Online car-hailing passenger-carrying dynamic optimal path recommendation method under multivariate benefit maximization

Abstract

The invention discloses an online car-hailing passenger-carrying dynamic optimal path recommendation method under multivariate benefit maximization, and belongs to the technical field of traffic management, and the method comprises the steps: determining a thought for constructing a path decision benefit maximization model, constructing a path decision multivariate benefit maximization objective function, quantifying environmental benefits, economic benefits and efficiency benefits, and constructing a path decision benefit maximization model. Designing a genetic algorithm improved by two-dimensional code gene coding, and synchronously considering comprehensive benefits of a grid region and a path during path selection to solve an optimal path under maximum benefits; according to the online car-hailing passenger-carrying dynamic optimal path recommendation method under the multi-element benefit maximization, through the thought of constructing a path decision benefit maximization model, macroscopic and microscopic environmental benefits, economic benefits and efficiency benefits are comprehensively considered, and the limitation of single path benefit analysis is broken through; and an improved genetic algorithm is adopted to realize dynamic recommendation of an optimal path.

Description

Technical Field

[0001] This invention relates to the field of traffic management technology, and in particular to a method for recommending the dynamic optimal route for ride-hailing passengers under the premise of maximizing multiple benefits. Background Technology

[0002] Current traditional route recommendation strategies primarily analyze and construct strategies from the perspectives of driver (economic benefits) and passenger (efficiency benefits), without focusing on the broader transportation environment or incorporating environmental benefits from a government perspective to achieve sustainable ride-hailing route planning analysis. Furthermore, research is often limited to the micro-level analysis of route benefits from individual vehicle trips, failing to examine the combined macro- and micro-level perspectives of the impact of a single vehicle's operation on the overall benefits of the region. Therefore, a multi-faceted benefit-maximizing route recommendation method suitable for sustainable urban development is needed. Summary of the Invention

[0003] To address the problems mentioned in the background section, this invention provides a method for recommending the dynamic optimal route for ride-hailing passengers under the principle of maximizing multiple benefits, comprising the following steps:

[0004] S1. Determine the approach to constructing a path decision-making benefit maximization model;

[0005] S2. Construct a multi-faceted benefit-maximizing objective function for path decision-making;

[0006] S3. Solving for the optimal path under the condition of maximizing benefits based on an improved genetic algorithm;

[0007] Preferably, the specific steps of S1 are as follows:

[0008] S11. Conduct problem analysis and modeling;

[0009] S12. Clarify the model construction approach, comprehensively consider environmental benefits, economic benefits and efficiency benefits from both macro and micro levels, and incorporate environmental benefits into path decision-making;

[0010] S13. Define the symbols and parameters involved in the model, including sets, parameters, decision variables, and computational variables.

[0011] Preferably, the specific steps of S11 are as follows:

[0012] S111. Based on the undirected network, a network model is constructed, and the study area is divided into grid areas. Within the road network area divided by the grid, the goal is to maximize the sum of the benefits of the path itself after the path is traveled and the initial benefits of the grid areas traversed by the path. The optimal route for ride-hailing vehicles with the same starting point and ending point within the grid area is then solved.

[0013] S112. Set the model assumptions, including that the starting point and destination of different ride-hailing routes are located in the same grid; the starting point and destination of the route are points on the actual road network within the grid; each vehicle route between the starting point and destination contains only one order; the ride-hailing vehicle does not exceed the maximum passenger capacity; and there are no unexpected situations in vehicle operation.

[0014] Preferably, the specific steps of S2 are as follows:

[0015] S21. Calculate the multiple benefits of ride-hailing services, including environmental benefits, economic benefits, and efficiency benefits;

[0016] S22. Construct a multi-faceted benefit maximization objective function for path decision-making, and determine the decision variables and constraints.

[0017] Preferably, the specific steps of S21 are as follows:

[0018] S211. Calculate environmental benefits, quantify carbon emissions and select influencing factors. Based on the GAMM model, calculate multi-dimensional regional carbon emissions. Through the calculation of carbon emissions along the path and in grid areas, obtain the total carbon emission cost-benefit of the grids traversed by path L.

[0019] The formula for calculating carbon emissions is:

[0020]

[0021] in, M represents the CO2 emissions of trajectory segment l in grid i within a given time period [T1, T2); M represents the total number of grid cells in the region. i This represents the total number of ride-hailing orders in grid i.

[0022] The calculation formula for the GAMM model is as follows:

[0023]

[0024] Among them, BU i WC i and W i f represents the linear variables of bus stop density, weather, and day of the week in grid i, respectively. i1 (RR i ), f i2 (PR i ), f i3 (DR i ), f i4 (CB i ), f i5 (LM i ), f i6 (OO i ) are the smoothing functions corresponding to the nonlinear variables; ui The random effect vector of grid i, ε i Refers to the random error term;

[0025] Total carbon emissions cost-effectiveness The formula is:

[0026]

[0027] The cost-effectiveness of carbon emissions from path L itself is:

[0028]

[0029] in, The carbon emissions of ride-hailing vehicles passing through grid i via path L, obtained from the GAMM model, where N represents the total number of grids traversed by path L, and C... o This refers to the cost per unit of carbon emissions. This represents the CO2 emissions of road segment j within grid i; i represents the grid number; j represents the road segment in grid i that path L passes through.

[0030] Substituting formula (2) into formula (3), the total carbon emission cost-benefit of the grid traversed by path L is:

[0031]

[0032] Substituting formula (1) into formula (4), the carbon emission cost-benefit of path L itself is:

[0033] in, This represents the length of the path segment L in grid i. This represents the speed of path L in segment j of grid i;

[0034] S212. Calculate economic benefits by measuring the actual operating income of ride-hailing drivers and the cost of carrying passengers in ride-hailing services.

[0035] S213. Analyze efficiency and cost-effectiveness, and introduce penalty costs. The efficiency and effectiveness of ride-hailing route L are represented by the following formula:

[0036]

[0037] in, Penalize the efficiency of route travel. The efficiency and effectiveness of route travel are determined solely by the goal of minimizing travel time. The efficiency benefit of route travel is defined with the shortest travel distance as the single objective; α1 and α2 are penalty factors, respectively, and t QLet Q be the travel time of the path obtained with the goal of minimizing the travel time; K Let K be the travel distance obtained with the goal of minimizing the travel distance.

[0038] Preferably, the specific steps of S212 are as follows:

[0039] (1) Calculate operating revenue, including the operating revenue of grid i traversed by the path. Passenger revenue from route L The specific formula is as follows:

[0040]

[0041] Among them, Num i l is the number of vehicles in grid i. L The distance traveled by the ride-hailing vehicle is represented by route L, t. L t represents the total travel time of the ride-hailing route L. s Let L be the starting price and travel time, (t) L -t s ) (v<12) This indicates the vehicle's low-speed travel time after excluding the time covered by the starting fare.

[0042] (2) Calculate the cost of ride-hailing services. The cost of ride-hailing services for grid i and the cost of ride-hailing services for the route are obtained by calculating the travel time cost and the distance cost.

[0043]

[0044] in, The travel time cost of ride-hailing services within grid i; The time cost of a ride-hailing vehicle within grid i; This represents the travel time of path j within grid i; This represents the distance traveled on path j within grid i; The average travel time cost of the route; Fuel costs for ride-hailing routes; P o This refers to the fuel consumption per unit price of Didi Chuxing vehicles in 2017.

[0045] (3) The passenger carrying efficiency of ride-hailing services is obtained based on the operating revenue and passenger carrying cost revenue of ride-hailing services. The specific formula is as follows:

[0046]

[0047] in, For the passenger carrying capacity of all road segments in the grid, To improve the passenger carrying capacity of the route.

[0048] Preferably, the specific steps of S22 are as follows:

[0049] S221. Constructing the objective function C for maximizing the multi-faceted benefits of path decision-making. L This includes the initial benefit C of the grid along the path. G and route travel benefits C R The specific formula is as follows:

[0050] maxC L =max[C G +C R (14)

[0051]

[0052] S222. Given grid numbers I = {i1, i2, ..., i n} and node numbers V={ν1,ν2,...,ν n}, determine decision variables Whether the ride-hailing vehicle passes through node ν m To node ν m+1 The path, and the specific formula are as follows:

[0053]

[0054] Where i' is the grid number and m is the node index;

[0055] S223. Construct the constraints for path decision-making, the specific formulas are as follows:

[0056] Restrictions on the start and end points of the path:

[0057]

[0058] Restrictions on driving routes:

[0059]

[0060] Limitations on feasible paths:

[0061]

[0062] Driving time restrictions:

[0063] 0 <t L ≤1h (21) Restrictions on path start and end times:

[0064]

[0065] Among them, t L T represents the total travel time for the ride-hailing route L. tLet t be the t-th hour of the day. This represents the start time of the path. This represents the end time of the path.

[0066] Preferably, the specific steps of S3 are as follows:

[0067] S31. Find the starting point o' of the path based on clustering algorithm. i and the endpoint d' j The traditional GA algorithm is used to number the actual nodes of the road network within the grid area, and to encode the decision variable path L in the grid to generate the initial population.

[0068] S32. Based on clustering calculations, the node numbers V in the road network can be obtained. The nodes between grids are encoded using gene encoding, and a path is abstracted as a chromosome. The specific representation of a chromosome is as follows:

[0069]

[0070] The chromosome length is n, which is the number of nodes n traversed by the start and end points. Each gene is represented by a two-dimensional vector. V i Indicates the node number, I i Indicates the grid number that the node passes through;

[0071] S33. Select individuals from the population based on the fitness function, select excellent individuals for crossover and mutation, and eliminate poor individuals.

[0072] S34. Calculate the grid benefits after each path is traveled in each iteration. Stop iterating when the maximum number of iterations is reached or the fitness of the population has converged, and output the optimal path that maximizes the multivariate benefits.

[0073] Therefore, the present invention employs the above-mentioned method for recommending dynamic optimal routes for ride-hailing passengers under the premise of maximizing multiple benefits, which has the following beneficial effects:

[0074] (1) Based on the analysis of spatiotemporal data such as meteorological environment, traffic indicators, time and space variables, a new perspective is proposed to quantify the regional environmental benefits of ride-hailing travel in a multi-dimensional "environment-traffic-time-space" context.

[0075] (2) Breaking through the previous benefit analysis based solely on a single path, this paper comprehensively calculates the multi-faceted benefits of ride-hailing route decision-making from both micro (single path) and macro (regional grid) levels, and proposes a method for recommending the optimal passenger-carrying route that maximizes ride-hailing benefits and is suitable for sustainable urban development.

[0076] (3) An improved GA algorithm was designed to construct a two-dimensional gene code. When selecting a path, both macroscopic (grid) and microscopic (path) benefits are considered. A method for finding the optimal path scheme that maximizes benefits is proposed, which provides more accurate guidance for specific emission reduction strategies for ride-hailing. Attached Figure Description

[0077] Figure 1 This is a flowchart of a method for recommending the dynamic optimal route for ride-hailing passengers under the premise of maximizing multiple benefits, as described in this invention.

[0078] Figure 2 This is a schematic diagram of a road network simulation based on grid regions according to the present invention;

[0079] Figure 3 This is a flowchart of the improved genetic algorithm of the present invention;

[0080] Figure 4 This is a schematic diagram of the grid division within the research scope of Embodiment 1 of the present invention;

[0081] Figure 5 This is a schematic diagram of the grid numbering of the research area in Embodiment 1 of the present invention;

[0082] Figure 6 This is a schematic diagram of the road network and node numbering in the study area of ​​Embodiment 1 of the present invention;

[0083] Figure 7 This is a graph showing the relationship between the number of iterations and the objective function in Embodiment 1 of the present invention;

[0084] Figure 8 This is a schematic diagram of the path to maximize efficiency at different times of the day in Embodiment 1 of the present invention;

[0085] Figure 9 This is a flowchart of the driver experience path algorithm in Embodiment 1 of the present invention;

[0086] Figure 10 This is a schematic diagram of the driver experience algorithm for path extraction in Embodiment 1 of the present invention. Detailed Implementation

[0087] The present invention will now be further described with reference to the accompanying drawings and specific embodiments.

[0088] like Figure 1 As shown, this invention provides a method for recommending the dynamic optimal route for ride-hailing passengers under the premise of maximizing multiple benefits, including the following steps:

[0089] S1. Determine the approach to constructing a path decision-making benefit maximization model.

[0090] S11. Conduct problem analysis and modeling.

[0091] This embodiment incorporates environmental benefits into the overall benefits of ride-hailing travel, proposing a multi-faceted benefit maximization concept for ride-hailing route decision-making: Through scientific and rational route selection, ride-hailing services can maximize driver income and passenger needs while ensuring environmental benefits. This involves exploring the optimal route for maximizing ride-hailing travel benefits through a comprehensive consideration of three factors: government macro-control, driver income, and passenger benefits. Based on this benefit maximization concept, this embodiment, building upon the traditional VPR problem, comprehensively maximizes the multi-faceted benefits of the grid area after route travel from three aspects: government macro-control, driver income, and passenger benefits, constructing an optimal route planning scheme specifically for ride-hailing drivers.

[0092] S111. Construct a network model based on the undirected network G(I,V,E), where I is the set of grid numbers I={i1,i2,...,i... n}, and the start and end grid numbers are O respectively. i and D j V represents the set of nodes (intersections) in the road network, V = {v1, v2, ..., v...} n}; E is the set of edges (paths) of the road network, E = {e1, e2, ..., e...} n}, and there is at most one edge between any two adjacent nodes. For a given edge (v) in graph G... i ,v j Correspondingly, there are one or more attributes representing the characteristics of this road segment, such as distance d(v). i ,v j If the two are not connected, it is denoted as ∞. A path matrix can be constructed based on relevant attributes (distance, time, etc.). For example, the distance matrix W = {d(v...} i ,v j ),|v i ,v j ∈V}), and then the optimal path can be solved. A specific road network diagram is shown below, such as... Figure 2 As shown.

[0093] This study recommends optimal routes by comprehensively considering the economic, efficiency, and environmental benefits of ride-hailing services. The route recommendation mainly involves the following benefits: ① initial carbon emission benefits of the grid; ② initial ride-hailing passenger-carrying benefits of the grid; ③ the ride-hailing passenger-carrying benefits of the planned route itself; ④ the passenger travel efficiency benefits of the planned route itself; and ⑤ the travel carbon emission benefits of the planned route itself. Specifically, the problem can be described as follows: The study area is divided into grid regions. Within a given grid-divided road network region, the goal is to maximize the sum of the route's own benefits after travel and the initial benefits (environmental benefits, passenger-carrying benefits, and travel efficiency benefits) of the grid regions traversed by the route. The aim is to find the optimal ride-hailing passenger-carrying route within the grid region that has the same starting and ending points.

[0094] S112. Set the model assumptions.

[0095] Based on the above problem description, the following assumptions are made for the model of recommending passenger transport routes for ride-hailing services to maximize efficiency:

[0096] (1) The starting point and destination of different ride-hailing routes are located in the same grid;

[0097] (2) Points O and D of the path are the points of the actual online car-hailing data set located in grid O and grid D, respectively, and the points are located on the actual road network.

[0098] (3) Each vehicle route from point O to point D must contain only one order;

[0099] (4) Ride-hailing vehicles shall not exceed their maximum passenger capacity;

[0100] (5) There are no emergencies during vehicle operation, such as vehicle damage or accidents.

[0101] S12. The model construction approach is clearly defined, comprehensively considering environmental, economic, and efficiency benefits from both macro and micro perspectives. Environmental benefits are incorporated into route decision-making. This embodiment solves for the optimal route based on the aforementioned model construction approach. On one hand, building upon the original model which only considered driver and passenger benefits, environmental benefits are incorporated into the model, specifically the impact of carbon emissions on ride-hailing route decisions. On the other hand, it breaks through the original model which only considered the travel benefits of a single route, examining the impact of a single vehicle's operation on the regional benefits from a combined macro and micro perspective. Therefore, this embodiment, based on the actual road network within the grid area, extracts the optimal route by comprehensively maximizing the multi-faceted benefits of the route and the grid areas it traverses. This achieves a win-win situation for ride-hailing revenue, environmental benefits, and travel efficiency benefits, providing ride-hailing services with an efficient, safe, and economical optimal route recommendation strategy.

[0102] S13. Define the symbols and parameters involved in the model, including sets, parameters, decision variables, and computational variables. The explanation of each parameter in the benefit maximization path recommendation model established in this embodiment is shown in Table 1.

[0103] Table 1. Explanation of Parameters for the Benefit Maximization Path Recommendation Model

[0104]

[0105]

[0106]

[0107] S2. Construct a multi-faceted benefit maximization objective function for path decision-making.

[0108] S21. Calculate the multiple benefits of ride-hailing services, including environmental benefits, economic benefits, and efficiency benefits.

[0109] This paper considers multiple benefits from three aspects: economic benefits (ride-hailing passenger-carrying benefits), efficiency benefits (passenger travel efficiency benefits), and environmental benefits (carbon emission environmental benefits). The goal is to maximize the initial multi-faceted benefits of the route itself and the grids it traverses, measuring the overall benefits of ride-hailing travel and finding the optimal route. This embodiment proposes quantitative methods for ride-hailing economic and environmental benefits at both the macro (grid area) and micro (single path) levels, laying the foundation for constructing an objective function to maximize the benefits of route decision-making.

[0110] S211. Calculate environmental benefits, and propose quantitative methods for ride-hailing travel environmental benefits from both macro (grid area) and micro (single path) levels.

[0111] The environmental benefit analysis mainly consists of two aspects. Firstly, the emissions from ride-hailing routes can be calculated using the COPERT model, taking speed as the basis for calculation. Secondly, changes in urban spatial structure, i.e., alterations in the spatial distribution of urban elements, affect ride-hailing travel patterns and volume, thus influencing emissions. Meteorological data, such as temperature and humidity, can affect vehicle drag and tire friction, while wind speed and direction influence driving speed and direction, increasing fuel consumption. Ride-hailing travel trajectory data features, such as speed, travel distance, and passenger volume, all affect vehicle operation and thus emissions. Temporal factors, such as whether travel occurs during peak hours, also affect emissions. Therefore, this embodiment selects and calculates regional carbon emissions based on these multi-dimensional factors, providing a new approach to quantifying carbon emissions for environmental benefits. Specifically, the measurement of ride-hailing emissions within a region can be modeled using the GAMM model, considering four dimensions: meteorological environment, traffic variables, and temporal and spatial indicators.

[0112] Based on the spatiotemporal distribution characteristics of ride-hailing vehicle emissions analyzed above, it is evident that carbon emissions are related to other pollutant emissions, and carbon emissions account for a relatively large proportion. Therefore, this embodiment selects carbon emissions as a representative indicator for measuring the environmental benefits of ride-hailing travel. Carbon emissions are quantified, and influencing factors are selected. Carbon emissions (CE) refer to the CO2 emissions of all vehicle trajectory segments in grid i within a given time period [T1, T2).

[0113] The formula for calculating carbon emissions is:

[0114]

[0115] Among them, among them, M represents the CO2 emissions of trajectory segment l in grid i within a given time period [T1, T2); M represents the total number of grid cells in the region.i This represents the total number of ride-hailing orders in grid i. Since the ride-hailing data sampling interval used in this embodiment is 3 seconds, when calculating the trajectory segment, the number of ride-hailing trajectory segments in a grid is equal to the number of ride-hailing orders by default.

[0116] In this embodiment, CO2 emissions were selected as the representative emissions from ride-hailing vehicles, and 19 independent variables were chosen from traffic indicators, meteorological indicators, temporal indicators, and spatial indicators. The descriptive statistics of the independent variables are shown in Table 2.

[0117] Table 2 Descriptive statistics of factors influencing regional carbon emissions

[0118]

[0119]

[0120] Based on the GAMM model, multi-dimensional regional carbon emissions are calculated. The "mgcv" extension package in R language is used to implement GAMM modeling and explore the linear and nonlinear relationships between carbon emissions and four dimensions: environment, transportation, time, and space. Based on the linear and nonlinear parameters, random error term, and residual term, the final calculation formula of the GAMM model is as follows:

[0121]

[0122] Where 1.8346, 1.5272, and 1.6536 are the linear variable coefficients of bus stop density, weather, and day of the week in grid i, BU i WC i and W i f represents the linear variables of bus stop density, weather, and day of the week in grid i, respectively. i1 (RR i ), f i2 (PR i ), f i3 (DR i ), f i4 (CB i ), f i5 (LM i ), f i6 (OO i ) are the smoothing functions corresponding to the nonlinear variables; u i The random effect vector of grid i, ε i Refers to the random error term;

[0123] Based on the carbon emission calculations for paths and grid regions, the unit emission cost of carbon emissions is further clarified to obtain the carbon emission cost function. Through the carbon emission calculations for paths and grid regions, the total carbon emission cost-benefit of the grids traversed by path L is obtained.

[0124] Total carbon emissions cost-effectiveness The formula is:

[0125]

[0126] The cost-effectiveness of carbon emissions from path L itself is:

[0127]

[0128] in, The carbon emissions (kg) of ride-hailing vehicles passing through grid i via path L, obtained from the GAMM model, where N represents the total number of grids traversed by path L, and C... o This refers to the unit carbon emission cost, which is approximately 0.12 yuan per kilogram of CO2 emission, i.e., 0.12 yuan / kg in this example. This represents the CO2 emission (g) of road segment j in grid i; i represents the grid number (i = 1, 2, ... N); j represents the road segment in grid i that path L passes through, j = 1, 2, ... J;

[0129] Substituting formula (2) into formula (3), the total carbon emission cost-benefit of the grid traversed by path L is:

[0130]

[0131] Substituting formula (1) into formula (4), the carbon emission cost-benefit of path L itself is:

[0132] in, This represents the length (km) of the path L segment within grid i. This represents the speed (km / h) of path L in segment j of grid i.

[0133] S212. Calculate the economic benefits. The economic benefits of ride-hailing services, namely the passenger-carrying benefits of ride-hailing services, refer to the difference between the actual operating income of ride-hailing drivers and the passenger-carrying costs (mainly including time and distance costs). The economic benefits of ride-hailing services are calculated by comparing the actual operating income of ride-hailing drivers with the passenger-carrying costs.

[0134] (1) Calculate the ride-hailing operating revenue, including the operating revenue of grid i traversed by the route. Passenger revenue from route L

[0135] Ride-hailing operating revenue refers to the product of the ride-hailing pricing standard and the mileage traveled. This example uses GPS data from Didi Chuxing's Chengdu ride-hailing service in 2017, therefore the pricing rules for Chengdu Didi Chuxing are adopted for calculation. In 2017, Didi Chuxing's starting price in Chengdu was 8 yuan, including 3km of mileage; when the distance exceeded 3km, the charge was 1.5 yuan per kilometer; Didi Chuxing also set a low-speed fee, which is 0.3 yuan per minute when the vehicle speed is below 12 km / h, excluding waiting time. Therefore, the revenue from a single ride-hailing trip mainly consists of three parts: the starting price, the mileage fee, and the low-speed fee.

[0136] Operating revenue of the grids traversed by the path The total revenue for the grid is calculated by summing the path distances of all vehicles within the grid. Since the grid size is 500m x 500m, the distance traveled by each vehicle within the grid does not exceed 3.0km.

[0137] Operating revenue of the grids traversed by the path Passenger revenue from routes The specific formula is:

[0138]

[0139] Among them, Num i l is the number of vehicles in grid i. L The distance (km) represented by the ride-hailing route L is t. L t represents the total travel time (h) for the ride-hailing route L. s The starting price for route L is the travel time (h), (t) L -t s ) (v<12) This represents the travel time (in hours) of the vehicle at low speed (v<12km / h) after deducting the time covered by the starting fare.

[0140] (2) Calculate the cost of ride-hailing services. The cost of ride-hailing services mainly includes passenger waiting time cost, time cost from boarding to disembarking, and distance cost. Since this study does not have data on ride-hailing services in empty states, this embodiment will ignore passenger waiting time cost when considering the revenue of ride-hailing services. That is, the cost of ride-hailing services is defined as travel time cost and distance cost. Among them, the travel time cost is calculated as follows: According to the data released by the National Bureau of Statistics, the per capita disposable income of Chengdu residents in 2017 was 32,038 yuan. Based on an 8-hour workday, the average wage is 16.34 yuan / hour. The distance cost is calculated as follows: This embodiment ignores other costs such as vehicle depreciation during the driving process and uses fuel cost to represent the distance cost. According to the official data released by Didi Chuxing, the average fuel consumption of Didi Chuxing vehicles in Chengdu in 2017 was about 7.5L per 100 kilometers, that is, fuel consumption was 0.075L / km.

[0141] The ride-hailing passenger cost for grid i is obtained by calculating travel time cost and distance cost. Passenger carrying costs of routes

[0142]

[0143] in, The cost of travel time (in yuan) for ride-hailing services within grid i; The time cost (in yuan) for a ride-hailing vehicle within grid i; This represents the travel time of path j within grid i; This represents the distance (km) traveled on path j within grid i; The average travel time cost (in yuan) for the route; Fuel cost (yuan) for ride-hailing routes; P o The figure represents the fuel consumption unit price for Didi Chuxing vehicles in 2017. At that time, the main fuels used were gasoline and diesel. Gasoline was mainly used in small cars and SUVs, with a fuel price of 6.7 yuan / L; diesel was mainly used in commercial vehicles and vans, with a fuel price of 5.9 yuan / L. This example assumes the vehicle model uses gasoline. P o The price is 6.7 yuan / L.

[0144] (3) The passenger carrying efficiency of ride-hailing services can be obtained by combining the operating revenue and passenger carrying cost revenue. The specific formula is as follows:

[0145]

[0146] in, For the passenger carrying capacity of all road segments in the grid, To improve the passenger carrying capacity of the route.

[0147] S213, Analysis efficiency and cost-effectiveness.

[0148] Because this embodiment considers environmental benefits when measuring the efficiency of ride-hailing services, the following situations may arise: Firstly, in congested conditions, unstable speeds may lead to increased emissions from ride-hailing vehicles. Secondly, to avoid congestion, drivers may choose to take detours, increasing travel distance and consequently travel costs. In such cases, the passenger-carrying efficiency of ride-hailing services may decrease, while the emission cost-benefit ratio may be relatively high. Therefore, to address these issues, considering ride-hailing driver preferences and the acceptability of passengers and drivers to incorporating environmental benefits into route recommendations, if a route does not meet the shortest travel time or shortest path rules, a penalty cost needs to be introduced. The efficiency and effectiveness of ride-hailing route L are represented by the following formula:

[0149]

[0150] in, Penalize the efficiency of route travel. The efficiency and effectiveness of route travel are determined solely by the goal of minimizing travel time. This refers to the route travel efficiency benefit with the shortest travel distance as the single objective; α1 and α2 are penalty factors, representing driver travel preferences and the acceptability of the route for both drivers and passengers. Their calculation formula can be based on the ratio of the actual travel distance or time to the shortest distance or minimum time, i.e., α1 = t L / t Q α2=l L / l K When α1 > α2, it indicates that ride-hailing drivers prefer the route with the shortest travel time; conversely, it indicates that ride-hailing drivers prefer the route with the shortest travel distance. Q Let Q be the travel time of the path obtained with the goal of minimizing the travel time; K Let K be the travel distance obtained with the goal of minimizing the travel distance.

[0151] Regarding the efficiency and effectiveness of grid-based travel, since the grid division breaks down the path length, the length (time) of each segment in the grid is less than the shortest travel distance (time). Therefore, the efficiency and effectiveness of ride-hailing services within the grid are ignored here.

[0152] S22. Based on the above multi-benefit calculations at the grid and regional levels, construct the objective function C for maximizing the multi-benefit of path decision-making. L It mainly includes two parts: the initial benefit C of the path passing through the grid. G and route travel benefits C RThe former includes the initial carbon emission benefit of the grid and the passenger carrying benefit. Since the calculation unit is the grid area, the path is truncated into road segments for calculation, so its travel efficiency benefit is ignored. The latter includes the path carbon emission benefit, passenger carrying revenue and travel efficiency benefit, and determines the decision variables and constraints.

[0153] S221. Constructing the objective function C for maximizing the multi-faceted benefits of path decision-making. L This includes the initial benefit C of the grid along the path. G and route travel benefits C R The specific formula is as follows:

[0154] maxC L =max[C G +C R (14)

[0155]

[0156] S222. Given grid numbers I = {i1, i2, ..., i n} and node numbers V={ν1,ν2,...,ν n}, determine decision variables Whether the ride-hailing vehicle passes through node ν m To node ν m+1 The path, and the specific formula are as follows:

[0157]

[0158] Where i' is the grid number and m is the node index;

[0159] S223. Construct the constraints for path decision-making, the specific formulas are as follows:

[0160] With restrictions on the origin and destination of a route, ride-hailing trips have only one origin and one destination:

[0161]

[0162] Due to the limitations of the driving routes, ride-hailing vehicles must start from one route and then traverse to another route:

[0163]

[0164] Feasible path restrictions: a path cannot be selected repeatedly, and it can only pass through adjacent paths; that is, two paths cannot both be 1.

[0165]

[0166] Due to the limitation on travel time, since grid carbon emissions are calculated based on the hour (e.g., 8:00-9:00), the travel time for the route must not exceed 1 hour.

[0167] 0 <t L ≤1h (21)

[0168] The path start and end times are restricted. To ensure consistency within the time range, the path's start and end times must both fall within this 1-hour timeframe.

[0169]

[0170] Among them, t L T represents the total travel time for the ride-hailing route L. t Let t be the t-th hour of the day. This represents the start time of the path. This represents the end time of the path.

[0171] S3. Solving the optimal path for maximizing benefits using an improved genetic algorithm: This embodiment transforms the benefit-maximizing path recommendation problem into a multi-objective optimization problem by referencing an improved genetic algorithm. This involves weighing multiple indicators to find a balance point that extracts the path with the highest overall benefit while satisfying constraints on carbon emissions, passenger revenue, and travel efficiency. Therefore, this embodiment improves the GA algorithm used to solve the benefit-maximizing ride-hailing route optimization model. The flowchart of the improved algorithm is shown below. Figure 3 As shown.

[0172] S31. Find the starting point o' of the path based on clustering algorithm. i and the endpoint d' j The traditional GA algorithm is used to number the actual nodes of the road network within the grid area, and the decision variables path in the grid are... Encode the data to generate the initial population;

[0173] S32. Based on clustering calculations, the node numbers V in the road network can be obtained. The nodes between grids are encoded using gene encoding, and a path is abstracted as a chromosome. The specific representation of a chromosome is as follows:

[0174]

[0175] The chromosome length is n, which is the number of nodes n traversed by the start and end points. Each gene is represented by a two-dimensional vector. V i Indicates the node number, I i Indicates the grid number that the node passes through;

[0176] S33. Select individuals from the population based on the fitness function, select excellent individuals for crossover and mutation, and eliminate poor individuals.

[0177] S34. Calculate the grid benefits after each path is traveled in each iteration. Stop iterating when the maximum number of iterations is reached or the fitness of the population has converged, and output the optimal path that maximizes the multivariate benefits.

[0178] Example 1

[0179] In this embodiment, the study area is divided into 289 grids using a 0.5km*0.5km grid as the analysis unit. The GPS data of Didi order pick-up points are then transformed and matched to the map to divide the study area into grids as follows: Figure 4 As shown.

[0180] Based on the constructed benefit-maximizing path decision-making model, this study examines the road networks in parts of Qingyang District and Jinniu District of Chengdu (e.g., Figure 5 Taking [example] as an example, this study explores the changes in the path for maximizing the travel efficiency of ride-hailing services at different times of the day. Grid 104 is the starting grid, and grid 38 is the ending grid. Based on the trend of the starting and ending grids, the grid network nodes are further numbered, resulting in a total of 211 nodes. Figure 6 As shown.

[0181] Analyze the total benefits of ride-hailing services at different times of the day.

[0182] To explore the dynamic changes of the optimal route at different times of the day, this embodiment uses ride-hailing trajectory data from November 17 (Thursday) as the starting point and grid 38 as the ending point to analyze the total travel benefits of the route itself and the grids it passes through after the ride-hailing route passes through each time period: 8:00-9:00, 13:00-14:00, 17:00-18:00, and 22:00-23:00.

[0183] The initial benefits of each grid at different times of the day were calculated, as shown in Tables 3-6.

[0184] Table 3 Initial Raster Benefits (8:00-9:00)

[0185]

[0186] Table 4 Initial Raster Benefits (13:00-14:00)

[0187]

[0188]

[0189] Table 5 Initial Raster Benefits (17:00-18:00)

[0190]

[0191] Table 6 Initial Raster Benefits (22:00-23:00)

[0192]

[0193] Determine the optimal path to maximize benefits at different times of the day.

[0194] Based on the acquisition of raster benefits, and using the improved GA algorithm, the benefits of the raster and path during algorithm traversal are calculated for each time period: 8:00-9:00, 13:00-14:00, 17:00-18:00, and 22:00-23:00. The applicability weight coefficient is set as follows: ω G =0.5. By adjusting the parameters of the model solving algorithm, the optimal parameters are as follows: population size of 200, number of iterations of 100, crossover probability of 0.7, selection probability of 0.2, and mutation probability of 0.05. Based on this, the relationship between the number of iterations and the objective function is obtained for four time periods: 8:00-9:00, 13:00-14:00, 17:00-18:00, and 22:00-23:00, as shown in the figure. Figure 7 As shown.

[0195] Based on the principle of maximizing benefits, a comprehensive analysis of the initial and path benefits of the grid is conducted. Figure 7 It can be seen that, under four different time periods within a day (8:00-9:00, 13:00-14:00, 17:00-18:00, 22:00-23:00), the objective function tends to stabilize after 100 iterations, yielding the maximized multivariate total benefits of paths 1-①, 1-②, 1-③, and 1-④ as RMB 15249.851, RMB 17954.830, RMB 15228.006, and RMB 10148.088, respectively. The optimal path diagrams for the four time periods are shown below. Figure 8 As shown:

[0196] Path 1-①: 104→87→88→71→70→55→54→37→20→21→38

[0197] Path 1-②: 104→87→70→53→54→37→20→21→38

[0198] Path 1-③: 104→121→105→89→72→55→56→39→38

[0199] Path 1-④: 104→87→70→53→54→55→38

[0200] Depend on Figure 8 Intuitively, the optimal travel route for ride-hailing services from grid 104 to grid 38 differs at different times, especially during peak hours. A detailed analysis follows: Compared to off-peak hours (… Figure 8 (d) Compared to the routes during peak periods (8(a), 8(b), and 8(c)), all of them involve detours, which is consistent with the phenomenon that the actual road conditions during peak periods are relatively more congested than during off-peak periods. This indicates that this embodiment takes into account the real-time operating status of the road network when selecting routes. That is, during peak periods, in order to avoid traffic congestion and improve passenger satisfaction, drivers choose certain detours so that passengers can reach their destination efficiently and avoid additional delays and expenses caused by congestion.

[0201] Calculate the optimal path and total grid benefit at different times of the day.

[0202] Based on the acquisition of the optimal routes for ride-hailing services at different time periods, the overall maximization of benefits after taking the optimal route can be calculated, as shown below:

[0203] The carbon emission cost-effectiveness of each pathway is shown in Table 7.

[0204] Table 7. Cost-Effectiveness of Optimal Pathway for Carbon Emissions

[0205]

[0206] Passenger carrying efficiency includes two parts: ride-hailing operating revenue and passenger carrying costs. The route passenger carrying efficiency can be obtained, as shown in Table 8.

[0207] Table 8 Passenger carrying capacity of each route

[0208]

[0209] Based on efficiency and benefit analysis, this embodiment assigns penalty factors to both route length and time for ride-hailing services that do not follow the shortest distance and shortest time routes. This approach aims to satisfy drivers' preferences while also protecting passengers' rights to some extent. For example, during peak hours, congested roads often occur, and drivers may choose to take detours to allow passengers to reach their destinations faster and more efficiently. However, detours may incur additional travel costs for passengers. Therefore, considering carbon emission benefits, the model incorporates penalty rules from both driver and passenger perspectives, proposing ride-hailing travel efficiency and benefit metrics to characterize the policy's acceptability. The travel efficiency and benefit metrics for each route are shown in Table 9.

[0210] Table 9. Travel Efficiency and Benefits of Each Route

[0211]

[0212] The total benefit of a route is obtained based on its carbon emission benefits, passenger capacity benefits, and travel efficiency benefits, as shown in Table 10.

[0213] Table 10 Optimal Path Benefits for Each Time Period

[0214]

[0215] Based on the above analysis, the optimal overall benefit of the grid under different time periods (8:00-9:00, 13:00-14:00, 17:00-18:00 and 22:00-23:00) on November 17 is obtained from the perspectives of path benefit and the benefit of the grids traversed by the path, as shown in Table 11.

[0216] Table 11 Total benefits of the grid after path travel at different time periods.

[0217]

[0218] This embodiment uses the driver experience path algorithm as the benchmark algorithm to solve and verify the effectiveness of the proposed efficiency-maximizing path. Specifically, it involves statistical analysis of real-time ride-hailing order travel trajectory data, clustering trajectories with the same grid start point O and end point D to obtain all path schemes between O and D. Simultaneously, it obtains the probability of each path selection and selects the path with the higher probability as the driver experience path. The flowchart of the driver experience path algorithm based on clustering is as follows: Figure 9 As shown.

[0219] Based on a driver experience-based route algorithm, route options are obtained for four different time periods throughout the day (8:00-9:00, 13:00-14:00, 17:00-18:00, and 22:00-23:00). Figure 10 As shown:

[0220] Path 2-①: 104→87→70→53→54→55→39→38

[0221] Path 2-②: 104→87→70→53→54→55→38

[0222] Path 2-③: 104→105→89→72→55→56→55→38→39→38

[0223] Path 2-④: 104→105→89→72→55→38

[0224] based on Figure 10The analysis of the driver experience route diagrams yielded the overall benefits of the grid (including carbon emission benefits, passenger carrying capacity benefits, and travel efficiency benefits) for different time periods on November 17th, namely 8:00-9:00, 13:00-14:00, 17:00-18:00, and 22:00-23:00, as shown in Table 12.

[0225] Table 12 Total benefits of the grid after drivers' experienced routes at different time periods.

[0226]

[0227] Table 13 shows a comparison of the total travel benefits of the two methods and routes at different times of the day.

[0228] Table 13 Comparison of total travel efficiency for the two methods at different times of the day

[0229]

[0230] Based on Table 13, it can be seen that the ride-hailing travel benefits vary at different times under the same method:

[0231] (1) The paths obtained by the same method (profit maximization method or driver experience path method) at different times of the day pass through the grid's initial benefit C. G Path benefits C R The path and the total grid benefit C are all different;

[0232] (2) For the benefit maximization method: the initial benefit C of the path passing through the grid G The overall benefit C after the route trip is ranked as follows: Route 1-② (13:00-14:00) > Route 1-① (8:00-9:00) > Route 1-③ (17:00-18:00) > Route 1-④ (22:00-23:00); Route benefit C R The order is: Path 1-② (13:00-14:00) > Path 1-③ (17:00-18:00) > Path 1-④ (22:00-23:00) > Path 1-① (8:00-9:00);

[0233] (3) For the driver experience-based route method: the initial benefit C of the route passing through the grid G The overall benefit C after the route trip is ranked as follows: Route 3-② (13:00-14:00) > Route 3-③ (17:00-18:00) > Route 3-① (8:00-9:00) > Route 3-④ (22:00-23:00); Route benefit C RThe order is: Path 3-② (13:00-14:00) > Path 3-④ (22:00-23:00) > Path 3-③ (17:00-18:00) > Path 3-① (8:00-9:00).

[0234] Based on the analysis results of the two methods mentioned above, it can be concluded that the travel efficiency is greatest during the peak period from 13:00 to 14:00 within a day. It can be seen that both the efficiency maximization method and the driver experience route method are consistent with the time-varying pattern of ride-hailing peak and off-peak travel.

[0235] Based on Table 13, the ride-hailing travel benefits differ between the two methods for the same time period:

[0236] (1) The path obtained by the benefit maximization method passes through the grid's initial benefit C G Path benefits C R The overall efficiency C, including both path and grid efficiency, is greater than that of the driver's experience-based path scheme. Specifically, compared to the baseline algorithm, C... G The added value of benefits were 2760.477, 3031.196, 2168.258, and 3077.298 respectively, C R The profit increments for C were 0.972, 0.003, 0.737, and 0.425, respectively, while the profit increments for C were 2761.449, 3031.199, 2168.995, and 3077.723, respectively.

[0237] (2) Regarding the initial benefit C of the path passing through the grid G Compared to the total benefit C of the route and the grid, the difference between the benefit maximization method and the driver's experience route is relatively large because the benefit calculation covers the benefit of different ride-hailing trip grids over an hour.

[0238] (3) Regarding path benefits C R Since the benefit is the benefit of a single path itself, the travel distance and travel time of the path are relatively small, so the difference between the benefit maximization method and the driver's experience path is relatively small.

[0239] Therefore, the present invention adopts the above-mentioned dynamic optimal route recommendation method for ride-hailing passengers under the multiple benefits maximization approach. Compared with the traditional method that only considers driver income and passenger efficiency, it achieves a win-win situation for government emission reduction regulation, driver income and passenger satisfaction, and provides a forward-looking route planning solution for sustainable transportation development.

[0240] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for recommending the dynamic optimal route for ride-hailing passengers under the premise of maximizing multiple benefits, characterized in that, Includes the following steps: S1. Determine the approach to constructing a path decision-making benefit maximization model; S2. Construct a multi-faceted benefit-maximizing objective function for path decision-making; S3. Solve the optimal path for maximizing benefits based on an improved genetic algorithm.

2. The method for recommending the dynamic optimal route for ride-hailing passengers under the principle of maximizing multiple benefits, as described in claim 1, is characterized in that... The specific steps of S1 are as follows: S11. Conduct problem analysis and modeling; S12. Clarify the model construction approach, comprehensively consider environmental benefits, economic benefits and efficiency benefits from both macro and micro levels, and incorporate environmental benefits into path decision-making; S13. Define the symbols and parameters involved in the model, including sets, parameters, decision variables, and computational variables.

3. The method for recommending the dynamic optimal route for ride-hailing passengers under the principle of maximizing multiple benefits, as described in claim 2, is characterized in that... The specific steps of S11 are as follows: S111. Based on the undirected network, a network model is constructed, and the study area is divided into grid areas. Within the road network area divided by the grid, the goal is to maximize the sum of the benefits of the path itself after the path is traveled and the initial benefits of the grid areas traversed by the path. The optimal route for ride-hailing vehicles with the same starting point and ending point within the grid area is then solved. S112. Set the model assumptions, including that the starting point and destination of different ride-hailing routes are located in the same grid; the starting point and destination of the route are points on the actual road network within the grid; each vehicle route between the starting point and destination contains only one order; the ride-hailing vehicle does not exceed the maximum passenger capacity; and there are no unexpected situations in vehicle operation.

4. The method for recommending the dynamic optimal route for ride-hailing passengers under the principle of maximizing multiple benefits, as described in claim 1, is characterized in that... The specific steps of S2 are as follows: S21. Calculate the multiple benefits of ride-hailing services, including environmental benefits, economic benefits, and efficiency benefits; S22. Construct a multi-faceted benefit maximization objective function for path decision-making, and determine the decision variables and constraints.

5. The method for recommending the dynamic optimal route for ride-hailing passengers under the principle of maximizing multiple benefits, as described in claim 4, is characterized in that... The specific steps of S21 are as follows: S211. Calculate environmental benefits, quantify carbon emissions and select influencing factors. Based on the GAMM model, calculate multi-dimensional regional carbon emissions. Through the calculation of carbon emissions along the path and in grid areas, obtain the total carbon emission cost-benefit of the grids traversed by path L. The formula for calculating carbon emissions is: in, M represents the CO2 emissions of trajectory segment l in grid i within a given time period [T1, T2); M represents the total number of grid cells in the region. i This represents the total number of ride-hailing orders in grid i. The calculation formula for the GAMM model is as follows: Among them, BU i WC i and W i f represents the linear variables of bus stop density, weather, and day of the week in grid i, respectively. i1 (RR i ), f i2 (PR i ), f i3 (DR i ), f i4 (CB i ), f i5 (LM i ), f i6 (OO i ) are the smoothing functions corresponding to the nonlinear variables; u i The random effect vector of grid i, ε i Refers to the random error term; Total carbon emissions cost-effectiveness The formula is: The cost-effectiveness of carbon emissions from path L itself is: in, The carbon emissions of ride-hailing vehicles passing through grid i via path L, obtained from the GAMM model, where N represents the total number of grids traversed by path L, and C... o This refers to the cost per unit of carbon emissions. This represents the CO2 emissions of road segment j within grid i; i represents the grid number; j represents the road segment in grid i that path L passes through. Substituting formula (2) into formula (3), the total carbon emission cost-benefit of the grid traversed by path L is: Substituting formula (1) into formula (4), the carbon emission cost-benefit of path L itself is: in, This represents the length of the path segment L in grid i. This represents the speed of path L in segment j of grid i; S212. Calculate economic benefits by measuring the actual operating income of ride-hailing drivers and the cost of carrying passengers in ride-hailing services. S213. Analyze efficiency and cost-effectiveness, and introduce penalty costs. The efficiency and effectiveness of ride-hailing route L are represented by the following formula: in, Penalize the efficiency of route travel. The efficiency and effectiveness of route travel are determined solely by the goal of minimizing travel time. The efficiency benefit of route travel is defined with the shortest travel distance as the single objective; α1 and α2 are penalty factors, respectively, and t Q Let Q be the travel time of the path obtained with the goal of minimizing the travel time; K Let K be the travel distance obtained with the goal of minimizing the travel distance.

6. The method for recommending the dynamic optimal route for ride-hailing passengers under the principle of maximizing multiple benefits, as described in claim 5, is characterized in that... The specific steps of S212 are as follows: (1) Calculate operating revenue, including the operating revenue of grid i traversed by the path. Passenger revenue from route L The specific formula is as follows: Among them, Num i l is the number of vehicles in grid i. L The distance traveled by the ride-hailing vehicle is represented by route L, t. L t represents the total travel time of the ride-hailing route L. s Let L be the starting price and travel time, (t) L -t s ) (v<12) This indicates the vehicle's low-speed travel time after excluding the time covered by the starting fare. (2) Calculate the ride-hailing passenger cost. Obtain the ride-hailing passenger cost of grid i by calculating the travel time cost and distance cost. Passenger carrying costs of routes in, The travel time cost of ride-hailing services within grid i; The time cost of a ride-hailing vehicle within grid i; This represents the travel time of path j within grid i; This represents the distance traveled on path j within grid i; The average travel time cost of the route; Fuel costs for ride-hailing routes; P o This refers to the fuel consumption per unit price of Didi Chuxing vehicles in 2017. (3) The passenger carrying efficiency of ride-hailing services is obtained based on the operating revenue and passenger carrying cost revenue of ride-hailing services. The specific formula is as follows: in, For the passenger carrying capacity of all road segments in the grid, To improve the passenger carrying capacity of the route.

7. The method for recommending the dynamic optimal route for ride-hailing passengers under the principle of maximizing multiple benefits, as described in claim 6, is characterized in that... The specific steps of S22 are as follows: S221. Constructing the objective function C for maximizing the multi-faceted benefits of path decision-making. L This includes the initial benefit C of the grid along the path. G and route travel benefits C R The specific formula is as follows: maxC L =max[C G +C R ] (14) S222. Given grid numbers I = {i1, i2, ..., i n } and node numbers V={ν1,ν2,...,ν n }, determine decision variables Whether the ride-hailing vehicle passes through node ν m To node ν m+1 The path, and the specific formula are as follows: Among them, i ' m is the raster number, and m is the node index; S223. Construct the constraints for path decision-making, the specific formulas are as follows: Restrictions on the start and end points of the path: Route restrictions: Limitations on feasible paths: Driving time restrictions: 0<t L ≤1h (21) Path start and end time restrictions: Among them, t L T represents the total travel time for the ride-hailing route L. t Let t be the t-th hour of the day. This represents the start time of the path. This represents the end time of the path.

8. The method for recommending the dynamic optimal route for ride-hailing passengers under the principle of maximizing multiple benefits, as described in claim 1, is characterized in that... The specific steps for S3 are as follows: S31. Find the starting point of the path based on clustering algorithm. ′ i and endpoint d ′ j The traditional GA algorithm is used to number the actual nodes of the road network within the grid area, and to encode the decision variable path L in the grid to generate the initial population. S32. Based on clustering calculations, the node numbers V in the road network can be obtained. The nodes between grids are encoded using gene encoding, and a path is abstracted as a chromosome. The specific representation of a chromosome is as follows: The chromosome length is n, which is the number of nodes n traversed by the start and end points. Each gene is represented by a two-dimensional vector. V i Indicates the node number, I i Indicates the grid number that the node passes through; S33. Select individuals from the population based on the fitness function, select excellent individuals for crossover and mutation, and eliminate poor individuals. S34. Calculate the grid benefits after each path is traveled in each iteration. Stop iterating when the maximum number of iterations is reached or the fitness of the population has converged, and output the optimal path that maximizes the multivariate benefits.

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