Flexible bus route resource reuse allocation and scheduling method

Abstract

The present invention discloses a flexible bus route resource reuse allocation and scheduling method, including site selection, which is to find B sites with the departure point of the online bus as the center and A as the radius; and select C sites from the smallest to the largest distance by radius or path planning algorithm. First, the allocation of all paths in area A is completed, all paths in area A are divided out, and the length is calculated. If some paths are not covered by any site or are only partially covered, the paths are pre-processed first and the paths are classified and sorted. The present invention utilizes the existing resources of public transportation to take into account both conventional public transportation and flexible public transportation routes, while considering the constraints of vehicles and stations, using scientific model algorithms, considering the relaxation of time and space, comprehensively analyzing the station shunting strategy, selecting the optimal vehicle from the existing idle conventional operating routes and stations, performing allocation and scheduling, completing orders, and gradually forming a flexible crowdsourcing mechanism within the bus company.

Description

Technical Field

[0001] The invention belongs to the technical field of bus route scheduling, and in particular relates to a scheduling method for realizing resource reuse allocation through flexible bus routes. Background Art

[0002] According to expert estimates, the urban population in China will reach 60% in 2020, which means that 900 million people will move to cities, and the traditional transportation mode will face challenges. In China today, the basic environment for the formation of a new generation of intelligent transportation has been prepared. After sorting out the "14th Five-Year Plan" intelligent transportation plans carried out by provinces and cities across the country, in the era of normalized transportation of autonomous driving, intelligent networked and non-networked, unmanned and manned mixed transportation, the development of vehicle networking and electrification, intelligence and sharing has become the main trend of the present and future. In particular, the interconnected and shared travel mode of people, cars, roads and objects has become a new field of research and development innovation of intelligent networked transportation in the current automotive industry.

[0003] Demand-responsive transportation service, referred to as DRT, originated from the telephone taxi service. It is a small and medium-sized bus operation mode that is user-oriented and has flexible boarding and alighting stations, routes and schedules. Most of the early demand-responsive buses served specific user groups, such as the disabled and the elderly. Another application scenario was to serve the small-scale passenger needs in the suburbs of cities where there was a lack of regular bus operations.

[0004] In recent years, with the development of information technology and communication technology, the flexibility of public transportation resources has increased. At the same time, the diversity of user needs faced by traditional public transportation has increased. Therefore, the mainstream development direction of demand-responsive public transportation has shifted to online-booked carpooling customized public transportation, which combines travel needs of roughly the same time and route, and uses the Internet to make demands for car bookings. Bus companies quickly respond to customized sharing needs and allocate idle bus resources to pick up passengers. With the rapid development of online-booked public transportation, bus companies need to study the issue of flexible scheduling.

[0005] The ensuing bus scheduling issues require special research. Currently, most of the research on flexible bus scheduling refers to the research on night flexible line scheduling, such as "Research on Night Flexible Bus Scheduling Based on Real-time Demand" by Shen Rui et al. in 2016 and "Research on Night Flexible Bus Scheduling under the Dual-Car Service Model" by Pan Lu et al. in 2018.

[0006] Similar technical solutions include various studies on customized bus scheduling, such as "Research and System Design of Variable Route Customized Bus Scheduling Algorithm" by Ding Jiqiang et al. in 2018.

[0007] However, most of the existing technical solutions are mathematical modeling, and they do not consider the perspective of operating bus companies, and often separate customized bus scheduling from existing conventional bus scheduling. Flexible bus routes need to solve the problem of vehicle resource allocation. In addition to some franchised vehicles, considering the idle cost issue, operating bus companies often choose to reuse vehicles to operate conventional routes and flexible routes at the same time. This practical problem needs to be solved urgently, and a new resource reuse vehicle scheduling and allocation method is needed to cooperate with the parallel development of flexible and conventional buses, and gradually implement the actual needs of online booking and customization. Summary of the invention

[0008] The present invention reuses vehicle resources for different flexible bus orders, establishes an objective function, and uses an algorithm to solve the model function, including a basic strategy scheduling algorithm and a field space relaxation algorithm.

[0009] The technical solution to achieve the above purpose is to adopt a flexible bus line resource reuse allocation and scheduling method, which includes the following contents.

[0010] (1) Site selection: With the online bus departure point as the center and A as the radius, search for B sites; use the radius or path planning algorithm to select C sites in ascending order of distance.

[0011] (2) Calculate the number of positions D based on the shift schedule: If there is a shift schedule for the day, calculate directly; if there is no shift schedule, calculate the maximum number of positions based on the historical shift schedule for the same working day.

[0012] (3) When the start and end times of the ride-hailing vehicle are at peak times, motor vehicles are mainly selected as the preferred target: the larger the value of (route allocation - number of locations D) / route allocation, the easier it is to ensure the route plan (later versions), and the lower the overlap between the start and end times of the ride-hailing vehicle and the peak times of the route, the preferred route is E1.

[0013] (4) When the starting and ending time of the ride-hailing service is in the off-peak or off-peak period, according to the planned or historical schedules for multiple days, the E2 routes are selected in descending order according to the ratio of (the number of available seats F in the corresponding time period of the schedule + the number of motor vehicles on the route) / the total number of allocated vehicles.

[0014] (5) Final optimization principle: sort by distance target from the site as the main factor and preferred route as the auxiliary factor; sort by preferred route as the main factor and distance target from the site as the auxiliary factor (default solution); if the corresponding weight can be provided, sort by weight result; and confirm whether the route meets the requirements for driver allocation by telephone communication. After a route is selected as the preferred route, adjust the weight of the next selected route.

[0015] For site selection, a site space relaxation algorithm is adopted, which includes the following steps.

[0016] 1. First, complete the allocation of all paths in area A, divide all paths in area A, and calculate their lengths.

[0017] 2. If some paths are not covered by any field or are only partially covered, the paths are pre-processed and classified.

[0018] Based on the path attribute classification of radius R, the path set is defined as: V(s(i, j)1, s(i, j)1, s(i, j)1, ..., s(i, j) n )(Assume there are n paths). Site node set Q i , i = 1, 2, ..., m, use Dijkstra algorithm to find the shortest set of distances between all nodes: d(i, j), i = 1, 2, ... define the radius R of the field control range.

[0019] The path category processing algorithm is as follows.

[0020] Classify the path s(i, j), corresponding to each node Q i , respectively solve d(Q i , i), d(Q i , j), if there exists a Q i So that d(Q i , i), d(Q i , j) are both less than R, then the attribute value of s(i, j) is 2; if there is a Q i , so that d(Q i , i), d(Q i , j) is less than R, then the attribute value of s(i, j) is 1; if for all Q i , if neither of the above two conditions is met, it is 0. That is, according to the above attributes, they are divided into Class 0 roads, Class 1 roads, and Class 2 roads. From the classification, it can be seen that Class 0 roads and Class 1 roads do not meet the field coverage, so further calculation is required.

[0021] Order rate calculation: The order rate Pr on a node is calculated by adding the order rates Nr of all paths connected to it. The order rate is calculated as follows:

[0022]

[0023] Where C represents the feasible domain of j(i) when i(j) is constant and a path exists, and s(i, j) represents the length of s(i, j).

[0024] Define the optimization goal to complete the task in the shortest time, that is, when the speed is constant, the task distance completed is the shortest:

[0025] L k(i，j)=min|s(k,i)|+min|s(i,j)|+min|s(k,j)||

[0026] Then define the shortest distance between the site and the road as

[0027] L′ k(i，j) =min|s(k,i)|

[0028] Since the speed is constant, the time to complete the task in task k is x k (i, j)*L k The minimum value among (i, j) is determined. k (i, j) is whether the path s(i, j) is assigned to platform k, if yes, it is 1, otherwise it is 0. i and j can be set as the customer's starting point and destination respectively. So its minimum value is used as the objective function, that is,

[0029] min[x k (i, j)*L k (i, j)]

[0030] Variance of the order rate assigned to the site: Assuming that the vehicle configuration of each site is roughly the same, the workload of the site should be roughly balanced after the route is assigned, otherwise it will affect the daily operation of the site. Introduce variance to quantify

[0031]

[0032] Nr(k)=[x(k,1),x(k,2),...,x(k,j),...]*Nr T

[0033] Distribute uniformity and perform optimization calculations.

[0034] Wherein k=1, 2, ..., m, Nr(k) represents the order rate of the area under the jurisdiction of the k site.

[0035] Allocation scheme for paths with attributes 0 and 1: We set the optimization goal of class 0 and class 1 roads to the shortest time. This type of road usually has a long path and many uncertain factors, so we consider setting a penalty function while determining the shortest distance. Penalty function definition:

[0036]

[0037] k represents the field number, i, j represent the endpoint numbers of the path, and x represents Lk(, j)

[0038] The 0-1 plan is:

[0039] min[x ik(i，j) *W k(i，j) ]

[0040]

[0041]

[0042] The attribute is the allocation plan of 2 paths. The optimization goal of this type of path is to minimize the time and ensure that the order rate in the later period is relatively balanced.

[0043] 1. Set the shortest distance as the optimization goal:

[0044] min[x k (i, j)*L k (i, j)].

[0045] 2. Convert the variance of the order rate assigned to each site into a condition, that is, set a certain maximum value for the variance as a constraint of the feasible domain. Then determine the optimal solution by changing the threshold. The determination of the threshold determines whether the planning of the dual objectives (shortest time and relatively balanced order rate in the later period) is reasonable. Different thresholds can be changed and the annealing algorithm can be used to obtain the normalized results of the two objectives.

[0046] The present invention uses existing public transportation resources to take into account both conventional public transportation and flexible public transportation routes, and studies the problem of flexible public transportation resource reuse in the emerging domestic online carpooling customized public transportation mode. It also considers the constraints of vehicles and stations, uses scientific model algorithms, and considers time and space relaxation. It comprehensively analyzes the station shunting strategy, uses existing vehicle operation data and scheduling plans, searches for the best vehicle and vehicle model selection, and forms a scheduling method for vehicle reuse. That is, the path classification algorithm, the area space relaxation algorithm, and the strategy scheme for multiplexing vehicle resources that meets the scheduling and dispatching habits, and verifies the effectiveness of the algorithm and applies it in practice. The optimal vehicle is selected from the existing idle conventional operating routes and stations, and the allocation and scheduling are carried out to complete the order and gradually form a flexible crowdsourcing mechanism within the bus company. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flowchart executed after receiving an online bus booking order.

[0048] Figure 2 It is a flowchart for selecting the optimal vehicle for allocation and scheduling.

[0049] Figure 3 This is the display screen when the method of the present invention is applied to the system. DETAILED DESCRIPTION

[0050] The present invention studies the problem of flexible bus resource reuse in the emerging domestic online carpooling customized bus mode, taking into account the constraints of vehicles and stations, using scientific model algorithms, namely path classification algorithms, field space relaxation algorithms, and finding a reuse vehicle resource strategy that conforms to the scheduling habits, and verifies the effectiveness of the algorithm, and applies it in practice. The following is a detailed description of the scheduling method for realizing resource reuse allocation of flexible bus lines.

[0051] 1. Description of the flexible bus line resource reuse allocation and scheduling problem.

[0052] The characteristics of flexible bus routes, that is, online-booked carpooling customized buses, can be seen by comparing them with some of the following familiar transportation service modes.

[0053] 1) Compared with conventional buses, online-booked, carpooling customized buses have flexible routes and schedules.

[0054] 2) Compared with the regional express shuttle buses, the pick-up and drop-off points for online-booked shared-ride customized buses are not fixed.

[0055] 3) Compared with shared taxis, online-booked customized buses require recruiting passengers in advance rather than being based on point-to-point matching.

[0056] The boundaries of several organizational forms of online-hailing public transportation are defined as follows: the operating entities are bus companies and some online-hailing car companies; the route characteristics determine the free route selection of the bus or based on the regular route; the recruitment methods include online recruitment and telephone recruitment; the gathering points and drop-off points are based on existing fixed routes or collective routes, and are selected from nearby bus stops; the platform center dispatch is responsible for station selection, vehicle and model selection; customer service is responsible for weighing waiting time, seats, fares, etc.

[0057] Among them, the upgrade of the platform center dispatching method is indispensable under the condition of taking into account both conventional bus and flexible bus routes by utilizing existing bus resources. This technical solution considers the time and space relaxation, comprehensively analyzes the station shunting strategy, uses the existing vehicle operation data and scheduling plan, searches for the optimal vehicle and model selection, and forms a dispatching method for vehicle reuse.

[0058] After receiving the online bus booking order, the information is summarized as required start time, required arrival time, vehicle number, license plate number, vehicle type, number of passengers, starting bus stop, and ending bus stop. The specific flow chart is as follows Figure 1 shown.

[0059] Select the best vehicles from the existing idle regular operation routes and stations, allocate and dispatch them, complete the orders and gradually form a flexible crowdsourcing mechanism within the bus company. The specific flow chart is as follows: Figure 2 shown.

[0060] 2. Flexible bus route resource reuse allocation scheduling algorithm

[0061] 1) Basic Strategy Principles

[0062] According to the conventional scheduling algorithm, the basic strategy considers six factors:

[0063] a. Site selection: Take the online bus departure point as the center and A as the radius to find B sites; use the radius or path planning algorithm to select C sites in ascending order of distance.

[0064] b. Calculate the number of positions D based on the shift schedule: If there is a shift schedule for the day, calculate directly; if there is no shift schedule, calculate the maximum number of positions based on the historical shift schedule for the same working day.

[0065] c. When the start and end time of the ride-hailing vehicle is at peak hours, motor vehicles are mainly selected as the preferred target: the larger the value of (route allocation - number of locations D) / route allocation, the easier it is to ensure the route plan (later versions), and the lower the overlap between the start and end time of the ride-hailing vehicle and the peak time of the route, the E1 route is selected as the preferred route.

[0066] d. If the starting and ending time of the ride-hailing service is in the off-peak or off-peak period, according to the planned or historical shift schedule for multiple days, select the E2 routes based on (the number of slots with vacancies in the corresponding time period of the shift schedule F + the number of motor vehicles on the route) / the total number of allocated vehicles from large to small.

[0067] e. Final optimization principle: sort by distance target from the site as the main factor and preferred route as the auxiliary factor; sort by preferred route as the main factor and distance target from the site as the auxiliary factor (default solution); if the corresponding weight can be provided, sort by weight result; and confirm whether the route meets the requirements for driver allocation by telephone communication. After a route is selected, adjust the weight of the next selected route.

[0068] 2) Principle of field space relaxation algorithm

[0069] Regarding site selection, this technical solution proposes a site space relaxation algorithm, and the basic process is as follows.

[0070] The specific calculation process is obtained based on the intersection distribution of the bus company's operating area A and the bus yard distribution map. All intersection nodes and paths in area A are rationally optimized and assigned to M bus yards for jurisdiction. The technical solution meets the following two constraints.

[0071] a. The customer initiates an order demand, requiring that the sum of the distances from the site to the departure point and the distance from the destination to the site be minimized.

[0072] The amount of tasks assigned to each bM site is as balanced as possible to meet the normal functions of the site's traditional scheduling.

[0073] The problem is analyzed as follows:

[0074] (1) First, complete the allocation of all paths in area A, divide all paths in area A, and calculate their lengths.

[0075] (2) If some paths are not covered by any field or are only partially covered, the paths are pre-processed and classified.

[0076] Based on the path attribute classification of radius R, define the path set: V(s(i,j)1,s(i,j)1,s(i,j)1,...,s(i,j) n )(Assume there are n paths). Site node set Q i ,i=1,2,...,m, use Dijkstra algorithm to find the shortest pairwise distance set between all nodes: d(i,j),i=1,2,... define the radius R of the field control range.

[0077] The path category processing algorithm is as follows:

[0078] Assume that the path s(i,j) needs to be classified, corresponding to each node Q i , respectively solve d(Q i ,i),d(Q i ,j), if there exists a Q i So that d(Q i ,i),d(Q i ,j) are both less than R, then the attribute value of s(i,j) is 2; if there is a Q i , so that d(Q i ,i),d(Q i ,j) is less than R, then the attribute value of s(i,j) is 1; if for all Q i , if neither of the above two conditions is met, then it is 0. That is, according to the above attributes, they are divided into Class 0 roads, Class 1 roads, and Class 2 roads. From the classification, it can be seen that Class 0 roads and Class 1 roads do not meet the field coverage, so further calculation is required.

[0079] Order rate calculation, assuming that the order rate Pr on a node is calculated by adding the order rates Nr of all paths connected to it.

[0080]

[0081] Where C represents the feasible domain of j(i) when i(j) is constant and a path exists, and |s(i,j)| represents the length of s(i,j).

[0082] Define the optimization goal to complete the task in the shortest time, that is, when the speed is constant, the distance between the completed tasks and the

[0083] Lk(i，j) =min|s(k,i)|+min|s(i,j)|+min|s(k,j)||

[0084] From the shortest:

[0085] Then define the shortest distance between the site and the road as

[0086] Since the speed is constant, the time to complete the task in task k is x k (i,j)*L k (i,

[0087] L′ k(i，j) =min|s(k,i)|

[0088] j) is determined by the minimum value of x k (i,j) is whether the path s(i,j) is assigned to platform k, if yes, it is 1, otherwise it is 0. i and j can be set as the customer's starting point and destination respectively. So its minimum value is used as the objective function, that is,

[0089] min[x k (i,j)*L k (i, j)].

[0090] Variance of the order rate assigned to the site: Assuming that the vehicle configuration of each site is roughly the same, the workload of the site should be roughly balanced after the route is assigned, otherwise it will affect the daily operation of the site.

[0091]

[0092] Nr(k)=[x(k,1),x(k,2),...,x(k,j),...]*Nr T

[0093] Match uniformity and perform optimization calculations.

[0094] Wherein k=1, 2, ..., m, Nr(k) represents the order rate of the area under the jurisdiction of the k site.

[0095] Allocation scheme for paths with attributes 0 and 1: We set the optimization goal of class 0 and class 1 roads to the shortest time. This type of road usually has a long path and many uncertain factors, so we consider the shortest distance while determining the

[0096]

[0097] Set the penalty function. Penalty function definition:

[0098] k represents the field number, i, j represent the endpoint numbers of the path, and x represents Lk(i, j)

[0099] The 0-1 plan is:

[0100] min[x ik(i，j) *W k(i，j) ]

[0101]

[0102]

[0103] The attribute is the allocation plan of 2 paths. The optimization goal of this type of path is to minimize the time and ensure that the order rate in the later period is relatively balanced.

[0104] (1) Set the shortest distance as the optimization goal:

[0105] min[x k (i,j)*L k (i, j)].

[0106] (2) The variance of the order rate assigned to each site is converted into a condition, that is, a certain maximum value is set for the variance as a constraint condition of the feasible domain. Then, the optimal solution is determined by changing the threshold. The determination of the threshold determines whether the dual-objective planning is reasonable. Different thresholds can be changed and the annealing algorithm can be used to obtain the normalized results of the two objectives.

[0107] Since the threshold with the smallest intra-class variance of order rate is the threshold with the largest inter-class variance of field orders, there is a corresponding formula: The weighted sum of the variances of the two classes is defined as

[0108]

[0109] where the weight W(t) is the probability of two classes separated by the threshold t, σ 2 is the variance of these two classes (b and f). The traversal method updates the probability W and the class mean by traversing all possible thresholds (t = 1 to the maximum intensity), and obtains the weighted sum of the variance of the calculation result. The threshold required corresponds to the maximum weighted sum of the variance. The improved simulated annealing algorithm is used to generate a sequence of optimized solutions with the Metropolis-Hastings algorithm, and the corresponding probability transfer is obtained to determine whether the current solution is transferred to the new solution. The formula is as follows:

[0110]

[0111] In this formula Used to determine whether the new solution is accepted. i and j represent the current solution and the new solution with a threshold t ranging from 1 to the maximum intensity. According to the commonly used Metropolis criterion, if f(i) < f(j), the new solution j is accepted as the new current solution. If it does not meet the criteria, j is accepted as the new current solution with the probability exp shown in the formula.

[0112] The threshold t determines the transfer acceptance probability of random movement. The larger t is, the stronger the algorithm's ability to improve the squared difference price weight and upward movement. The simulated annealing algorithm can effectively improve the computing time efficiency compared to the traversal method.

[0113] 3. Algorithm Application

[0114] The above method is applied to the system through software, and the results are as follows Figure 3 shown.

Claims

1. A flexible bus route resource reuse allocation and scheduling method, characterized in that: Include the following: a. Site selection: With the online bus departure point as the center and A as the radius, find B sites; use the radius or path planning algorithm to select C sites in ascending order of distance; b. Calculate the number of parts D based on the shift schedule: If there is a shift schedule for the day, calculate directly; if there is no shift schedule, calculate the maximum number of parts based on the historical shift schedule for the same working day; c. The start and end time of the ride-hailing service is at peak hours, and motor vehicles are mainly selected as the preferred target: the larger the value of (route allocation - number of locations D) / route allocation, the easier it is to ensure the route plan, and the lower the overlap between the start and end time of the ride-hailing service and the peak time of the route, the preferred route E1 is selected; d. If the start and end time of the ride is in the off-peak or off-peak period, according to the plan or the historical shift schedule for multiple days, select E2 routes according to (the number of positions with vacancies in the corresponding time period of the shift schedule F + the number of motor vehicles on the route) / the total number of allocated vehicles from large to small; e. Final selection principle: sort by distance target from the site as the main factor and preferred route as the auxiliary factor; sort by preferred route as the main factor and distance target from the site as the auxiliary factor; if the corresponding weight can be provided, sort by weight result; and confirm whether the route meets the requirements for driver allocation through telephone communication; after a route is selected as the preferred route, adjust the weight of the next selected route; For site selection, the site space relaxation algorithm is adopted, which includes the following steps: 1) First, complete the allocation of all paths in area A, divide all paths in area A, and calculate their lengths; 2) If some paths are not covered by any field or are only partially covered, the paths are preprocessed and classified. When classifying the paths, the path attribute classification based on the radius R is used to define the path set: V(s(i, j)1, s(i, j)1, s(i, j)1, ..., s(i, j)n) (assuming there are n paths); the field node set Qi, i = 1, 2, ..., m, using the Dijkstra algorithm, find the shortest pairwise distance set between all nodes: d(i, j), i = 1, 2, ..., define the field control range radius R; Classify the path s(i, j), and solve d(Qi, i) and d(Qi, j) for each node Qi. If there is a Qi such that d(Qi, i) and d(Qi, j) are both less than R, then the attribute value of s(i, j) is 2; If there exists a Qi such that only one of d(Qi, i) and d(Qi, j) is less than R, then the attribute value of s(i, j) is 1; if for all Qi, the above two conditions are not met, then it is 0; that is, according to the above attributes, they are divided into Class 0 roads, Class 1 roads, and Class 2 roads respectively; The path processing algorithm when the attribute classification is Class 0 or Class 1 is as follows: The order rate is calculated as follows Where C represents the feasible domain of j(i) when i(j) is constant and a path exists, |s(i, j)| represents the length of s(i, j); the optimization goal is to complete the task in the shortest time, that is, when the speed is constant, the task distance is the shortest: L k(i，j) =min|s(k,i)|+min|s(i,j)|+min|s(k,j)|| Then define the shortest distance between the site and the road as L′ k(i，j) =min|s(k,i)| Since the speed is constant, the time to complete the task in task k is x k (i, j)*L k (i, j) is determined by the minimum value; x k (i, j) is whether the path s(i, j) is assigned to platform k, if yes, it is 1, otherwise, it is 0; i, j can be set as the customer's departure point and destination respectively; therefore, the minimum value is taken as the objective function, i.e., min[xk(i, j)*Lk(i, j)]; Variance of order rates assigned to sites: Nr(k)=[x(k,1),x(k,2),...,x(k,j).,..]*Nr T Variance is introduced to quantify the distribution uniformity and perform optimization calculations; where k = 1, 2, ..., m, Nr(k) represents the order rate of the area under the jurisdiction of the k site; Allocation scheme for paths with attributes 0 and 1: We set the optimization target of class 0 and class 1 paths to be the shortest time; This type of road usually has a long path and many uncertain factors, so when determining the shortest distance, consider setting a penalty function; penalty function definition: k represents the site number, i and j represent the endpoint numbers of the path, and x represents L k (i, j) The 0-1 plan is: min[x ik(i，j) *IN k(i，j) ]; The allocation scheme with the attribute of 2 paths has the following optimization goals: shortest time and relatively balanced order rate in the later period; 1) Set the shortest distance as the optimization goal: min[xk(i, j)*Lk(i, j)]; 2) Convert the order rate variance assigned to each site into a condition, that is, set a certain maximum value for the variance as a constraint condition of the feasible domain; Then, the optimal solution is determined by changing the threshold. The determination of the threshold determines whether the dual-objective planning is reasonable. Different thresholds can be changed and the annealing algorithm can be used to obtain the normalized results of the two objectives.

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