WO2011074369A1 - コスト評価システム、方法及びプログラム - Google Patents
コスト評価システム、方法及びプログラム Download PDFInfo
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- WO2011074369A1 WO2011074369A1 PCT/JP2010/070503 JP2010070503W WO2011074369A1 WO 2011074369 A1 WO2011074369 A1 WO 2011074369A1 JP 2010070503 W JP2010070503 W JP 2010070503W WO 2011074369 A1 WO2011074369 A1 WO 2011074369A1
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- 238000000034 method Methods 0.000 title claims abstract description 44
- 238000011156 evaluation Methods 0.000 title abstract description 7
- 238000004364 calculation method Methods 0.000 claims description 28
- 238000012549 training Methods 0.000 claims description 26
- 238000012545 processing Methods 0.000 claims description 19
- 230000008569 process Effects 0.000 claims description 17
- 230000008859 change Effects 0.000 claims description 7
- 238000005457 optimization Methods 0.000 claims description 6
- 238000012886 linear function Methods 0.000 claims description 4
- 230000006870 function Effects 0.000 description 22
- 239000011159 matrix material Substances 0.000 description 12
- 238000006243 chemical reaction Methods 0.000 description 9
- 238000010586 diagram Methods 0.000 description 5
- 239000006227 byproduct Substances 0.000 description 2
- 238000002790 cross-validation Methods 0.000 description 2
- 238000000611 regression analysis Methods 0.000 description 2
- 239000000523 sample Substances 0.000 description 2
- 230000008901 benefit Effects 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 238000002939 conjugate gradient method Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 238000013480 data collection Methods 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
- G01C21/34—Route searching; Route guidance
- G01C21/3446—Details of route searching algorithms, e.g. Dijkstra, A*, arc-flags, using precalculated routes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
- G01C21/34—Route searching; Route guidance
- G01C21/3453—Special cost functions, i.e. other than distance or default speed limit of road segments
- G01C21/3469—Fuel consumption; Energy use; Emission aspects
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
- G01C21/34—Route searching; Route guidance
- G01C21/3453—Special cost functions, i.e. other than distance or default speed limit of road segments
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- 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
- G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
- G06Q50/40—Business processes related to the transportation industry
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- G—PHYSICS
- G08—SIGNALLING
- G08G—TRAFFIC CONTROL SYSTEMS
- G08G1/00—Traffic control systems for road vehicles
- G08G1/09—Arrangements for giving variable traffic instructions
Definitions
- the present invention relates to a system, method, and program for evaluating or predicting costs such as required time along a certain route, power consumption, and CO 2 emission amount in a route such as a traffic route.
- Japanese Patent Laid-Open No. 2002-367071 discloses each link (road connecting adjacent intersections), traffic level data at each time, and travel at each time of the section necessary for determining the average speed for each traffic level. Collect and record time data, use the average speed for each congestion level assumed from the definition of the congestion level, determine the arrival time of each link and the congestion level data at that time, and determine the arrival time for each link. The average speed for each traffic level is calculated using the traffic level data for each link, and the length of the traffic level is divided by the average speed for each traffic level using the calculated average speed for each traffic level. It is disclosed that the travel time is calculated by adding together.
- Japanese Patent Laid-Open No. 2005-208791 discloses a road link travel time estimation device for calculating a road link travel time from a road link congestion degree using a relationship between a past road link travel time and a road link congestion degree. The next conversion function is obtained, a multiple regression analysis is performed with the coefficient of the conversion function as an objective variable and road attribute information as an explanatory variable, and n + 1 multiple regression equations for calculating the coefficient of the conversion function from the road attribute information are obtained.
- the road attribute information of the road link subject to the road link travel time estimation is substituted into the multiple regression equation to calculate the coefficient of the conversion function, the coefficient is applied to the conversion function, and the road at the time of movement Disclosed is to calculate an estimated value of road link travel time by substituting the link congestion degree into the conversion function.
- Japanese Patent Laid-Open No. 2008-282161 uses the relationship between the calculated past link congestion degree and the normalized link travel time to calculate the coefficient of the first conversion formula for calculating the normalized link travel time, Using each coefficient of the equation as a variable, a regression equation is obtained by a mixed model of multiple regression analysis and quantification theory type I analysis, the calculated traffic congestion target travel time is applied to the regression equation, and the second conversion equation A coefficient is calculated, the calculated coefficient is applied to the second conversion formula, an estimated value of the normalized link travel time of the travel time estimation target is calculated, and the road link travel time is calculated based on the normalized link travel time. Disclosed is an estimation value.
- Japanese Patent Laid-Open No. 2002-367071 certainly gives travel time, but it is assumed that the average speed does not change regardless of the route (link), and such an assumption is unrealistic, so that sufficient prediction accuracy can be obtained. I can't expect it.
- an object of the present invention is to provide a technique that makes it possible to predict the cost between a certain starting point and an ending point even if past route information is insufficient.
- a further object of the present invention is to provide a technique that makes it possible to predict an appropriate route between a certain start point and an end point even if past route information is insufficient.
- data D including information on the start point and the end point and the cost between them is prepared. Further, when a set of (route, cost of the route) is given as training data, a subroutine for calculating the cost c e along the arbitrary link e is prepared based on the set.
- c e is a linear function of fe .
- the user inputs a start point and an end point for calculating the cost according to a user interface such as an appropriate mouse.
- variable f e is initialized to 0 for all links e by computer processing.
- the minimum cost path is obtained from the current ⁇ f e ⁇ for all the start / end pairs included in the data D by the processing of the computer.
- the data D is converted into a set of (route, cost of the route). Therefore, the converted D is represented as D ′.
- ⁇ f e ⁇ calculated this time is compared with ⁇ f e ⁇ calculated last time, and if the change is equal to or greater than a certain threshold value, the process returns to the step of obtaining the minimum cost path.
- ⁇ f e ⁇ can be considered as a vector, and f this time -f last time can be evaluated with an appropriate norm such as max norm.
- a cost such as a required time between a certain start point and an end point even if past route information is insufficient. At that time, a rational route between a certain start point and end point is also obtained.
- FIG. 1 there is shown a block diagram of computer hardware for realizing a system configuration and processing according to an embodiment of the present invention.
- a CPU 104 a main memory (RAM) 106, a hard disk drive (HDD) 108, a keyboard 110, a mouse 112, and a display 114 are connected to the system bus 102.
- the CPU 104 is preferably based on a 32-bit or 64-bit architecture, such as Intel Pentium (TM) 4, Intel Core (TM) 2, DUO, AMD Athlon (TM), etc. Can be used.
- the main memory 106 preferably has a capacity of 1 GB or more, more preferably 2 GB or more.
- the hard disk drive 108 stores an operating system.
- the operating system may be any compatible with the CPU 104, such as Linux (trademark), Microsoft Windows 7, Windows XP (trademark), Windows (trademark) 2000, or Mac OS (trademark) of Apple Computer.
- the hard disk drive 108 further stores data D of past history of routes and costs, and a processing program according to an embodiment of the present invention.
- the past history data D and the processing program will be described in more detail later with reference to FIG.
- the hard disk drive 108 may store map information data and a program for displaying the map information, or although not shown, the hard disk drive 108 is connected to the Internet via a communication card and a predetermined server. You may use the data of map information that can be used in.
- the keyboard 110 and the mouse 112 are used to operate graphic objects such as icons, taskbars, and windows displayed on the display 114 in accordance with a graphic user interface provided by the operating system.
- the keyboard 110 and the mouse 112 are also used to perform an input operation of a start point and an end point by a user and an operation to start or end a program according to an embodiment of the present invention.
- the display 114 is not limited to this, but is preferably a 32-bit true color LCD monitor having a resolution of 1024 ⁇ 768 or higher.
- the display 114 is used to display a map including a route for predicting costs such as required time.
- data D 202 is data of past history along the target route, and is expressed as follows.
- D ⁇ (((a (n) .b (n) ), y (n) )
- n 1,2, ..., N ⁇
- a (n) is the starting point of the nth point
- b (n) is the ending point of the nth point
- y (n) is the cost recorded from a (n) to b (n) It is.
- the cost may be various times such as required time, power consumption, CO 2 emission amount, etc., but here it is assumed that it is the required time for convenience of explanation.
- there are methods that utilize probe car data and it should be understood that the data available in the present invention is not limited to a particular data collection method.
- the route here is based on the following reasonable assumptions. 1.
- the driver makes an intelligent route selection. That is, it follows the least cost path. 2. Traffic jams propagate. That is, a link in the vicinity of a link (edge) in which a singular state occurs is also affected in some way.
- the data format for recording the data D 202 on the hard disk drive is not particularly limited as long as it is computer readable.
- a generally well-known data format such as CSV or XML. .
- the main routine 204 reads the information of the data D, calls the data D update routine 206, the fe calculation routine 208, and the output routine 210 as appropriate, and performs predetermined processing.
- the data D update routine 206 receives the data D passed from the main routine 204, and uses ⁇ f e ⁇ , which is a parameter value corresponding to the cost associated with the edge, to add data D ′ with path information. 212 is created and recorded on the hard disk drive 108. The data of ⁇ f e ⁇ is prepared over all of e ⁇ E, where E is the set of edge of the path. Note that the data D ′ 212 is also recorded using a generally well-known data format such as CSV, XML, etc., like the data D 202.
- Data D ′ is expressed as follows.
- D ' ⁇ (((a (n) .b (n) ), x (n) , C (x (n) ))
- n 1,2, ..., N ⁇
- x (n) is an ordered sequence of links when a road is represented by a graph, and represents a route.
- C (x (n) ) is a cost value along x (n) .
- the meaning of other notations is the same as that of data D.
- the path from the start point to the end point is indicated by a thick line. Such a route is calculated in step 406 described later.
- f e calculation routine 208 calculates the value of the passed from the main routine 204 ⁇ f e ⁇ , and a value of the data D '212, the updated ⁇ f e ⁇ .
- the f e calculation routine 208 calls the ⁇ calculation routine 214 to calculate the parameter ⁇ used in the calculation.
- the main routine 204 receives the value of ⁇ f e ⁇ calculated by the fe calculation routine 208 and passes it to the data D update routine 206.
- the data output routine 210 is appropriately called from the main routine 204, and based on the data D ′ recorded in the hard disk drive 108, the time required between the start point and the end point specified by the keyboard 110 and the mouse 112 is calculated.
- the display 114 has a function of displaying the predicted value and the predicted route.
- the main routine 204, the data D update routine 206, the fe calculation routine 208, the data output routine 210, and the ⁇ calculation routine 214 in FIG. 2 are known, such as C, C ++, C #, and Java (R).
- the executable file is compiled into an executable file and stored in the hard disk drive 108, and is called up to the main memory 106 by the operation of the operating system and executed according to the user's operation as necessary.
- FIG. 4 is a flowchart showing the processing of the main routine 204.
- the main routine 204 reads the original data D.
- step 404 the main routine 204 sets all elements of ⁇ f e
- f e 0 means running at legal speed in the context of this embodiment. Therefore, f e ⁇ 0 means a deviation from the legal speed.
- the data of ⁇ f e ⁇ is preferably arranged in a predetermined area of the main memory 106, but may be stored in the hard disk drive 108.
- step 406 the main routine 204 calls the data D update routine 206 to perform processing for converting D into data D ′ with route information using fe .
- the data D update routine 206 will be described in more detail later with reference to the flowchart of FIG.
- step 408 the main routine 204 calls the fe calculation routine 208 to perform a recalculation of ⁇ fe ⁇ based on D ′.
- the f e calculation routine 208 will be described in more detail later with reference to the flowchart of FIG.
- step 410 the main routine 204 determines whether ⁇ f e ⁇ has converged. This convergence, the main routine 204 has been previously calculated in advance holds ⁇ f e ⁇ , the newly calculated ⁇ f e ⁇ ⁇ f 'When e ⁇ , ⁇ f e ⁇ and ⁇ f' The distance between e ⁇ is calculated by an appropriate norm such as max norm, and if the value is smaller than a predetermined threshold, it is considered that the distance has converged.
- an appropriate norm such as max norm
- the main routine 204 returns to step 406 with the newly calculated ⁇ f e ⁇ and calls the data D update routine 206 again.
- step 410 If the main routine 204 determines at step 410 that ⁇ f e ⁇ has converged, the process is complete and step ⁇ f e ⁇ is finalized. Since fe of all the links on the road is given, it is possible to obtain the required time and route between any two points on the road 302 by any method such as Dijkstra method.
- FIG. 5 is a flowchart showing the processing of the data D update routine 206.
- the data D update routine 206 receives data D and ⁇ f e ⁇ as inputs.
- the data D refers to the time when the data D update routine 206 is called for the first time from step 404 in FIG. 4 when the data D update routine 206 is called. Should be read as data D ′.
- step 506 and step 508 are executed for all start point / end point pairs.
- n 1,2, ..., N ⁇ in, that the (a (n) .b (n )) It is.
- N is the number of start / end pairs as past history data. That is, in the case of this data D, step 506 and step 508 are executed N times.
- the data D update routine 206 obtains a minimum cost path between the start point / end point pair based on ⁇ f e ⁇ .
- This is a normal shortest path search weighted by ⁇ f e ⁇ , and for this purpose, any known shortest path search algorithm such as Dijkstra method, A * method, or Warsal Floyd method can be used. it can.
- step 508 the data D update routine 206 adds the path x (n) between the start point and the end point obtained in this way and the cost C (x (n) ) of the path to the data D ′.
- the cost C (x) is calculated as follows.
- An example of a specific definition of the expression of c e (f e ) is as follows.
- c e (f e ) l e (f e + f e 0 )
- fe is a deviation of the cost per unit length from the normal time, and this is an unknown quantity.
- f e 0 is a cost per unit length (known amount) estimated from a reference state such as legal driving.
- l e is the length of the link e and is a known amount.
- step 506 and step 508 are executed for all the start / end pairs
- data D ′ with route information is obtained in step 510 as follows.
- D ' ⁇ (((a (n) .b (n) ), x (n) , C (x (n) ))
- n 1,2, ..., N ⁇
- D ′ and the similarity matrix S are used. Since D ′ is known, the similarity matrix S will be described.
- the similarity between link e and link e ′ is generally defined as a decreasing function of the distance d (e, e ′) between them.
- d (e, e ') and the definition of similarity are arbitrary, one preferred form is given as follows. S e, e ' ⁇ ⁇ 1 + d (e, e')
- d (e, e ′) is the number of links that pass to reach the link e ′ from the link e with the shortest distance.
- d (e, e ′) 2.
- a line shown in bold is a link connecting the link e and the link e ′.
- f e calculation routine 208 starts at step 604 from D ′ as follows: Create a Q matrix and y N. First, instead of y (n) And y N is a vector in which N pieces of y ⁇ (n) are arranged vertically. That is, y N ⁇ [y ⁇ (1) , y ⁇ (2) , ..., y ⁇ (n) ] T
- the quantity q M ⁇ R M is defined as follows as an indicator vector representing the length of the road. Then, a matrix in which these are arranged is defined as follows. Q ⁇ [q (1) , ..., q (N) ]
- step 606 the fe calculation routine 208 creates a matrix L from S by the following equation.
- this type of matrix is called a graph Laplacian.
- M is the total number of links on the map and ⁇ ij is the Kronecker delta.
- step 608 the fe calculation routine 208 calls the ⁇ calculation routine 214 to determine the value of ⁇ .
- the details of the ⁇ calculation routine 214 will be described later with reference to the flowchart of FIG. 8. Here, it is assumed that the value of ⁇ has been determined, and the process proceeds to step 610.
- f is a vector in which ⁇ f e ⁇ are arranged.
- the first term on the right side of this equation is a loss function, and the second term is the penalty for the discrepancy between the surrounding links and the situation multiplied by ⁇ .
- preferable ( ⁇ , ⁇ ) is (1,1) or (2,2).
- a set of candidate values ⁇ 1 ,..., ⁇ p ⁇ of ⁇ is prepared.
- the optimum value of ⁇ varies depending on the nature of the data, but usually ⁇ is a number on the order of 1. Therefore, for example, ⁇ 10 ⁇ 2 , 10 ⁇ 1 , 1, 10 1 , 10 2 ⁇ can be given as an initial value.
- f [ ⁇ D ′ s ] is a solution obtained by using data obtained by removing the s-th data D ′ s .
- the optimum value of ⁇ can be selected from the candidate values. The value of ⁇ so selected is returned to step 608 of FIG. If the interval where the evaluation value is minimum is found to be between 10 -1 and 1, for example, then give ⁇ 0.1, 0.3, 0.6, 0.9 ⁇ etc. and this subroutine can be turned again. . In this way, the optimum value of ⁇ can be determined with an arbitrary fineness. In this way, the process of gradually approaching the optimum section from the engraved range can be fully automated as appropriate.
- step 902 of FIG. 9 in addition to the above-described Q matrix and L matrix, a set of candidate values of ⁇ ⁇ 1 , ..., ⁇ p ⁇ are prepared. Preparation of values of ⁇ 1 ,..., ⁇ p ⁇ is the same as the processing of the flowchart of FIG.
- ⁇ calculation routine 214 results in obtaining ⁇ that minimizes the following evaluation function.
- f ( ⁇ n) is a solution obtained by using data from which the nth sample is omitted.
- IM is an M-dimensional unit matrix
- diag () is a function that outputs a diagonal matrix
- H is expressed as follows.
- step 410 if the main routine 204 determines in step 410 that ⁇ f e ⁇ has converged, the process is complete and ⁇ f e ⁇ is determined. Then, at this point, fe of all links of the target road is given. Therefore, the user designates the start point and the end point with the keyboard 110 or the mouse 112 while looking at the display 114. Then, the main routine 204 uses the parameter ⁇ f e ⁇ corresponding to the cost of the link on the data of the original map, and the shortest distance between any two points on the road 302 by any method such as Dijkstra method. A process for obtaining the route x is performed.
- the cost which is the required time can be obtained from the route according to the following formula.
- the route and cost thus obtained are displayed on the display 114 by the data output routine 210.
- the travel is expressed as a weighted graph in which a single cost is assigned to one link.
- the present invention is not limited to this, and for example, in the forward path and the return path.
- a solution can be obtained assuming different costs for the forward path and the return path. This corresponds to the case of a slope, for example.
- a route that travels in the reverse direction of the link may be excluded.
- the past history data does not give a route at all.
- the past history data includes a part of the route information, a route that passes through the actual route is used. Just choose.
- the past history data D is a cost function prediction model stratified by time of day such as D (morning), D (daytime), D (evening), and D (night). You may make it.
- ⁇ ) shown in the above embodiment is used to calculate the link parameter corresponding to the cost if the route between the start point and the end point is included in the training data.
- this calculation process alone can be used for the cost estimation processing of the graph link independently of the step 406 in the flowchart of FIG. Is possible.
- the present invention is not limited to roads, and can be applied to any example in which routes are expressed in a graph structure and costs can be considered in relation to the links.
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Abstract
Description
D = {((a(n).b(n)),y(n))|n = 1,2,...,N}
ここで、a(n)はn番目の点の始点、b(n)はn番目の点の終点、y(n)は、a(n)からb(n)までにかかったと記録されたコストである。ここで、コストは、所要時間、消費電力、CO2排出量などいろいな場合が考えられるが、ここでは説明の便宜上、所要時間であるとする。
1.運転手は、理性的な経路選択をする。すなわち、最小費用の経路を通る。
2.渋滞は伝播する。すなわち、特異状態が生じているリンク(エッジ)の近隣のリンクも何らかの影響を受ける。
D' = {((a(n).b(n)),x(n),C(x(n)))|n = 1,2,...,N}
ここで、x(n)は、道路をグラフ表記したときのリンクの順序付けられた並びであり、経路をあらわす。C(x(n))は、x(n)に沿ったコストの値である。その他の記法の意味は、データDと共通である。尚、図3には、始点から終点までの経路が、太い線で示されている。このような経路は、後述のステップ406で計算される。
データD = {((a(n).b(n)),y(n))|n = 1,2,...,N}における、(a(n).b(n))のことである。Nが、過去履歴データとしての始点・終点ペアの数である。すなわち、このデータDの場合、ステップ506とステップ508は、N回実行される。
ce(fe)の式の具体的な定義の例は、以下のとおりである。
ce(fe) = le(fe + fe 0)
ここで、feは、単位長さあたりのコストの、通常時からのずれであり、これは未知量である。
fe 0は、法定走行などの基準状態から概算される、単位長さあたりのコスト(既知量)である。
leは、リンクeの長さであり、既知量である。
D' = {((a(n).b(n)),x(n),C(x(n)))|n = 1,2,...,N}
Se,e' ≡ γ1+d(e,e')
ここで、d(e,e')とは、リンクeからリンクe'に最短距離で到達するために通るリンクの数であり、図7に示す例702では、d(e,e') = 2である。太字で示す線が、リンクeとリンクe'の間をつなぐリンクである。
γは、1以下の正の既知量で、例えば、0.5と選ぶ。
また、d(e,e')がある値を超えると、Se,e' = 0とする。例えば、d(e,e') > 3の場合、Se,e' = 0とする。
Q行列とyNを作る。まず、y(n)の代わりに改めて
とし、このy~(n)を縦にN個並べたベクトルを、yNとする。すなわち、
yN ≡ [y~(1),y~(2),...,y~(n)]T
ここでMは、地図上のリンクの総数であり、δijはクロネッカーのデルタである。
この式の左辺で、fは、{fe}を並べたベクトルである。また、この式の右辺の第1項は損失関数であり、第2項は、周囲のリンクと状況の食い違いに対するペナルティにλを掛けたものである。
これは、線形計画問題を解くことに帰着でき、市販のソルバーを使うことで容易に最適解を求められる。(α,β) = (2,2)の場合と比べた利点は、外れ値に頑強である、という点である。一般に交通データは多くの外れ値(例外的な振る舞いをする経路など)を含むので、この性質は実用上好ましい。
これが、ステップ610に記述されている式である。この式は、連立一次方程式なので、線形計画問題よりもさらに容易に解ける。連立一次方程式の解き方として、従来よりガウス・ザイデル法などが知られているが、この場合、一般的に左辺が疎行列になるので、共役勾配法または類似の方法を使って解くのが、計算量の観点から、合理的である。
以上の処理により、ステップ810で、候補値の中から最適なλの値を選ぶことができる。そのようにして選ばれたλの値は、ステップ812で、図6のステップ608に戻される。尚、評価値が最小になる区間が例えば、10-1と1の間であると見いだされれば、次に、{0.1, 0.3, 0.6, 0.9} などと与え、再びこのサブルーチンを回すことができる。このようにして任意の細かさでλの最適値を定めることができる。なお、このように、刻まれた範囲から次第に最適な区間に近づく処理は、適宜、完全自動化することもできる。
{λ1,...,λp}が用意される。{λ1,...,λp}の値の用意については、図8のフローチャートの処理と同様である。
ここで、f(-n)は、第nサンプルを抜いたデータを使って求めた解である。
λiについてLLOOCV(λi)が計算され、ステップ906とステップ908がi = 1からpまで実行された後は、ステップ910で、LLOOCV(λ)を最小にするλが選ばれる。そのようにして選ばれたλの値は、ステップ912で、図6のステップ608に戻される。
104 CPU
106 主記憶
108 ハードディスク・ドライブ
110 キーボード
112 マウス
114 ディスプレイ
204 メイン・ルーチン
206 データD更新ルーチン
208 計算ルーチン
210 出力ルーチン
108 ハードティスク・ドライブ
214 計算ルーチン
210 データ出力ルーチン
Claims (23)
- 複数のノードと、該ノード間を接続するリンクからなるグラフ上で、始点と終点と、該始点と該終点の間のコストを含む複数の訓練データの集合に基づき、コンピュータの処理によって、該リンクに関連付けられたパラメータを用いて該グラフの任意のリンク上のコストを計算する方法であって、
前記グラフの各リンクに割り当てるパラメータの値を初期化するステップであって、該パラメータは、前記コストと所定の一次関数で関連付けられているステップと、
前記グラフ上で、前記訓練データの集合と、前記コストを用いて、前記始点から前記終点に至るすべての経路における最小コスト経路を計算することにより、前記訓練データの集合の値を再計算するステップと、
前記再計算された訓練データの集合の値を含む目的関数の最適化問題を解くことによって、前記グラフの各リンクに割り当てるパラメータの値を再計算するステップと、
再計算の前後での前記パラメータの変化量が所定の閾値以下であることに応答して、前記パラメータを確定するステップを有する、
経路のコストの計算方法。 - 前記再計算の前後での前記パラメータの変化量が所定の閾値より大きいことに応答して、前記訓練データの集合の値を再計算するステップに戻るステップをさらに有する、請求項1に記載の方法。
- 前記目的関数が、コストの損失関数の項と、周囲のリンクとの状況の食い違いに対するペナルティの項とを含む、請求項1に記載の方法。
- (α,β) = (1,1)である、請求項4に記載の方法。
- (α,β) = (2,2)である、請求項4に記載の方法。
- 複数のノードと、該ノード間を接続するリンクからなるグラフ上で、始点と終点と、該始点と該終点の間のコストを含む複数の訓練データの集合に基づき、コンピュータの処理によって、該リンクに関連付けられたパラメータを用いて該グラフの任意のリンク上のコストを計算するプログラムであって、
前記コンピュータに、
前記グラフの各リンクに割り当てるパラメータの値を初期化するステップであって、該パラメータは、前記コストと所定の一次関数で関連付けられているステップと、、
前記グラフ上で、前記訓練データの集合と、前記コストを用いて、前記始点から前記終点に至るすべての経路における最小コスト経路を計算することにより、前記訓練データの集合の値を再計算するステップと、
前記再計算された訓練データの集合の値を含む目的関数の最適化問題を解くことによって、前記グラフの各リンクに割り当てるパラメータの値を再計算するステップと、
再計算の前後での前記パラメータの変化量が所定の閾値以下であることに応答して、前記パラメータを確定するステップを実行させる、
経路のコストの計算プログラム。 - 前記再計算の前後での前記パラメータの変化量が所定の閾値より大きいことに応答して、前記訓練データの集合の値を再計算するステップに戻るステップをさらに有する、請求項7に記載のプログラム。
- 前記目的関数が、コストの損失関数の項と、周囲のリンクとの状況の食い違いに対するペナルティの項とを含む、請求項7に記載のプログラム。
- (α,β) = (1,1)である、請求項10に記載のプログラム。
- (α,β) = (2,2)である、請求項10に記載のプログラム。
- 複数のノードと、該ノード間を接続するリンクからなるグラフ上で、始点と終点と、該始点と該終点の間のコストを含む複数の訓練データの集合に基づき、コンピュータの処理によって、該リンクに関連付けられたパラメータを用いて該グラフの任意のリンク上のコストを計算するシステムであって、
前記グラフの各リンクに割り当てるパラメータの値を初期化する手段であって、該パラメータは、前記コストと所定の一次関数で関連付けられている手段と、、
前記グラフ上で、前記訓練データの集合と、前記コストを用いて、前記始点から前記終点に至るすべての経路における最小コスト経路を計算することにより、前記訓練データの集合の値を再計算する手段と、
前記再計算された訓練データの集合の値を含む目的関数の最適化問題を解くことによって、前記グラフの各リンクに割り当てるパラメータの値を再計算する手段と、
再計算の前後での前記パラメータの変化量が所定の閾値以下であることに応答して、前記パラメータを確定する手段を有する、
経路のコストの計算システム。 - 前記目的関数が、コストの損失関数の項と、周囲のリンクとの状況の食い違いに対するペナルティの項とを含む、請求項13に記載のシステム。
- (α,β) = (1,1)である、請求項15に記載のシステム。
- (α,β) = (2,2)である、請求項15に記載のシステム。
- 複数のノードと、該ノード間を接続するリンクからなるグラフ上で、始点と終点と、該始点と該終点の間のコストと、該始点と該終点の間の経路含む複数の訓練データの集合に基づき、コンピュータの処理によって、該リンクに関連付けられたパラメータを用いて該グラフの任意のリンク上のコストを計算する方法であって、
前記訓練データの集合の値を含む下記の目的関数
ここで、Nは前記訓練データの数、y(n)はn番目のデータのコスト、feは、リンクeに関連付けられた前記パラメータ、ce(f@e)は、前記パラメータをコストに変換する関数てあり、α、βは整数値であり、λは適当に定めた正の数である、
の最適化問題を解くことによって、前記グラフの各リンクに割り当てるパラメータの値を再計算するステップを有する、
経路のコストの計算方法。 - (α,β) = (1,1)である、請求項18に記載の方法。
- (α,β) = (2,2)である、請求項18に記載の方法。
- 複数のノードと、該ノード間を接続するリンクからなるグラフ上で、始点と終点と、該始点と該終点の間のコストと、該始点と該終点の間の経路含む複数の訓練データの集合に基づき、コンピュータの処理によって、該リンクに関連付けられたパラメータを用いて該グラフの任意のリンク上のコストを計算するプログラムであって、
前記コンピュータをして、
前記訓練データの集合の値を含む下記の目的関数
ここで、Nは前記訓練データの数、y(n)はn番目のデータのコスト、feは、リンクeに関連付けられた前記パラメータ、ce(f@e)は、前記パラメータをコストに変換する関数てあり、α、βは整数値であり、λは適当に定めた正の数である、
の最適化問題を解くことによって、前記グラフの各リンクに割り当てるパラメータの値を再計算するステップを実行させる、
経路のコストの計算プログラム。 - (α,β) = (1,1)である、請求項21に記載のプログラム。
- (α,β) = (2,2)である、請求項21に記載のプログラム。
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