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SUPPLEMENTARY MATERIAL
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This supplementary material mainly describes the simulation optimization, objective
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functions, constraints and the reservoir operation rules used for simulation
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optimization. In addition, the tools used are described.
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Simulation optimization
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Simulation optimization composed of simulation and optimization is a process of
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finding the best input variable values (optimal decision variables) from among all
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possibilities by searching for best output variable values (maximization or
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minimization of objective functions) (Kang & Park 2014). The simulation is used to
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represent the process of the reservoirs’ release and storage based on water balance
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(Equation S.4 provided in the constraints section of the Supplementary materials).
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The optimization uses the objective functions of simulation to provide feedback on
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progress of the search for best input variables, and in turn guides further input to the
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simulation.
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In the process of simulation optimization, the basic data used are inflows, water
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demands, leakage losses and initial reservoir storage volume during operation periods.
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Historical inflow data used are from year 1958 to year 2013 and 10-day average
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inflow data are used for simulation. The water demands used are the annual local
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water demand data and joint water demand data provided in the case study section,
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which are divided into 36 equal 10-day periods. Leakage loss is calculated by using
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the leakage loss rate of each reservoir: 13.24 × 104 m3/day for Biliuhe reservoir and
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3.35 × 104 m3/day for Yingnahe reservoir. The initial water storage volume of Biliuhe
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reservoir is 291.5 × 106 m3 and Yingnahe reservoir is 110 × 106 m3.
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Objective functions
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WSR is defined as
WSR 
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Maximize
T'
T +1
(S.1)
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where T is the total number of the operation periods, T' is the number of periods that
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the water demands of 10-day are supplied as required.
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SP is defined as
SP 
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Minimize
1 T J
 SPi j
N i 1 j 1
(S.2)
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where N is the total number of the simulated year and is equal to 56 , i is the period
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index, j is a reservoir, J is the total number of reservoirs (here J is 2, including Biliuhe
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reservoir and Yingnahe reservoir), SPij represents spills from reservoir j at study
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period i.
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DW is defined as
DW 
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Minimize
1
N
T
 DW
i 1
i
(S.3)
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where DWi represents the volume of diverted water from Dahuofang Reservoir at
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study period i.
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Constraints
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For the reservoir optimization problem, it has to satisfy the mass balance equation.
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The mass balance equation is written as
Si 1  Si  Ii  DWi  WSi  SPi  Ei
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(S.4)
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where Si and Si+1 represent the initial storage and end storage; Ii, DWi, WSi, SPi and Ei
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represent the natural inflow, the amount of diverted water, the water supply amount
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for the urban area, the amount of water spills and the evaporation and leakage loss at
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study period i respectively.
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Si and Si+1 are subject to
Smin  Si  Smax
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(S.5)
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where Smin and Smax represent the dead storage and maximum storage. The maximum
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storage is different for the flood and dry season. In the flood season, the storage is the
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flood-control storage for flood control safety, while the maximum level is the normal
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storage in the dry season.
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DWi is subject to
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0  DWi  DWmax
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where DWmax is the maximum diversion, which is limited by the diversion pipeline
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from Dahuofang reservoir to Biliuhe reservoir.
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Decision variables
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The decision variables are shown in Table S1.
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Table S1| Decision variables
Decision variables
Reservoir storage volume(m3)：
water-supply rule curve
Reservoir storage volume(m3)：
upper water-diversion rule
curve
Reservoir storage volume(m3)：
lower water-diversion rule
curve
Allocation proportions for joint
water demand
(S.6)
Scenario 1
Scenario 2
Scenario 3
xi1 , i  1, 2, …, 36
xi1 , i  1, 2, …, 36
xi1 , i  1, 2, …, 36
xi2 , i  1, 2, …, 36
xi2 , i  1, 2, …, 36
xi2 , i  1, 2, …, 36
xi3 , i  1, 2, …, 36
xi3 , i  1, 2, …, 36
xi3 , i  1, 2, …, 36
--
xi4 , i  1, 2, …, 36
xi4 , i  1, 2, …, 36
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Remarks: i represents time periods of operation. Each simulation year is divided into 36 time
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periods (with ten days as a time period). There are 36 decision variables on each of three rule
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curves and allocation proportions for joint water demand.
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Reservoir operation rules
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The reservoir operation rules used in this paper are reservoir water supply operation
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rule curves and reservoir water diversion rule curves. The reservoir water supply
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operation rule curves, based on 36 10-day periods, are shown in Figure S1(a). When
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the water storage lies in zone 1, the amount of water supply is the same as the amount
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of water demand. When the water storage of reservoir is in zone 2, water supply is
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equal to the value of water demand multiplied by a water rational coefficient µ. The
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reservoir water diversion rule curves are shown in Figure S1(b). Water diversion rule
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curves divide the active water storage into three parts, i.e., zone I, zone II and zone III.
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When the water storage of reservoir lies in zone I, the amount of water diversion is 0.
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When in zone II, the amount of water diversion is equal to the conveyance capacity of
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the water diversion pipelines multiplied by a coefficient ɛ. ɛ is defined as

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Upperi  Si
Upperi  Loweri
(S.7)
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where Upperi and Loweri represent the upper bound and the lower bound of diversion
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at study period i; Si represents water storage of reservoir at study period i. When in
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zone III, the amount of water diversion is equal to the conveyance capacity of the
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water diversion pipeline.
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Figure S1 | Diagrammatic sketch of reservoir operation rule curves. (a) Water supply
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Each optimal solution of each scenario corresponds to a similar set of reservoir
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operation rule curves. For practical operability, the operation rule curves should not
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have frequent fluctuations, but be as flat as possible. Considering reasonability, the
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points of diversion rule curves and water supply rule curves should be lower, to
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restrict diversion from Dahuofang reservoir and increase water supply as much as
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possible in wet periods while higher in dry periods comparatively. To make reservoir
rule curves; (b) water diversion rule curves.
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operation rules easy to understand, one is obtained from the numerous optimal
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solutions in the pipeline connection scenario to show the actual reservoir operation
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curves. The selected one is shown in Figure S2.
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Figure S2 | One of the reservoir operation rule curves in the pipeline connection
scenario.
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Tools used for optimization and visualization
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The optimization is implemented using ɛ-NSGAII within the MOEA Framework
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(http://moeaframework.org/), which is a free, open-source Java framework for
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experimenting with several popular multi-objective evolutionary algorithms. The
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water supply system is simulated for computing reservoir storage volumes, water
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supply, diversion and water spills based on water balance.
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Reference
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Kang, M. G. & Park, S. W. 2014 Combined simulation-optimization model for assessing irrigation
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water supply capacities of reservoirs. Journal of Irrigation and Drainage Engineering, 140 (5),
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04014005.
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