CN111222692B - Reliability discrete addressing method considering return under limited information situation - Google Patents

Reliability discrete addressing method considering return under limited information situation Download PDF

Info

Publication number
CN111222692B
CN111222692B CN201911393880.2A CN201911393880A CN111222692B CN 111222692 B CN111222692 B CN 111222692B CN 201911393880 A CN201911393880 A CN 201911393880A CN 111222692 B CN111222692 B CN 111222692B
Authority
CN
China
Prior art keywords
facility
customer
follows
facilities
model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201911393880.2A
Other languages
Chinese (zh)
Other versions
CN111222692A (en
Inventor
员丽芬
范宏强
朱璟怡
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Jiaotong University
Original Assignee
Beijing Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Jiaotong University filed Critical Beijing Jiaotong University
Priority to CN201911393880.2A priority Critical patent/CN111222692B/en
Publication of CN111222692A publication Critical patent/CN111222692A/en
Application granted granted Critical
Publication of CN111222692B publication Critical patent/CN111222692B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G06Q10/043—Optimisation of two dimensional placement, e.g. cutting of clothes or wood
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/067—Enterprise or organisation modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/08—Logistics, e.g. warehousing, loading or distribution; Inventory or stock management
    • G06Q10/083—Shipping
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q30/00—Commerce
    • G06Q30/02—Marketing; Price estimation or determination; Fundraising
    • G06Q30/0201—Market modelling; Market analysis; Collecting market data
    • G06Q30/0206—Price or cost determination based on market factors

Abstract

The invention relates to a reliability discrete addressing method considering return under a limited information scene, which comprises the following steps: the method comprises the following technical key points of site selection model hypothesis, variable definition, site selection model construction and site selection model solution: the method comprises the following steps of describing access strategies of clients in a transport network under the condition of information failure, constructing a regional transport network reliability address selection discrete model under the condition of information failure, solving the regional transport network reliability address selection discrete model under the condition of information failure, constructing a solving method based on a Lagrange relaxation algorithm, and verifying the high efficiency and the applicability of the model and the algorithm by using example data. It is observed that the marginal gain of the backup facility will decrease when more backup facilities are set up. Round trips require consideration of reliable facility location issues, particularly incomplete information issues. It is also noted that the correct information routing scheme is important to obtain the correct facility location. The sensitivity analysis result of the key parameters shows that the model has stability.

Description

Reliability discrete addressing method considering return under limited information situation
Technical Field
The invention relates to an optimized layout of infrastructure and node site selection in traffic and transportation engineering and logistics engineering, in particular to a reliable discrete site selection method considering return under a limited information scene.
Background
Whether in a commercial transportation system (such as a logistics network) or a public transportation system, how to select the optimal facility position is a primary problem of the whole planning system and a central decision problem. The essence of the addressing problem is to build a certain number of facilities in a given area to meet the service requirements of all customers in the area, in the process, the one-time construction cost of the facilities and the long-term transportation cost of the customers are generated: the optimal site selection model is to construct service facilities in the most economical way to obtain relatively optimal system performance. As is well known, there is a back-off effect between construction costs and long-term transportation costs in the siting model, in brief, if we intend to reduce construction costs, the number of facilities built is necessarily reduced, the average distance from the customer to the facilities is increased, eventually leading to an increase in transportation costs; conversely, if we want to reduce the transportation costs, meaning that customers are more likely to reach the service facilities, more facilities must be built, resulting in higher construction costs. This relationship is rather similar to a balance, if one decreases it is equivalent to a certain increase of the other, and the aim of the optimization is to find a balance point such that the sum of the two is minimal.
It has been found that in both natural and man-made disasters, facilities may be damaged, and it is appreciated that factors to be considered in site selection should take into account the reliability of the system in addition to its efficient operation. The classical approach to the problem of reliable site selection is to use the concept of backup facilities, namely the fixed-cost reliable site selection model proposed by Snyder and Daskin in 2005.
The first prior art is as follows: the existing reliability addressing model has a basic assumption, also called a complete information assumption, that is, each customer has a main service facility and several backup service facilities, and when the main service facility fails, the customer immediately knows the real-time status information of the facilities and gains service by accessing other available backup service facilities. The customer will get real-time status information of the facility so that he can reach the location of an available facility directly from his location according to the assigned priority level.
The second prior art is: however, in reality, this assumption is not always true due to technical barriers, information propagation failures and the like, so the second prior art proposes an incomplete information assumption which is more realistic, that is, a customer cannot know information about the real-time operation state of a facility, and visits nearby facilities one by one according to a predetermined sequence until finding a facility in a normal operation state and getting service, or visits all designated facilities and finds all damages, and then abandons service and receives penalty cost.
However, the second prior art has the following disadvantages:
(1) the prior art discusses passenger transport phenomena in traffic, obtains a site selection optimization method of a comprehensive passenger transport hub, does not discuss the freight transport phenomena in traffic, and ignores the return cost characteristic of freight transport. Because of the particularities of the transportation activities, when the activity ends-after the cargo is handed over, the vehicle generally returns to the original origin, i.e., the transportation cost of the return trip is present.
(2) The model constructed in the second prior art is a discrete model, and the time for obtaining the accurate solution is long, so that the model can only be applied to small-scale or medium-scale scenes, and the large-scale scenes have poor large data processing capability and cannot obtain the accurate solution within a certain time.
The prior art is three: reliable continuous address selection method CRLP-IITT considering return under limited information scene
The third prior art has the following defects: the continuous model in the addressing problem generally cannot be solved directly, and only a continuous approximation method is used for converting a formula to obtain a formula capable of obtaining an approximate optimal solution, and a discrete addressing scheme needs to be obtained by further solving a model result by a discretization algorithm. The operation is complex and the utilization is inconvenient.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a reliability discrete addressing method considering return under the limited information scene, and a transport node reliability discrete addressing model, namely a DRLP-IIRT model, in a round-trip double-path mode, which increases the transport return cost under the incomplete information scene is constructed.
In order to achieve the above purposes, the technical scheme adopted by the invention is as follows:
a reliability discrete addressing method considering return under the limited information scene comprises the following steps:
step 1, site selection model assumption
(1) After the transportation node is built and put into use, the transportation node is not permanently available, and certain damage probability exists;
(2) the damage probability among the transport nodes is independent;
(3) the client only knows the initial information of the transport node and does not know the real-time information of the transport node;
(4) the client will visit the main transport node and the standby transport node in sequence according to the distribution sequence, and only visit the transport node distributed to the client, no matter whether obtaining the service, no longer visit other transport nodes;
(5) if the client does not obtain the service finally, the client can only give up and accept certain penalty cost;
(6) whether the client obtains the service or not, the client finally returns to the original starting place, namely, the return cost exists;
step 2, defining variables
With dispersed customers in the addressing area, the locations of which are grouped together
Figure GDA0003570623720000031
Representation, collection
Figure GDA0003570623720000032
The candidate position set of the facility construction is represented, and the facility construction is arranged at the candidate position
Figure GDA0003570623720000033
(facility j for short) will generate a one-off fixed construction cost fjFacility j has an independent probability of damage qjThe customer at position i (abbreviated as customer i) generates a demand λiOr service appeal amount λiEvery customer can be coveredPre-allocating facilities with a fixed order to obtain service, wherein the facilities comprise a main facility and a standby facility, R represents the level of the facilities visited by a customer in the visiting order, R is 0 represents that the facilities visited by the customer are the main facilities, R represents the maximum number of the standby facilities pre-allocated, and the penalty cost for giving up seeking transportation service to the customer i is that
Figure GDA0003570623720000041
cij、cij'Respectively representing the transportation costs of a customer visiting a facility j, j' from an initial location i, cijj'rRepresenting the transportation cost of a customer i visiting a facility j' at a level r from a facility j, and introducing the concept of a virtual facility (emergency facility) with a damage probability of 0 in order to construct a compact model, using j0Represent and
Figure GDA0003570623720000042
when customer i gives up seeking service at any level r, it is assumed that customer i has access to a virtual facility j0The transportation cost is
Figure GDA0003570623720000043
Customer slave virtual facility j0The transportation cost in the return process is
Figure GDA0003570623720000044
Step 3, site selection model construction
Figure GDA0003570623720000045
The representation is a set of all facility candidate locations including the virtual facility,
Figure GDA0003570623720000046
representing the set of all candidate locations accessible before candidate location j,
Figure GDA0003570623720000047
indicating all candidate locations that can be visited after visiting candidate location jSet, the expression is as follows:
Figure GDA0003570623720000048
introducing 0-1 aid decision variables: one is a position decision variable
Figure GDA0003570623720000049
The other is customer facility allocation decision variable
Figure GDA00035706237200000410
And
Figure GDA00035706237200000411
the expression is as follows:
Figure GDA00035706237200000412
Figure GDA00035706237200000413
Figure GDA0003570623720000051
definition set
Figure GDA0003570623720000052
Wherein p isijj'rRepresenting the probability of customer i visiting facility j' at level r from facility j, the expression is as follows:
Figure GDA0003570623720000053
the total cost expression of the fixed construction of the facility is as follows:
Figure GDA0003570623720000054
the probability that customer i gets service and returns directly after visiting primary facility j is 1-qjThe operation cost is as follows:
Figure GDA0003570623720000055
the possibility that customer i returns to the starting position after visiting facility j at level r is that all facilities below level r-1 are interrupted and only facility j is operating, the corresponding operating cost calculation formula is as follows:
Figure GDA0003570623720000056
the total operating cost calculation formula of the customer is as follows:
Figure GDA0003570623720000057
constructing a discrete addressing model objective function, wherein the expression is as follows:
Figure GDA0003570623720000058
the constraints are as follows:
Figure GDA0003570623720000061
Figure GDA0003570623720000062
Figure GDA0003570623720000063
Figure GDA0003570623720000064
Figure GDA0003570623720000065
Figure GDA0003570623720000066
Figure GDA0003570623720000067
Figure GDA0003570623720000068
Figure GDA0003570623720000069
Figure GDA00035706237200000610
equation (10) represents the minimum total cost by determining the optimal facility addressing scheme and the optimal facility access order of the customer, equation (11) represents that the customer must access the facilities at level 0, equation (12) represents that the customer can only access the facilities already constructed and each facility can only be accessed once, equations (13) and (14) are used to ensure that the customer can only access the facilities in turn in a pre-assigned order, equation (15) ensures that the customer eventually accesses the virtual facilities in order to correctly calculate the penalty cost, equations (16) and (17) represent the iterative relationship between the facility access probabilities of adjacent levels, and equations (18) - (20) represent that the decision variables are variables 0-1;
step 4, solving the site selection model
The lagrangian relaxation algorithm customized for solving the discrete addressing model is as follows:
first using non-negative Lagrange multipliers
Figure GDA0003570623720000071
The relaxation constraint is equation (12) and is added to equation (10) to obtain the corresponding relaxation problem, as follows:
Figure GDA0003570623720000072
the constraint conditions are formula (11), formula (13) to formula (20).
On the basis of the scheme, the relaxation problem in the step 4 is decomposed into two relatively independent sub-problems,
the calculation formula for subproblem 1 is as follows:
Figure GDA0003570623720000073
the constraint condition is formula (20);
the calculation formula of the subproblem 2 is as follows:
Figure GDA0003570623720000074
the constraint conditions are formula (11), formula (13) to formula (19);
if the current coefficient is set
Figure GDA0003570623720000075
When y isj1 is ═ 1; otherwise yjThe result of solving subproblem 1 is obtained, and subproblem 2 is solved as a shortest path problem by Dijkstra's algorithm.
On the basis of the scheme, if the optimal solution of the relaxation problem is the feasible solution of the discrete addressing model, if the feasible solution is brought into the initial model to obtain the completely same target value, the feasible solution is the optimal solution of the discrete addressing model, otherwise, the solution of the relaxation problem is used as the lower boundary of the discrete addressing model, and the upper boundary of the discrete addressing model is solved.
On the basis of the scheme, according to the solving result of the sub problem 1 in the relaxation problem, the constructed node set is defined as
Figure GDA0003570623720000081
Based on sets
Figure GDA0003570623720000082
Solving for
Figure GDA0003570623720000083
A feasible solution for the other variables is obtained,
Figure GDA0003570623720000084
the calculation formula of (a) is as follows:
Figure GDA0003570623720000085
the constraint conditions are formulas (11) - (19);
solving the formula (24) by using a heuristic algorithm to obtain a feasible solution { X, X ', Y }, adding the feasible solution { X, X', Y }, and obtaining an upper bound of the discrete addressing model, wherein if the upper bound and the lower bound are the same, the feasible solution is the optimal solution; otherwise, iterating the multiplier mu through a sub-gradient algorithm, re-solving the upper and lower boundaries of the discrete model, and repeating the Lagrange relaxation algorithm process until the algorithm termination condition is met, so as to finally obtain a better solution and an optimal target value;
the sub-gradient algorithm is used for iterating the multiplier mu, the multiplier adopted in the k iteration step
Figure GDA0003570623720000086
Indicating that the multiplier is initialized first
Figure GDA0003570623720000087
In each iteration step k, the multiplier mukThe iteration is muk+1Entering the next iteration step with the iteration formula as：
Figure GDA0003570623720000088
The iteration step is tkNamely:
Figure GDA0003570623720000089
in the above formula, UBkIs the best upper bound at present; LBkIs the lower bound obtained in the k-th iteration step, in each iteration step k, the parameter ukIs fixed, initially set to (0, 2)]If LB in successive K-6 stepskAre not optimized, then parameter ukWill be updated to uk:＝ukθ, where θ is a shrinkage factor greater than 1;
the termination condition of the Lagrange relaxation algorithm is to satisfy any one of the following conditions:
condition 1: optimizing the difference Gk:＝(UBk-LBk)/UBkNot more than epsilon, and the tolerance of epsilon is 0.005;
condition 2: k is less than kmax，kmax＝106Is the maximum iteration number;
condition 3: u. ofk≤10-3；
Condition 4: the solution time exceeds the maximum time limit T1800.
Drawings
The invention has the following drawings:
fig. 1 is a schematic diagram illustrating the influence of R on the total cost of the system when ρ is 0.05.
Fig. 2 is a schematic diagram illustrating the influence of R on the total cost of the system when ρ is 0.2.
FIG. 3 optimizes the facility layout according to transportation cost and information scheme. FIG. 3(a) is a fragmentary message that considers round trips; FIG. 3(b) is a fragmentary message considering only outbound shipments; FIG. 3(c) considers full information of round trips; fig. 3(d) is full information considering only outbound shipping.
Detailed Description
The present invention is described in further detail below with reference to figures 1-3.
Step 1, site selection model assumption
(1) After the transportation node is built and put into use, the transportation node is not permanently available and has a certain damage probability;
(2) the damage probability among the transport nodes is independent;
(3) the client only knows the initial information of the transport node and does not know the real-time information of the transport node;
(4) the client will visit the main transport node and the standby transport node in sequence according to the distribution sequence, and only visit the transport node distributed to the client, no matter whether obtaining the service, no longer visit other transport nodes;
(5) if the client does not obtain the service finally, the client can only give up and accept certain penalty cost;
(6) whether the client obtains the service or not, the client finally returns to the original starting place, namely, the return cost exists;
step 2, defining variables
With dispersed customers in the addressing area, the locations of which are grouped together
Figure GDA0003570623720000101
Representation, collection
Figure GDA0003570623720000102
The candidate position set of the facility construction is represented, and the facility construction is arranged at the candidate position
Figure GDA0003570623720000103
(facility j for short) will generate a one-off fixed construction cost fjFacility j has an independent probability of damage qjThe customer at position i (abbreviated as customer i) generates a demand λiOr service appeal amount λiEach customer is pre-assigned a fixed order of facilities to obtain service, including primary and backup facilities, and r represents what the customer visitsThe facilities are ranked in the order of visit, R-0 indicates that the facility visited by the customer is the primary facility, R indicates the maximum number of pre-assigned spare facilities, and the penalty cost for customer i to forego seeking transportation service is
Figure GDA0003570623720000104
cij、cij'Respectively representing the transportation costs of a customer visiting a facility j, j' from an initial location i, cijj'rRepresenting the transportation cost of a customer i accessing a facility j' located at a level r from a facility j, in order to construct a compact model, the concept of introducing a virtual facility (emergency facility) with a damage probability of 0 is introduced, and j is adopted0Is shown and
Figure GDA0003570623720000105
when customer i gives up seeking service at any level r, it is assumed that customer i has access to a virtual facility j0The transportation cost is
Figure GDA0003570623720000106
Customer slave virtual facility j0The transportation cost in the return process is
Figure GDA0003570623720000107
Step 3, site selection model construction
Figure GDA0003570623720000108
The representation is a set of all facility candidate locations including the virtual facility,
Figure GDA0003570623720000109
representing the set of all candidate locations that can be accessed before the access candidate location j,
Figure GDA0003570623720000111
representing the set of all candidate locations that can be visited after visiting candidate location j, the expression is as follows:
Figure GDA0003570623720000112
introducing 0-1 aid decision variables: one is a position decision variable
Figure GDA0003570623720000113
Another is customer facility allocation decision variable
Figure GDA0003570623720000114
And
Figure GDA0003570623720000115
the expression is as follows:
Figure GDA0003570623720000116
Figure GDA0003570623720000117
Figure GDA0003570623720000118
definition set
Figure GDA0003570623720000119
Wherein p isijj'rRepresenting the probability of customer i visiting facility j' at level r from facility j, the expression is as follows:
Figure GDA00035706237200001110
the total cost expression of the fixed construction of the facility is as follows:
Figure GDA00035706237200001111
customer i obtains service after visiting primary facility jAnd directly returned with a probability of 1-qjThe operation cost is as follows:
Figure GDA00035706237200001112
the possibility that customer i returns to the starting position after visiting facility j at level r is that all facilities below level r-1 are interrupted and only facility j is operating, the corresponding operating cost calculation formula is as follows:
Figure GDA0003570623720000121
the total operating cost calculation formula of the customer is as follows:
Figure GDA0003570623720000122
constructing a discrete addressing model objective function, wherein the expression is as follows:
Figure GDA0003570623720000123
the constraints are as follows:
Figure GDA0003570623720000124
Figure GDA0003570623720000125
Figure GDA0003570623720000126
Figure GDA0003570623720000127
Figure GDA0003570623720000128
Figure GDA0003570623720000129
Figure GDA00035706237200001210
Figure GDA00035706237200001211
Figure GDA0003570623720000131
Figure GDA0003570623720000132
equation (10) represents the minimum total cost by determining the optimal facility addressing scheme and the optimal facility access order of the customer, equation (11) represents that the customer must access the facilities at level 0, equation (12) represents that the customer can only access the facilities already constructed and each facility can only be accessed once, equations (13) and (14) are used to ensure that the customer can only access the facilities in turn in a pre-assigned order, equation (15) ensures that the customer eventually accesses the virtual facilities in order to correctly calculate the penalty cost, equations (16) and (17) represent the iterative relationship between the facility access probabilities of adjacent levels, and equations (18) - (20) represent that the decision variables are variables 0-1;
step 4, solving the site selection model
The Lagrange relaxation algorithm customized for solving the discrete addressing model is as follows:
first using non-negative Lagrange multipliers
Figure GDA0003570623720000133
The relaxation constraint equation (12) is added to equation (10) to obtain the corresponding relaxation problem, as follows:
Figure GDA0003570623720000134
the constraint conditions are formula (11), formula (13) to formula (20).
On the basis of the scheme, the relaxation problem in the step 4 is decomposed into two relatively independent sub-problems,
the calculation formula for subproblem 1 is as follows:
Figure GDA0003570623720000141
the constraint condition is formula (20);
the calculation formula of the subproblem 2 is as follows:
Figure GDA0003570623720000142
the constraint conditions are formula (11), formula (13) to formula (19);
if the current coefficient is set
Figure GDA0003570623720000143
When y isj1 is ═ 1; otherwise yjThe result of solving subproblem 1 is obtained, and subproblem 2 is solved as a shortest path problem by Dijkstra's algorithm.
On the basis of the scheme, if the optimal solution of the relaxation problem is the feasible solution of the discrete addressing model, if the feasible solution is brought into the initial model to obtain the completely same target value, the feasible solution is the optimal solution of the discrete addressing model, otherwise, the solution of the relaxation problem is used as the lower boundary of the discrete addressing model, and the upper boundary of the discrete addressing model is solved.
Based on the above scheme, according to the relaxationThe solution result of the sub-problem 1 in the problem is defined as the set of nodes which are already built
Figure GDA0003570623720000144
Based on sets
Figure GDA0003570623720000145
Solving for
Figure GDA0003570623720000146
And obtaining feasible solutions of other variables, wherein the calculation formula is as follows:
Figure GDA0003570623720000147
the constraints are equations (11) to (19).
The formula (24) is solved using a heuristic algorithm to obtain a feasible solution { X, X', Y }, and added to the formula (10) to obtain an upper bound of the discrete addressing model. If the upper and lower boundaries are the same, the feasible solution is the optimal solution; otherwise, iteration is carried out on the multiplier mu through a sub-gradient algorithm, and the upper and lower bounds of the discrete model are solved again. The Lagrange relaxation algorithm process is repeated until the algorithm termination condition is met, and a better solution and an optimal target value are finally obtained.
The sub-gradient algorithm is used for iterating the multiplier mu, the multiplier adopted in the k iteration step
Figure GDA0003570623720000151
And (4) showing. First, initialize the multiplier
Figure GDA0003570623720000152
In each iteration step k, the multiplier mukThe iteration is muk+1And entering the next iteration step, wherein the iteration formula is as follows:
Figure GDA0003570623720000153
the iteration step is tkNamely:
Figure GDA0003570623720000154
in the above formula, UBkIs the currently best upper bound; LBkIs the lower bound obtained in the k-th iteration step, in each iteration step k, the parameter ukIs fixed, initially set to (0, 2)]If LB in successive K ═ 6 stepskAre not optimized, then parameter ukWill be updated to uk:＝ukθ, where θ is a shrinkage factor greater than 1;
the termination condition of the Lagrange relaxation algorithm is to satisfy any one of the following conditions:
condition 1: optimizing the difference Gk:＝(UBk-LBk)/UBkNot more than epsilon, and the tolerance of epsilon is 0.005;
condition 2: k is less than kmax，kmax＝106Is the maximum iteration number;
condition 3: u. ofk≤10-3；
Condition 4: the solution time exceeds the maximum time limit T1800.
The beneficial effects of the method are discussed by taking the large-scale city of the United states as a backup site selection point.
1. Data sources
Three sets of data are included in the case: the first set of data is 49-point data (hereinafter referred to as 49-point data), which includes 48 states in the united states, the prefecture and washington, d.c., data derived from 1990 population and housing census data in the united states; the second set of data is 88-point data (hereinafter 88-point), which contains the 50 cities with the most dense population in the united states and 48 state prefectures (with duplicates removed), and is derived from the 1990 population and housing census data in the united states; the third set of data is 150-point-to-point data (hereinafter referred to as 150-point-to-point data) containing the largest 150 cities in the united states, which is derived from the us 2000 population and housing census data.
2. Data processing
(1) Raw data setup
To eliminate the magnitude of the difference in population size across cities, the customer needs are correlated with the local population number
Figure GDA0003570623720000161
Treated separately, 49 points of urban population divided by 10588 and 150 points by 104. Median house value per city represents a fixed construction cost fj. To reflect the detour distance in a road network, according to the research of Qureshi et al, the distance between two locations is calculated using a great circle distance coefficient multiplied by 1.2. Probability of facility outage qjIs arranged as
Figure GDA0003570623720000162
The coefficient ρ determines the magnitude of the outage probability. The unit penalty cost is the same for all customers
Figure GDA0003570623720000163
(2) Parameter setting
Default settings for parameters in the DRLP-IIRT model are as follows: ρ -0.05, α -1 and R-3. The basic parameters in the lagrangian relaxation algorithm set the following parameters: u. ofk＝2，θ＝1+0.1ρ，K＝6，ξ＝0.5％，kmax＝106，umin＝10-3And T1800 seconds.
3. Model validation
The performance of the LR algorithm was tested by comparison with Gurobi mathematical optimization software. Gurobi's gap and time limits are set to 0.5% and 1800 seconds, respectively, corresponding to the settings in the LR algorithm. The other options of Gurobi are set to their default values. The results are shown in Table 1.
This table shows that all the examples can be resolved by LR within time limits and the gap is less than 5%, which is acceptable in most engineering practices. However, Gurobi only solved the 49-point case with longer solution time, indicating that the algorithm proposed by the present invention performs well. It can also be observed from table 1 that the optimal solution increases with increasing p, which means that a higher outage probability results in a higher total cost of operation for counteracting the higher uncertainty. The number of facilities also increases with increasing ρ to ensure that customers can obtain service. As the scale of the example increases, the solution time grows in a super-linear manner, and the optimum gap is greatly widened.
TABLE 1 comparison of the Properties of the different examples
Figure GDA0003570623720000171
Figure GDA0003570623720000181
In a reliable location design environment, it is important to provide backup services to customers to reduce penalty costs (and the total system cost). Thus, the present invention investigated the benefits of the DRLP-IIRT backup facility, as shown in Table 2 and FIGS. 1 and 2. In this table, R ═ 0 means that only one master facility is provided to each customer, without any backup facilities. When R ═ 1, one additional backup facility is provided to each customer, the total system cost is reduced by 34% (54%) for 49 point-to-point instances with ρ ═ 0.05(ρ ═ 0.2); for the 88-node example with ρ 0.05(ρ 0.2), the total system cost is reduced by 36% (56%); for the 150 node example with ρ ═ 0.05(ρ ═ 0.2), the overall system cost is reduced by 32% (35%). These cost reductions can be interpreted as marginal benefits of an additional backup facility. As backup facilities increase, the marginal benefits of backup facilities still exist, but start to flatten out. When there is sufficient backup facility, the total cost is reduced to 64% (36%) for 49 node instances; for 88 node instances, the total cost is reduced to 62% (35%); the total cost is reduced to 67% (55%) for 150 node instances. As p increases, the marginal gain of the backup facility also increases, indicating that consideration of the backup facility is important for unreliable scenarios. We observed that when R ═ 3, the maximum cost was cut down while larger R did not significantly increase the marginal gain. This trend is clearly shown in fig. 1 and 2.
TABLE 2 backup facility revenue
Figure GDA0003570623720000182
Figure GDA0003570623720000191
Figure GDA0003570623720000201
Optimal placement under different parameter settings is discussed. Fig. 3 compares the optimal facility location layout for 49 node instances with the following four cases: FIG. 3(a) is a fragmentary message that considers round trips; FIG. 3(b) is a fragmentary message considering only outbound shipments; FIG. 3(c) considers full information of round trips; fig. 3(d) is full information considering only outbound transports. Only the connections between the customer and its main facilities are shown in fig. 3.
Comparing fig. 3(a) and 3(b), when the customer considers the round trip transportation to shorten the trip distance and reduce the transportation cost, more facilities are built. Although the round trip is the same under full information, omitting the round trip will reduce the proportion of the transportation cost to the total cost, resulting in an undesirable facility layout, as shown in fig. 3(c) and 3(d) versus fig. 3(a) and 3(c), with some facility layouts under incomplete information more aggregated than shown in the circle under full information. The same result is also found when fig. 3(b) and fig. 3(d) are compared. This is because the customer must individually access pre-assigned facilities based on incomplete information, and more aggregated facility layouts facilitate the customer's service at lower shipping costs. Comparing fig. 3(a) and 3(c), in the case of incomplete information, some facility layouts are more aggregated than the layouts shown in circles under complete information. The same result is also found when fig. 3(b) and fig. 3(d) are compared. This is because customers with imperfect information must individually access pre-assigned facilities, while more aggregated facility layouts facilitate customers to obtain service at lower shipping costs. Such aggregated facility layouts are common in areas with dense customer demand. Given that customer demand is spread across a region, such as the western united states, the plant layout may not converge. Comparing fig. 3(b) and fig. 3(d), it is noted that the number of facilities in fig. 3(b) is greater than the number of facility points in fig. 3 (d). This is because the expected travel distance of the customer under the incomplete information is longer than the expected travel distance of the customer under the complete information. To ensure that customers can be served at reasonable distances and to avoid penalty costs as much as possible, more facilities can be built to shorten the travel distance in the case of imperfect information.
The overall cost of the system for the round trip and outbound trip only is compared just to emphasize the importance of considering the return trip. Optimal system cost for outbound trips
Figure GDA0003570623720000211
And (4) showing. When only the optimal facility layout with outbound trips is implemented, C is usedRTTo represent the actual total system cost and inbound trip.
Figure GDA0003570623720000212
Represents the difference in the total cost of the round-trip and outbound-only systems, and εRT＝(CRT-C*)/C*Representing the actual system cost bias after applying the "wrong" facility location design. Table 3 shows the total system cost for several examples of problems for 49 node sets for round-trip and outbound-only trips.
The total optimal cost of a system considering outbound trips alone is lower than the round-trip cost in all cases. EpsilonOTA value of about 30% represents the return trip cost as one third of the total system cost. However, for systems that do make round trips (e.g., in an electric car community charging system, the need to return home after finding a charging spot or giving up a search) omitting the round trip may result in a non-ideal layout of the facility. Table 3 shows that the actual total system cost (neglecting trip cost) is higher than the optimal system cost C at the suboptimal facility location design*，εRTReflecting the percentage of this increase, the value is greater than 6%. The results indicate that if the customer has a return trip after the outbound trip, the facility location design should take into account both of these limits. Otherwise, the overall system cost will increase with sub-optimal facility location design, due to neglect of return trip cost.
TABLE 3 Total cost of System for round trip and outbound only trips
Figure GDA0003570623720000221
The technical key points of the invention are as follows:
(1) access policy description of customers in a transport network in information failure scenarios
Based on the assumption of information failure, the invention provides a brand-new client access strategy according to the characteristic that the transportation activities generally have return trip cost.
In any case, whether the transport node is invalid or not, the client cannot know the real-time operation state of the nodes, and only can access a group of transport nodes in a specified sequence one by one, obtain service after finding an available node and return to the original place of departure, or return to the place of departure after finding no result and accept penalty fees. The transit node location and access order are determined based on the expected failure probability and the total cost of the system.
In this access policy similar to the trial-and-error process, in any case, each client will only access the designated transportation nodes in turn according to the access order determined in advance, and will stay at the first node where the transportation service is available, or after no result of the access, abandon the transportation service and accept the penalty fee.
(2) Construction of regional transport network reliability address selection discrete model under information failure scene
Based on the access strategy description of the service sought by the client in the regional transportation network under the information failure situation, the reliability continuous discrete model of the transportation node is constructed.
(3) Solution of regional transport network reliability address selection discrete model under information failure situation
A solving method based on a Lagrange relaxation algorithm is constructed, and the high efficiency and the applicability of the model and the algorithm are verified by using example data. It is observed that the marginal gain of the backup facility will decrease when more backup facilities are set up. Round trips require consideration of reliable facility location issues, particularly incomplete information issues. It is also noted that the correct information routing scheme is important to obtain the correct facility location. The sensitivity analysis result of the key parameters shows that the model has stability.
Abbreviations, English and Key term definitions
1. DRLP-IIRT model: english is Discrete reusable allocation protocol with objective information and round-trip, that is, the reliability Discrete addressing model considering the round trip under the limited information situation constructed by the invention.
Those not described in detail in this specification are within the skill of the art.

Claims (4)

1. A reliability discrete addressing method considering return under the limited information scene is characterized by comprising the following steps:
step 1, site selection model
(1) After the transportation node is built and put into use, the transportation node is not permanently available, and certain damage probability exists;
(2) the damage probability among the transport nodes is independent;
(3) the client only knows the initial information of the transport node and does not know the real-time information of the transport node;
(4) the client will visit the main transport node and the standby transport node in sequence according to the distribution sequence, and only visit the transport node distributed to the client, no matter whether obtaining the service, no longer visit other transport nodes;
(5) if the client does not obtain the service finally, the client can only give up and accept certain penalty cost;
(6) whether the client obtains the service or not, the client finally returns to the original place of departure, and the return cost exists;
step 2, defining variables
With dispersed customers in the addressing area, the locations of which are grouped together
Figure FDA0003570623710000011
Representation, collection
Figure FDA0003570623710000012
A set of candidate locations representing the construction of a facility, the construction of a facility j at candidate location j,
Figure FDA0003570623710000013
will generate a disposable fixed construction cost fjFacility j has an independent probability of damage qjCustomer i at location i will generate demand λiEach customer is pre-assigned a fixed order of facilities for service, including primary and backup facilities, R indicates the level of facilities visited by the customer in the visit order, R-0 indicates that the facilities visited by the customer are primary facilities, R indicates the maximum number of pre-assigned backup facilities, and the penalty cost for customer i to forego seeking transportation service is as follows
Figure FDA0003570623710000021
cij、cij'Respectively representing the transportation costs of customer i visiting facilities j, jijj'rRepresenting the transportation cost of a customer i visiting a facility j' at a level r from a facility j, and introducing a virtual facility concept with a damage probability of 0 for constructing a compact model, using j0Is shown, and
Figure FDA00035706237100000212
when customer i gives up seeking service at any level r, it accesses a virtual facility j0The transportation cost is
Figure FDA0003570623710000022
Customer slave virtual facility j0During the return strokeThe transportation cost is
Figure FDA0003570623710000023
Step 3, site selection model construction
Figure FDA0003570623710000024
The representation is a set of all facility candidate locations including virtual facilities,
Figure FDA0003570623710000025
representing the set of all candidate locations that can be accessed before the access candidate location j,
Figure FDA0003570623710000026
representing the set of all candidate locations that can be visited after visiting candidate location j, the expression is as follows:
Figure FDA0003570623710000027
introducing 0-1 aid decision variables: one is a position decision variable
Figure FDA0003570623710000028
The other is a customer facility allocation decision variable, which specifically includes:
customer facility allocation decision variables when customer i visits facility j at level 0
Figure FDA0003570623710000029
And
customer facility allocation decision variables when customer i visits facility j at level r from facility j at level r-1
Figure FDA00035706237100000210
The expression is as follows:
Figure FDA00035706237100000211
Figure FDA0003570623710000031
Figure FDA0003570623710000032
definition set
Figure FDA0003570623710000033
Wherein p isijj'rRepresenting the probability of customer i visiting facility j' at level r from facility j at level r-1, the expression is as follows:
Figure FDA0003570623710000034
the total cost expression of the fixed construction of the facility is as follows:
Figure FDA0003570623710000035
the probability that customer i gets service and returns directly after visiting primary facility j is 1-qjThe operation cost is as follows:
Figure FDA0003570623710000036
the possibility that customer i returns to the home position after visiting a facility j at level r is that all facilities below level r-1 are interrupted and only facility j is operating, and the corresponding operating cost calculation formula is as follows:
Figure FDA0003570623710000037
the total operating cost calculation formula of the customer is as follows:
Figure FDA0003570623710000038
constructing a discrete addressing model objective function, wherein the expression is as follows:
Figure FDA0003570623710000039
the constraints are as follows:
Figure FDA0003570623710000041
Figure FDA0003570623710000042
Figure FDA0003570623710000043
Figure FDA0003570623710000044
Figure FDA0003570623710000045
Figure FDA0003570623710000046
Figure FDA0003570623710000047
Figure FDA0003570623710000048
Figure FDA0003570623710000049
Figure FDA00035706237100000410
equation (10) represents the minimum total cost by determining the optimal facility addressing scheme and the optimal facility access order of the customer, equation (11) represents that the customer must access the facilities at level 0, equation (12) represents that the customer can only access the facilities already constructed and each facility can only be accessed once, equations (13) and (14) are used to ensure that the customer can only access the facilities in turn in a pre-assigned order, equation (15) ensures that the customer eventually accesses the virtual facilities in order to correctly calculate the penalty cost, equations (16) and (17) represent the iterative relationship between the facility access probabilities of adjacent levels, and equations (18) - (20) represent that the decision variables are variables 0-1;
step 4, solving the site selection model
The lagrangian relaxation algorithm customized for solving the discrete addressing model is as follows:
first using non-negative Lagrange multipliers
Figure FDA0003570623710000051
The relaxation constraint is equation (12) and is added to equation (10) to get the corresponding relaxation problem, as follows:
Figure FDA0003570623710000052
the constraint conditions are formula (11), formula (13) to formula (20).
2. The method for reliable discrete addressing with return considerations in a limited information scenario as claimed in claim 1, wherein the relaxation problem in step 4 is decomposed into two relatively independent sub-problems,
the calculation formula for subproblem 1 is as follows:
Figure FDA0003570623710000053
the constraint condition is formula (20);
the calculation formula of the subproblem 2 is as follows:
Figure FDA0003570623710000054
the constraint conditions are formula (11), formula (13) to formula (19);
if the current coefficient is set
Figure FDA0003570623710000055
When y isj1; otherwise yjThe result of solving subproblem 1 is obtained, and subproblem 2 is solved as a shortest path problem by Dijkstra's algorithm.
3. The method for reliable discrete addressing with return taken into account in the limited information scenario of claim 2, wherein if the optimal solution of the relaxation problem is a feasible solution of the discrete addressing model, if the feasible solution is brought into the initial model and the exact same target value is obtained, the feasible solution is the optimal solution of the discrete addressing model, otherwise, the solution of the relaxation problem is taken as the lower bound of the discrete addressing model and the upper bound of the discrete addressing model is solved.
4. The method for reliable discrete addressing with return taken into account in the limited information scenario of claim 3, wherein the set of nodes that have been constructed is defined as the set of nodes that have been constructed according to the solution result of the sub-problem 1 in the relaxation problem
Figure FDA0003570623710000061
Based on sets
Figure FDA0003570623710000062
Solving for
Figure FDA0003570623710000063
A feasible solution for the other variables is obtained,
Figure FDA0003570623710000064
the calculation formula of (c) is as follows:
Figure FDA0003570623710000065
the constraint conditions are formulas (11) - (19);
solving the formula (24) by using a heuristic algorithm to obtain a feasible solution { X, X ', Y }, adding the feasible solution { X, X ', Y }, and adding the feasible solution { X, X ', Y }, to the formula (10), and obtaining an upper bound of the discrete addressing model, wherein if the upper bound and the lower bound are the same, the feasible solution is the optimal solution; otherwise, iterating the multiplier mu through a sub-gradient algorithm, re-solving the upper and lower bounds of the discrete model, and repeating the Lagrange relaxation algorithm process until the algorithm termination condition is met, so as to finally obtain the optimal target value;
the sub-gradient algorithm is used for iterating the multiplier mu, the multiplier adopted in the k iteration step
Figure FDA0003570623710000066
Indicating that the multiplier is initialized first
Figure FDA0003570623710000067
At each stackIn the step k, the multiplier mukThe iteration is muk+1And entering the next iteration step, wherein the iteration formula is as follows:
Figure FDA0003570623710000068
the iteration step is tkThe expression is as follows:
Figure FDA0003570623710000071
in the above formula, UBkIs the best upper bound at present; LBkIs the lower bound obtained in the k-th iteration step, in each iteration step k, the parameter ukIs fixed, initially set to (0, 2)]If LB in successive iterations in 6 stepskAre not optimized, then parameter ukWill be updated to uk:＝ukθ, where θ is a shrinkage factor greater than 1;
the termination condition of the Lagrange relaxation algorithm is to satisfy any one of the following conditions:
condition 1: optimizing the difference Gk:＝(UBk-LBk)/UBkNot more than epsilon, and the tolerance of epsilon is 0.005;
condition 2: k is less than kmax，kmax＝106Is the maximum iteration number;
condition 3: u. ofk≤10-3；
Condition 4: the solution time exceeds the maximum time limit T1800.
CN201911393880.2A 2019-12-30 2019-12-30 Reliability discrete addressing method considering return under limited information situation Active CN111222692B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911393880.2A CN111222692B (en) 2019-12-30 2019-12-30 Reliability discrete addressing method considering return under limited information situation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911393880.2A CN111222692B (en) 2019-12-30 2019-12-30 Reliability discrete addressing method considering return under limited information situation

Publications (2)

Publication Number Publication Date
CN111222692A CN111222692A (en) 2020-06-02
CN111222692B true CN111222692B (en) 2022-05-31

Family

ID=70828000

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911393880.2A Active CN111222692B (en) 2019-12-30 2019-12-30 Reliability discrete addressing method considering return under limited information situation

Country Status (1)

Country Link
CN (1) CN111222692B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113537828B (en) * 2021-08-04 2022-11-29 拉扎斯网络科技（上海）有限公司 Virtual site mining method and device

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2881033A1 (en) * 2015-02-03 2015-04-06 1Qb Information Technologies Inc. Method and system for solving lagrangian dual of a constrained binary quadratic programming problem
CN109685244A (en) * 2018-11-08 2019-04-26 北京交通大学 The continuous site selecting method of reliability of return is considered under limited information scene

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2881033A1 (en) * 2015-02-03 2015-04-06 1Qb Information Technologies Inc. Method and system for solving lagrangian dual of a constrained binary quadratic programming problem
CN109685244A (en) * 2018-11-08 2019-04-26 北京交通大学 The continuous site selecting method of reliability of return is considered under limited information scene

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
"Reliable facility location design with round-trip transportation under imperfect information Part I: A discrete model";Lifen Yun，Xifu Wang，Hongqiang Fan，Xiaopeng Li;《Transportation Research Part E》;20200131;全文 *
"信息缺失下考虑预算约束的物流设施可靠性选址研究";董鹏，王喜富，员丽芬;《北京交通大学学报》;20180630;全文 *
"非完美信息下京津冀区域物流设施选址研究";董鹏，，王喜富，员丽芬;《交通运输系统工程与信息》;20171231;全文 *

Also Published As

Publication number Publication date
CN111222692A (en) 2020-06-02

Similar Documents

Publication Publication Date Title
Unterluggauer et al. Electric vehicle charging infrastructure planning for integrated transportation and power distribution networks: A review
Rigas et al. Managing electric vehicles in the smart grid using artificial intelligence: A survey
Sun et al. Optimisation model for power system restoration with support from electric vehicles employing battery swapping
Bessler et al. Routing EV users towards an optimal charging plan
Kabir et al. Demand-aware provisioning of electric vehicles fast charging infrastructure
CN115547052B (en) Dynamic demand response electric bus scheduling method for improving self-adaptive large neighborhood algorithm
Mourad et al. Owning or sharing autonomous vehicles: comparing different ownership and usage scenarios
CN111222692B (en) Reliability discrete addressing method considering return under limited information situation
Lee et al. A simulation-based iterative method for a trauma center—Air ambulance location problem
Bayram et al. Location analysis of electric vehicle charging stations for maximum capacity and coverage
Raboaca et al. An overview and performance evaluation of open charge point protocol from an electromobility concept perspective
Xiang et al. Reliability‐oriented optimal planning of charging stations in electricity–transportation coupled networks
Bayram et al. Could petrol stations play a key role in transportation electrification? a gis-based coverage maximization of fast ev chargers in urban environment
Ullah et al. Optimal deployment of electric vehicles’ fast-charging stations
Maljkovic et al. A pricing mechanism for balancing the charging of ride-hailing electric vehicle fleets
Loni et al. Data-driven equitable placement for electric vehicle charging stations: Case study San Francisco
US20240067039A1 (en) Server and vehicle management method
Paudel et al. Infrastructure planning for ride-hailing services using shared autonomous electric vehicles
Ilango et al. Charging demand based on the interaction among electric vehicles and renewable energy sources using hybrid technique
Koháni et al. Location-scheduling optimization problem to design private charging infrastructure for electric vehicles
KR101634870B1 (en) Tour scheduler of electric vehicles having charger selection mechanism
Torres Franco et al. Electric vehicle charging stations’ location in urban transportation networks: A heuristic methodology
Dutta et al. Convergence Prediction of Mobile Nodes for Energy Transaction in 5G Network
Bessler et al. Supporting E-mobility Users and Utilities towards an Optimized Charging Service
CN109685244A (en) The continuous site selecting method of reliability of return is considered under limited information scene

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant