Urban drainage decision model for storm emergency management based on multi-objective optimization

This study proposes a solution to prevent urban waterlogging, a challenging environmental issue, by integrating waterlogging prediction and drainage optimization schemes based on cellular automaton and multi-objective optimization theories. An urban waterlogging model for uncertain flow was constructed considering urban surface fragmentation and space complexity. For dynamic simulation, outputs of water depth and flooded areas were projected with inputs of rainfall, soil infiltration, plant interception, gully discharge, and outflow to its neighbors in each cell at any moment. Using a multi-objective optimization approach, the drainage decision model for optimal solutions calculated the maximal amount of water for pumping from flooded zones to candidate reservoirs with minimal energy cost. This integrated approach was successfully applied to the DongHaoChong catchment, an 11 km2 watershed in Guangzhou, southern China and validated by comparing the simulated flood areas with flooded points from two historical rainstorms (August 15, 2013 and June 23, 2014). The RMSE of the maximum waterlogging depth were 26.89 and 78.48 mm, respectively. Therefore, the proposed model was reliable and capable of simulating uncertain flow at any position and moment with minimal data input and parameters in an urban environment. Water-logged area and depth could be predicted based on the given rainfall assuming 1-, 10-, 50-, and 100-year storm data in the study area, and optimal drainage solutions could be obtained and verified. The proposed urban waterlogging prediction and drainage emergency models could optimize decision-making to improve emergency plans and reduce losses due to urban waterlogging.


Introduction
In recent decades, urban waterlogging has become a challenging environmental issue in many developing countries, often resulting in serious disasters, including traffic breakdown, property loss, and even loss of life. Urban waterlogging is largely influenced by climate change and rapid urbanization and is likely to occur when climate extremes with torrential rain, heavy rainfall, and continuous precipitation become frequent, exceeding urban drainage capacity (Gu and Gu 2014). For example, an extremely serious urban flooding disaster in Zhengzhou was caused by a maximum daily rainfall of 624.1 mm on July 20, 2021, close to the average annual rainfall in Zhengzhou (640.8 mm). Continuous heavy rainfall in June 2022 caused severe flooding and water logging in many parts of Shaoguan, Guangdong, with 285.7 mm of rainfall on June 19, 2022, significantly breaking the local record for daily rainfall in June (180.2 mm on June 17, 1994). Urban waterlogging is intensified by rapid urbanization with increased impervious surfaces, insufficient construction, maintenance of drainage systems, and a laggard civil engineering management system (Valipour 2014).
To prevent and alleviate urban waterlogging, main measures have been proposed that includes engineering measures for sponge city, low-impact development (LID) measures, and model-based simulation and precautionary measures. Model-based simulation and prediction have become a hotspot in urban stormwater research (Elliott and Trowsdale 2007). Various models have been developed to address water flow within canals and rivers. These models evolved from simple empirical hydrology descriptions into incredibly complex models based on discretized, numerical solutions of general laws (Parsons and Fonstad 2007;Spitz 2007). Traditional equations of continuity and motion have also been used to simulate approximate waterlogging depth on overland surfaces (Dong and Lu 2008;Quan et al. 2010). Surface flood is similar to unsteady flow in an open channel, which can be simulated by Saint-Venant equations using characteristics and finite difference methods (Hughes et al. 2014;Ostad-Ali-Askari et al. 2018;Shayannejad et al. 2022). However, numerical simulations require certain assumptions in the governing equations, and the effects of infrastructure or complex overland flow are difficult to precisely simulate urban waterlogging without sufficient input data and hydraulic parameters.
Previous studies are successful applications of numerical simulations of surface water systems and provide a useful means to understand and predict regional hydrology processes in a natural environment. However, describing stochastic and uncertain surface flow in relatively small temporal and spatial scales in urbanized areas remains difficult. Urban areas differ from natural areas in their high fragmentation of land cover and dense distribution of civil buildings and infrastructure. However, a cellular automaton (CA) model, a self-organization approach, provides an efficient alternative to physicalbased models for simulating complicated hydrologic processes. The CA model with simple local interaction rules has been successfully applied in water flow simulations (Cirbus and Podhoranyi 2013; Ma et al. 2009). For example, Parsons and Fonstad (2007) coupled the conservation of mass and Manning's equations with an algorithm to slow down the movement of water flow from one pixel to the next until the correct timing was achieved. Ma et al. (2009) developed a novel, quantitative automaton model that projected hillslope runoff and soil erosion caused by rainfall events. Cirbus and Podhoranyi (2013) simulated the spreading of liquid using a CA and comparatively simple rules and conditions, which included several factors. Liu et al. (2015) developed a twodimensional CA model using the Von Neumann neighborhood to simulate flood inundation on urban roads. These applications suggest that a CA model is feasible and has significant potential to simulate uncertain water flow in urban areas.
Despite progress in sustainable urban water management, developing efficient decision support systems to reduce costs for water management remains imperative (Bach et al. 2014;Ellis et al. 2004;Marlow et al. 2013;Ostad-Ali-Askari 2022). Although the investigation of multi-objective issues in water resources has received considerable attention in large basins and for predicting flooding events in cities, less attention has been focused on urban drainage decisions (Labadie et al. 2012;Park et al. 2012;Penn et al. 2013;Wang et al. 2013;Woodward et al. 2014). Hence, functional tools for efficient decision-making to improve urban stormwater management and utilization for waterlogging prevention are urgently needed (Ressano-Garcia 2014).
To this end, this study primarily aimed to provide a solution to urban waterlogging by integrating waterlogging predictions and drainage optimization schemes based on theories of CA and multi-objective optimization. Our findings may provide an effective way to improve drainage decision-making and emergency response measures based on existing conditions. More specifically, if urban waterlogging can be accurately simulated according to the rainfall forecast and urban situations, potentially flooded areas can be predicted. In this study, an urban waterlogging simulation model was constructed using CA and rules in place of definite mathematical equations. The outputs of this model included uncertain flow and water depth at random places and times, with required inputs of rainfall precipitation, digital elevation model (DEM), land use cover, and drainage gully geometry. A drainage decision model supported by multi-objective optimization is then proposed to pump water from flooded zones to candidate reservoirs. The emergency response based on optimal drainage decisions for stakeholders is then determined in advance, and water is transported from flooded areas into candidate reservoirs, thereby decreasing the negative impacts of waterlogging and property loss. Collectively, an integrated solution is proposed based on the input simulation results to dynamically compute numerous optimal drainage schemes for decision-makers using genetic algorithms. Lastly, after calibration and validation, this optimal solution to urban waterlogging prediction and drainage decisions was applied in the DongHaoChong catchment located in the central urban area of Guangzhou, China. We validated predicted waterlogging data based on an accurate simulation of uncertain flow on the urban ground and optimized the drainage solutions for emergency decision-making. The proposed solution integrated urban waterlogging simulation and drainage optimization models, which could optimize decision-making to reduce losses due to urban waterlogging and improve emergency plans for drainage management.

Water-log simulation model
An urban waterlogging model was designed based on a regular CA model by simplifying the computation of the hydrology process with a grid-based simulation frame. The cells of the CA were defined as a square grid filling a twodimensional (2D) space, which follows the grid cell of raster data covering the whole study area. The Moore neighborhood comprising eight directions (D8) surrounding the central cell (Cirbus and Podhoranyi 2013) was used. The status sets were divided into static and dynamic statuses in the computation of the central cell. The static status of the current cell retained values of height H(c), sink reservoir S(c), and plant interception I(c). The dynamic status included rainfall r(c,t), soil infiltration sI(c,t), outflow o(c,t), gully discharge g(c,t), and water depth h(c,t). The next status of the central cell depended on the current status of the adjacent eight neighbors and its status according to the CA regulation. Transition rules and regulations mainly determine the direction and depth of surface flow between the central cell and adjacent cells. The regulation can be expressed as follows: where Dh is the change of inundated water depth in the central cell at current time t since previous time h(c, t-1); o(B,t) represents the potential outflow from its eight neighbors to the central cell at time t while its neighbors individually become the central cell; and o(c, t) denotes probable outflow from the central cell to its neighbors. The production of runoff depends on the kind of urban ground surface during a storm. According to the difference in runoff production, the urban surface is divided into permeable (green land, lake, river, and railway) and impermeable surfaces (building, road, square, and viaduct). The following assumptions are applied in this model: (1) If an impervious surface covers the cell, both soil infiltration sI(c) and plant interception(c) always equal zero; (2) Water on cells covered by buildings or viaducts are fully collected by the sewer system; thus, these cells are never inundated, and their water depth always equals zero; and (3) If no gully is in the current cell, the cell's outflow from the drainage system is always zero. Therefore, the calculation of water depth depends on the surfaces (Table 1).
Here, rainfall r(c,t) is assigned values (mm/min) from the observed or estimated data. Both the sink reservoir, S(c), and plant interception, I(c), are constants and depend on empirical values with different surfaces or parameters determined using repeated experiments. The soil infiltration loss, sI(c,t), is calculated using Horton's equation where f(t) is the infiltration rate (mm per min) at time t (min); f c and f 0 are the stable and initial infiltration rates (mm per min), respectively; Dt is the iteration interval (ms); and k is a constant. The g(c,t) of gully discharge is calculated using the hydraulics equation (Eq. 4) (Gao 2006): where W is the surface area of the drainage gully in the current cell (m 2 ); C is the flow coefficient of the gully; K is the blocking coefficient of the gully; S is the surface area of the current cell (m 2 ); h(c,t) is the previous depth of the current cell before the gully discharges (mm); and g is the gravitational acceleration constant (9.81 m/s 2 ). After considering sink reservoirs, plant interception, soil infiltration, and gully discharge, the rest of the stormwater may produce a surface flow of uncertain direction and velocity. The distribution flow between the central cell and its neighbors is the key to cellular regulation. Usually, the direction of slow flow is determined mainly by gravity in laminar flow, which can be judged by the Reynolds number (Ma et al. 2009). The laminar flow occurs from the central cell to one of the adjacent cells uncovered by buildings with the steepest descent or maximum drop. If there are more than two of the same maximum drops in laminar flow, the water randomly flows onto one of its neighbors  Ma et al. 2009). The flow velocity directly influences intervals, Dt(s), of the simulation iterations, which should approximate the minimal time of flow through the current cell in the whole grid space. Then, the amount o(c,t) of interchanged water in time Dt(s) from the central cell to one neighborhood is formulated using Eq. (5): where V (m s -1 ) is the flow velocity, depending on the water depth of the current cell (h), its water surface slope (j), and Manning's roughness coefficient on its cover (n'); S' (m 2 ) is the area of the flow side from the central cell to its neighbor with a maximum drop; S (m 2 ) is the surface area of the central cell; and L is the length of the cellular side (m). The water surface slope, j, is computed by using the slope algorithm of Burrough and McDonnell (1998). However, the Manning formula diverges from supposed optimal conditions (García Díaz 2005), while the flow becomes turbulent with higher velocity and depth, and viscous forces have little effect. The accuracy of the Manning formula is lacking at a larger Reynolds number, indicating that the fluid undergoes irregular fluctuations or mixing when fully turbulent (Engineeringtoolbox 2015). In turbulent flow, the speed of the fluid at a point is continuously changing in both magnitude and direction, replacing the steady direction from the central cell to its one neighbor with a maximum drop in laminar flow. Liu et al. (2015) distributed water from a central cell to its four neighbors in their CA model based on an algorithm that aims to minimize the water surface elevation difference between cells regardless of whether the flow is laminar or turbulent; however, they ignored a violation instance of the central cell with a high elevation and low water depth. In the current study, an improved algorithm is proposed to calculate minimal water surface elevation during an iteration time between the current cell and its neighbors with low water surface in a turbulent flow. The core of the improved algorithm is to minimize the water surface elevation ave t 0 À Á after distribution of the water from the central cell to adjacent cells uncovered by buildings with low water surfaces (Eq. (6)): where l is the amount of set (S), including the central cell and its neighbors with lower elevation; k is variable and depends on the elevation, which is not less than ave t 0 À Á . If the elevation of those cells is greater than ave t 0 À Á , k equals l, and the water depth of all cells is ave t 0 À Á ; otherwise, the water depth of the cell with an elevation higher than the average water surface elevation equals zero or a minuscule number, and k individually decreases until ave t 0 À Á is greater than the highest elevation in the remaining cells.

Drainage optimization model
Among the several measures employed for drainage emergency management, forced drainage by pumping is the most efficient. When all flood water is pumped from the selected water-logged areas to candidate reservoirs, drainage decisions should be optimized to a certain extent. Some recent studies on water management optimization are noteworthy, such as that of Kaveh, who proposed an optimal design model of furrow irrigation based on the minimum cost and maximum irrigation efficiency developed by Ostad-Ali-Askari (2022). Maximizing pumping volume and minimizing energy cost under some constraints are the basic concerns. A practical optimization model is proposed using the following variables: x i , index of a flooded area i from 0 to I, where i depends on the simulation results of the waterlogging model; j, index of candidate reservoirs j from 1 to J, where J is a constant; V i , original volume of the flooded area i in unit m 3 ; C j , maximal capacity volume that the potential reservoir j, which is a given value in unit m 3 ; A ij , distance of the cost path to transfer the flood from area i to reservoir j, which depends on the distance and slope between i and j in unit m; H i , height of the deepest place in a flooded area i; H j , height of the deepest point in the reservoir j; Using the cube of the height difference not only shows its contribution but also represents its influence on being downstream or upstream.
g, gravitational acceleration constant; q, density of water, a given value; and.
x ij , binary decision variant indicating whether the flooded area i is transferred to reservoir j; if it equals 1, then all of the flood at area i is transferred to the reservoir j; otherwise, it equals 0.
Objective function: PowerCost : min q Ã g subject to X J j¼1 x ij 1 8i ð10Þ Objective (7) seeks to maximize the volume of the transferred flood (unit: m 3 ).
Objective (8) seeks to minimize the power cost of transferring the flood (unit: kWh). Here, the cost is the product of transferring volume (m 3 ), distance (m), density (1020 kg per m 3 ), and acceleration of gravity (9.81 kg per s 2 ).
Constraint (9) ensures that the total transferred flood does not exceed the maximal capacity of every reservoir.
Constraint (10) indicates that one flooded area can only transfer to one reservoir.
Constraint (11) specifies the binary restrictions on variables.
Many algorithms can be applied to resolve such multiobjective optimization issues. An important feature in multi-objective optimization is to find a diverse set of optimal solutions for the problem such that the Pareto front can be approximated. Recent studies in the optimization literature have demonstrated the effectiveness of genetic algorithms (GAs) in solving multi-objective problems. GAs are among the most promising techniques and has received wide attention owing to their flexibility and effectiveness in optimizing complex systems.
Here, the gamultiobj algorithm used in Matlab2014, a controlled elitist genetic algorithm and a variant of NSGAII, is used. An elitist GA always favors individuals with a better fitness value (MathWorks 2012), effectively solving highly nonlinear, mixed integer optimization problems that are typical of complex engineering systems. For additional details regarding the use of GAs in solving multi-objective optimization problems, relevant literature was perused (Deb 2001;GarcíarPalomares et al. 2012;Liu et al. 2005;Samanlioglu 2013;Xiao et al. 2007).

Study area and datasets
DongHaoChong catchment with an area of 11 km 2 is in the central urban area of Guangzhou. The DongHaoChong river is a main branch of the Pearl River, with a full length of 4,225 m and a width of 7-11 m. It originates in Luhu Lake in the south of Baiyun Mountain, and its elevation in the catchment decreases from north to south (Fig. 1). The river flows through an old urban area of Guangzhou from north to south, with part of a closed conduit. Big flooding has occurred for decades, and waterlogging risk has recently intensified owing to increased building density and old drainage infrastructure in the downstream area of this river.
The data primarily comprised spatial information related to the CA model (Table 2). All source data were obtained from the Drainage Facilities Management Center in Guangzhou, including DEM, green land, buildings, roads, reservoirs, lakes, rivers, drain gullies, and rainfall. The resolution of the original DEM data was 5 m. The cellular space was built following DEM in the study area and was divided into 790,860 square grids with 980 columns and 807 rows of 5 m width. The land use layer was composed of green land, building, road, river, and lake. The land-use layer was converted into raster data and snapped to the DEM data with a 5 m resolution. The gully is a part of the sewer system in the urban environment, usually present along the road edges. Gully data are a geographic point vector, with a geometry point location and certain attributes, including surface size and a block coefficient. In the CA model, gully data can be transferred into three grid layers of surface size (m 2 ), flow, and block coefficient, explicitly represented by individual pixels. Rainfall is a time-series dataset from observation or prediction, assuming that the rain is well-distributed at a small scale.

Simulation, calibration, and validation
Based on the described two models, a workflow of computation was developed using Matlab2014 (Fig. 2). First, the rainfall and spatial data listed in Table 2 were processed into arrays, then cells and parameters were initialized. According to the simulation duration and initial iteration interval, the number of iterations was calculated, and the iterations began. With the change in x and y in the circular body of the cellular array, every current cell became a central cell and was first judged by its cover type. If its cover was not building and margin, its current water depth H(c,t) was computed according to regulations (2) and (3), including computing soil infiltration sI(c,t), gully discharge g(c,t), and outflow to its neighbor, o(c,t). Based on the velocity of outflow from the central cell to its neighbor with a positive maximal drop, the iteration interval was refined by comparing the time of flow from the central cell to its orthogonal or diagonal cell. If the iteration interval was less than the minimal time of outflow from the central cell to its neighbor, the depth of outflow was calculated and added to the neighbor. Otherwise, a new process was recomputed according to a new iteration interval. The Reynolds number was calculated to judge whether outflow is fully turbulent. If the flow was turbulent, the improved algorithm that minimizes the lowest water surface was used to distribute water to the nine adjacent cells. Water depth in every cell was updated at every iteration. The iteration amount was determined by dividing the simulation time (min) by the iteration interval (s), which did not cause a significant increase in the computational complexity. After all iterations, water-logged depth grids at all times were generated, and a grid at any time point could be obtained as an output in a raster format.
Two representative rainstorm-flooding events (August 15, 2013, andJune 23, 2014), which resulted in severely water-logged areas, were selected to validate the proposed model. The rainstorm on August 15, 2013 lasted for 14 h with a total rainfall precipitation of 122.7 mm (with 78.5 mm at the first 5 h) and inundated half of the study area. Meanwhile, that on June 23, 2014 lasted for 3 h with a rainfall precipitation of 96 mm, resulting in obvious inundation.
The simulated results coincided well with the observed waterlogging in the study area. Certain main water-logged areas, which are usually located near roads, were observed and reported by the Center of Drainage Facility Management in Guangzhou. A total of 13 flooded points from August 15, 2013 and 23 points from June 23, 2014 were observed (Fig. 3a). The root mean standard error (RMSE) values calculated by comparing the max simulated depth with the max observation were 26.89 mm and 78.48 mm in 2013 and 2014, respectively. Waterlogging was heavier on June 23 than on August 15, as the storm on the format date was heavier in rainfall intensity and precipitation. The predicted value at certain flooded areas was higher than the observed depth on June 23 due to hysteretic measurement of the flooded areas. Moreover, the deviation of the predicted data for June 23 was larger than that for August 15, which may be influenced by several factors and will be discussed in Sect. 4.1. Thus, the simulation model was precise and valid ( Figs. 3a and b).
By validating the simulation results, some parameters were further calibrated ( Table 3). The values of parameters were revised to minimize the deviation between observations and simulation results, most of which were initialized and evaluated based on empirical values (Fu-ping et al. 2010;Schaffranek 2004;Valipour 2014).

Water-log prediction
To reduce losses due to urban waterlogging and improve emergency drainage management levels, water depth on urban surfaces was simulated with given rainfalls based on the above models. The study area comprised encounters of 1-, 10-, 50-, and 100-year storms, which refer to total rainfalls that have a probability of occurring during those years. According to the central urban rainstorm formula and the calculation chart in Guangzhou City (Guangzhou Water Authority 2011), the amount of rainfall in 1 h for a 100-year storm was 115 mm, 106 mm for a 50-year storm, 85 mm for a 10-year storm, and 55 mm for a 1-year storm. Given the rainfall gross, the rainfall per minute can be simulated based on rainstorm intensity. Running the simulation model, a three-dimensional matrix (980, 807, 60) of water depth in the study area was generated for 60 min of the 100-year rainfall. The array at random times can be chosen as the result of simulation and as a template to create a new zero matrix for marking flooded areas. First, the deepest cell was searched in the result array, and the value of the corresponding cell was updated to the ID of the flooded area in the marked array. Using the searching method with a 3 9 3 window, all neighbors with values greater than the waterlogging tolerance (50 mm) were found, and the corresponding cells were marked with the same ID as the deepest cell. The second deepest cell was then searched at unmarked  Similarly, the rest of the marked array was updated with the IDs, and waterlogging areas were predicted. More detailed information was extracted and recorded, such as the sum flood volume and area, depth, height, and the row and column of the deepest cell in every waterlogging area. Similarly, waterlogging was predicted by inputting the amounts of 50-, 10-year, and 1-year storm data. The predicted waterlogging is useful to implement drainage decisions and emergency measures by pumping the flood water into reservoirs to avoid life and property loss. As a measure of LID, forced drainage by pumping is currently one of the most popular emergency measures in many Chinese cities. The drainage solutions should meet the maximum pumping volume with minimum energy cost. Based on the above drainage optimization model, designing numerous optimal drainage decisions becomes simple.

Prediction results and accuracy
The predicted waterlogging for different storms is shown in Fig. 4. With an increase in rainfall, the area and depth of waterlogging gradually rose. According to the 100-year rainfall forecast in the study area, the heaviest waterlogging areas with a volume above 50 m 3 and a depth beyond 150 mm were identified. A total of 60 heavy-flood areas and eight reservoirs are shown on the map (Fig. 5). There are nine waterlogging areas around Luhu Lake influenced by the undulating terrain with many marshlands. Other waterlogging areas are mainly located near roads with few gullies; a few are on green land.
The simulation model in this study is reliable overall; however, the accuracy of the CA model needs refinement. The accuracy of the simulation depends on many factors, including the basic data and simulation parameters. First, the precision of basic data directly influences the accuracy of flow simulation, such as refinement of land use and resolution of DEM and cellular. Second, the precision of the parameters listed in Table 3 has a comprehensive impact on simulation accuracy. Certain empirical parameters, e.g., Horton equation parameters and the Manning coefficient, can be calibrated gradually to coincide with real conditions related to ground runoff and inundation in the urban environment. Recent research indicates that the Manning coefficient at the same patch during a storm may not be constant owing to a decrease in the relative roughness, such as greater depth, increased slope, and turbulent flow velocity (García Díaz 2005;Parsons and Fonstad 2007). It is therefore necessary to check the status of flow using the Reynolds number or other formulas. Iteration interval has a unique influence on simulation and may result in accumulated errors in a long simulation, such as the larger deviation observed on June 23, 2014 (Fig. 3). In this study, the setting of the iteration interval(s) was close to the minimal time of the water flow from the cell center to its adjacent cell with the velocity calculated the using Manning equation.
Storm sewer surcharge is not considered in the model, and the storm sewerage system is assumed to operate adequately and normally during a storm event. The static block coefficient of the gully should be dynamic to generate a more accurate contribution to the simulation.
Finally, the CA model should consider sophisticated urban hydrologic environments to improve the precision of urban waterlogging stimulation. For example, the outflow could be synchronized with other factors, including surface infiltration, deterrence, and acceleration by various urban facilities.

Optimization results and improvement
Considering sewer surcharge, waterlogging may be heavier during the 100-year storm, causing a severe threat of loss of property and life. By running the optimization program, optimal drainage solutions were obtained. Since the biobjective model has multiple objectives, it often has many optimal solutions. For example, let us consider an optimal solution to such a problem that has a volume of v1 and cost of c1. There may exist another solution with a lower volume of v2 \ v1, but a cost of c2, which is less than c1. Since neither option is inherently better than the other, they are both considered optimal or none are dominant. The set of all optimal solutions to the problem is called the Pareto front, representing the trade-offs between the two objectives (Fig. 6).
To assess the optimization solutions, a weighted-sum method was selected, which applies a set of weights to the objectives such that they are converted into a single objective. Hence, two objectives are combined in Eqs. (7) and (8) as follows: By systematically changing the weights, the optimal solutions can be found on the Pareto front, which may be discrete, and its shape may not be convex. An open-source solver called LP_Solve was used to find five optimal solutions setting the weight w equal to 0.1, 0.3, 0.5, 0.7, and 0.9, respectively (Fig. 7). The five optimal solutions were identical to the corresponding solutions obtained The optimal solution with the maximum volume of transferred flood at minimum power cost was chosen ( Table 4). The first part was 60 flooded area characters, including floodID, largest depth (mm), flooded area (m 2 ), and flood volume (m 3 ). The second part was the optimal drain destination transferred from every flooded area.
During decision-making on the drainage, many other issues may be considered. For example, a flood at one waterlogged area would be transferred simultaneously to more than one reservoir, and the priority of transferring the flood would minimize the loss of waterlogged areas. The above drainage optimization model could be improved to meet these requirements by adjusting variables and objectives.
PowerCost : min q Ã g  Objective (13) seeks to maximize the volume of the transferred flood (unit: m 3 ). The output volume of the flooded area i is transferred into reservoir j (m 3 ), a decision variable. Objective (14) seeks to minimize the power cost of transferring flood (kWh). Objective (15) seeks to minimize the loss of flooded area according to different land use types ($). The s ik denotes the remainder of the flooded area of land-use type k in flooded area i after transferring water (m 2 ), a decision variable. P k is the average loss price of land-use type k in flooded area i, a given value.
The optimization model with three objective functions is an improved version, in which some constraints can be considered, such as the waterlogging loss. It is also applicable in emergency decision-making regarding urban waterlogging.

Conclusion
Urban waterlogging is inevitable and poses a significant challenge for urban drainage management and emergency decision-making. This study proposed a method for integrating simulation-based, urban waterlogging prediction and drainage decision optimization. For the fragmentation and space complexity of urban surfaces, urban waterlogging was simulated using a CA model and rules, instead of mathematical runoff equations. The principle of the CA model is simple, yet powerful: it can simulate uncertain flow at any position and predict waterlogging depth at any moment based on DEM, land use, gully, and rainfall data. This approach assumes that the urban drainage line system can absorb all down-seeping rainwater through the stormwater inlet and works smoothly.
The results for urban waterlogging were confirmed and in line with the observed outcomes in two real rainfall events in the DongHaoChong basin located in the urban area of Guangzhou, China. Moreover, urban waterlogging was predicted using 100-year storm data for drainage decisions. A multi-objective optimization model for drainage decision-making was proposed and applied to pump the flood from the water-logged areas to candidate reservoirs in the study area. The Pareto front was determined and tested using a weighted method, allowing the simple selection of an optimal drainage solution. The optimization model can be improved to meet three objectives including maximizing volume, minimizing the cost of transferring the flood, and minimizing the loss in the remaining flooded areas. The integrated process of waterlogging prediction and drainage optimization is useful for designing urban emergency plans to alleviate waterlogging. Further, more quantitative factors and potential reciprocal effect will be calculated in the CA model to improve the precision and efficiency of waterlogging simulation.