: Discussionmentioning

confidence: 97%

“…Next, the 'fitness function' was assigned. In this research, the fit of the model was evaluated by the error between the output provided by the model and the desired actual output (Nikoo et al, 2011). The fit, f i , of an individual chromosome i was measured with the following expression:…”

Section: Genetic Programmingmentioning

confidence: 99%

Estimation of saturated hydraulic conductivity from double‐ring infiltrometer measurements

Fatehnia

Tawfiq

2016

European J Soil Science

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“…Non-Dominant Sorting Genetic Algorithm (NSGA-II) is a powerful optimization algorithm, proposed by Deb et al (2002). This algorithm, which solves multi-objective optimization problems, has been widely used in the literature (Nikoo et al, 2011;Nikoo et al, 2012;Nikoo et al, 2014;Monghasemi et al, 2015;Alizadeh et al, 2017). Fig.…”

Section: The Nsga-ii Multiobjective Optimization Modelmentioning

confidence: 99%

Developing a non-cooperative optimization model for water and crop area allocation based on leader-follower game

Sedghamiz

Nikoo

Heidarpour

et al. 2018

Journal of Hydrology

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In this paper, a mathematical model for conflict resolution among a diverse set of agricultural water users in Golestan province, Iran, is developed. Given the bi-level nature of the distribution of power in the current problem, a combination of Leader-Follower game and Nash-Harsanyi bargaining solution method is employed to find optimal water and crop area allocations. The Golestan Regional Water Authority is the leader in this setting, controlling the total water allocations; and the agricultural sectors are the followers, competing over the allocated water. Two objectives for the leader are (i) maximizing profits, and (ii) maximizing share of green water in total agricultural production through selecting more efficient crop patterns. The followers' objective is merely maximizing obtained benefits for the selected crop patterns. Virtual water concept is also factored into the related objective functions, and the water allocation problem is solved considering spatio-temporal crop pattern along with a dynamic water pricing system. This involves using a hybrid optimization structure as a new approach to solving two level optimization problems. The results show that the leader's income is independent of total water allocation and is only affected by crop pattern and crop area, two factors which drive water price too. The followers' benefit also depends on crop pattern and crop area, as they influence the crop yield, cost and water price. Finally, green water plays a key role in selecting the optimal crop pattern and crop area.

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“…Non-Dominant Sorting Genetic Algorithm (NSGA-II) was firstly proposed by Deb et al [33] to solve multi-objective optimization problem and has been used by many researchers so far [23,32,34,35]. In this type of problems, there is no single optimal solution since there could be various conflicts between objectives.…”

Section: Nsga-ii Multi-objective Optimization Modelmentioning

confidence: 99%

A Game Theory Approach for Conjunctive Use Optimization Model Based on Virtual Water Concept

et al. 2018

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In this study to allocate the agricultural and environmental water, considering virtual water concept, a multi-objective optimization model based on NSGA-II is developed. The objectives consist of equity maximization, agricultural benefit maximization for each region, maximization of green water utilization and finally minimization of environmental shortage. Then a cooperative game (Grand Coalition) model is presented by forming all possible coalitions. By the game model including Nucleolus, Proportional Nucleolus, Normal Nucleolus and Shapley methods, the benefit is reallocated based on all Pareto optimal solutions obtained from multi-objective optimization model. Then using two famous fallback bargaining methods, Unanimity and q-Approval, preferable alternative (solution) for each of the cooperative games is determined. Finally, based on the obtained benefit for each selected alternatives, the two most beneficial alternatives are chosen. The proposed methodology applied for water allocation of Minoo-Dasht, Azad-Shahr and Gonbad-Kavoos cities in Golestan province, Iran for a 3-year period as a case study. Also, eight crops including Wheat, Alfalfa, Barley, Bean, Rice, Corn, Soya, and Cotton are selected based on local experts' recommendations. The models' results indicated no significant difference between the grand coalition model and the multi-objective optimization model in terms of the average cultivation area (a relative change of 2.1%), while lower agricultural water allocation occurred for the grand coalition model (about 10.35 percent average) compared with the multi-objective optimization model. It is also observed that more agricultural benefit gained by the grand coalition model (32 percent average). Finally, it is found that Wheat and Corn hold the most rates of import and export, respectively, and Rice was the crop which has the least shortage of production to supply food demand.

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A Game Theoretic Model for Trading Pollution Discharge Permits in River Systems

Cited by 14 publications

References 17 publications

Estimation of saturated hydraulic conductivity from double‐ring infiltrometer measurements

Estimation of saturated hydraulic conductivity from double‐ring infiltrometer measurements

Developing a non-cooperative optimization model for water and crop area allocation based on leader-follower game

A Game Theory Approach for Conjunctive Use Optimization Model Based on Virtual Water Concept

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