1 V yt a ut as M a g n us U ni versit y, F ac ult y of I nf or m atics, De p art me nt of M at he m atics a n d St atistics, Vilei k os street 8, L T- 4 4 4 0 4 K a u n as, Lit h u a ni a 2 V yt a ut as M a g n us U ni versit y, F ac ult y of I nf or m atics, De p art me nt of A p plie d I nf or m atics, Vilei k os street 8, L T- 4 4 4 0 4 K a u n as, Lit h u a ni a 3 Ce ntre f or A p plie d Rese arc h a n d De vel o p me nt, Lit h u a ni a A b str a ct T h e p o p ul arit y of r o a d tr a ns p ort is gr o wi n g e v er hi g h er i n t h e m o d er n d a y of a g e a n d is t h e m ost p o p ul ar m o d e f or tr a ns p orti n g g o o ds [1 ]. Us u all y, tr a ns p ort ati o n i n cr e as es t h e pri m e c ost of t h e g o o ds or s er vi c es, t h us, t o i n cr e as e a c o m p a n y's pr o fit, e ff e cti v e v e hi cl e r o uti n g b e c o m es e ss e nti al. I n t his r es e ar c h, w e h a v e a n al ys e d t h e p ossi bilit y of i m pr o vi n g t h e f or e c ast of esti m at e d ti m e of arri v al b y r a n ki n g t h e dri v ers b as e d o n t h eir b e h a vi o ur d at a a n d esti m ati n g d e vi ati o ns fr o m pl a n n e d arri v al ti m e usi n g di ff er e nt m a c hi n e l e ar ni n g m et h o ds. T h e r a n ki n g w as p erf or m e d wit h T O P SI S a n d VI K O R m et h o ds, w hil e t h e f or e c asti n g w as p erf or m e d usi n g fi v e m a c hi n e l e ar ni n g al g orit h ms: d e cisi o n tr e e, r a n d o m f or est, X G B o ost, S u p p ort Ve ct or M a c hi n e a n d k - N e ar est N ei g h b o urs. T h e p erf or m a n c e of t h e f or e c asti n g m o d els w as e v al u at e d usi n g t h e a dj ust e d c o e ffi ci e nt of d et er mi n ati o n, r o ot s q u ar e m e a n err or a n d m e a n a bs ol ut e err or m etri cs. It w as c o n cl u d e d t h at t h e VI K O R m et h o d s h o ul d b e us e d t o r a n k t h e dri v ers. M or e o v er, r es e ar c h r es ults r e v e al e d t h at t h e b est f or e c asti n g p erf or m a n c e w as a c hi e v e d usi n g a n e ns e m bl e m o d el b as e d o n r a n d o m f or est a n d S u p p ort Ve ct or M a c hi n e m o d els. K e y w o r d s Esti m at e d ti m e of arri v al ( E T A), fr ei g ht tr a ns p ort, d ri v er's s c or e, ra n ki n g, m a c hi n e l e ar ni n g, T O P SI S, VI K O R, D e cisi o n Tr e e, R a n d o m F or est, X G B o ost, S u p p ort Ve ct or M a c hi n e, k - N e ar est N ei g h b o urs 1. I nt r o d u cti o n T o i m pr o v e t h e tr a n s p ar e n c y of a s u p pl y c h ai n, it s p arti ci p a nt s u s e tr a n s p ort m a n a g e m e nt s y st e m s a s w ell a s tr a c ki n g a n d m o nit ori n g s y st e m s. Ve hi cl e s ar e g etti n g e q ui p p e d wit h str o n g er mi cr o pr o c e s s or s, l ar g er m e m or y c a p a cit y a n d r e al-ti m e o p er ati n g s y st e m s. T h e n e wl y i n st all e d t e c h n ol o gi c al pl atf or m s c a n u s e m or e a d v a n c e d 2. R el at e d w o r k a p pli c ati o n s of t h e o p er ati n g s y st e m, i n cl u di n g m o d elb a s e d pr o c e s s c o ntr ol f u n cti o n s, arti fi ci al i nt elli g e n c e, T o b ett er u n d erst a n d w h at attri b ut es a n d m et h o ds c a n b e a n d c o m pr e h e n si v e c o m p ut ati o n. u s e d f or r a n ki n g dri v er s, r e s e ar c h [2 ] w a s st u di e d. T h e T h er ef or e, a n i n cr e a si n g tr e n d of i m pl e m e nti n g t h e ai m of t hi s r e s e ar c h w a s t o c at e g ori z e dri v er s a c c or dl at e st d e v el o p m e nt s i n i nf or m ati o n a n d i nt er n et t e c h- i n g t o t h eir ri s k- pr o n e n e s s b y a n al y si n g a G P S- b a s e d n ol o gi e s i n t h e tr a n s p ort s e ct or a s w ell a s a t e n d e n c y of d e vi c e' s ur b a n tr a ffi c d at a. Hi er ar c hi c al Cl u st eri n g Al g od e v el o pi n g n e w r e s e ar c h- b a s e d s y st e m s t h at c a n q ui c kl y rit h m ( H C A) a n d Pri n ci p al C o m p o n e nt A n al y si s ( P C A) a d a pt t o a n e v er- c h a n gi n g e n vir o n m e nt i s o b s er v e d. T h e w er e us e d f or t h e st atisti c al a n al ysis of t h e f oll o wi n g dri vg o al of t hi s st u d y i s t o i d e ntif y m et h o d s, b e st s uit e d f or i n g p ar a m et er s: S p e e d o v er 6 0 k m/ h , S p e e d , Ac c el er ati o n , s ol vi n g t h e e sti m at e d ti m e of arri v al ( E T A) f or e c a sti n g P ositi v e a c c el er ati o n , Br a ki n g a n d M e c h a ni c al w or k . T h e pr o bl e m. a ut h ors of t his r es e ar c h c o n cl u d e t h at w hil e it is p ossi bl e T h e r e st of t h e p a p er i s or g a ni z e d a s f oll o w s. R el at e d t o cl a s sif y t h e dri v er s a c c or di n g t o t h e s e p ar a m et er s, a w or k i n t hi s ar e a i s pr e s e nt e d i n S e cti o n 2 . S e cti o n 3 i n- l ot of e xt er n al f a ct or s, s u c h a s t h e dri vi n g e n vir o n m e nt or t h e c o n diti o n of t h e ass ess e d dri v er, ar e n ot t a k e n i nt o I V U S 2 0 2 2: 2 7t h I nter n ati o n al C o nfere nce o n I nf or m ati o n Tec h n ol o g y, a c c o u nt. M a y 1 2, 2 0 2 2, K a u n as, Lit h u a ni a A c o m p ar ati v e a n al y si s of t w o m ulti- crit eri a d e ci si o n* C orr es p o n di n g a ut h or. m a ki n g ( M C D M) m et h o d s T O P SI S a n d VI K O R i s pr e† T h es e a ut h ors c o ntri b ut e d e q u all y. s e nt e d i n [3 ]. It w a s f o u n d t h at t h e s e t w o m et h o d s u s e g a bri el e. k as p ut yt e @ v d u.lt ( G. K as p ut ytė); di ff er e nt ki n ds of n or m ali z ati o n ( T O P SI S u s es v e ct or n orar n as. m at us e vi ci us @ v d u.lt ( A. M at us e vi či us); m ali z ati o n, VI K O R - li n e ar) t o eli mi n at e t h e u nit s of t o 0m 0as0.0k-r0il0a0v1i-c8i 5u0s 9-@4v2d0u.Xlt((T.T. KKrriillaavviiččiiuuss)) crit eri o n f u n cti o n s a n d u s e di ff er e nt a g gr e g ati n g f u n c© 2022 C o p yri g ht f or t his pa per b y its a ut h ors. Use per mitte d u n der Creati ve C o m m o ns Lice nse ti o ns f or r a n ki n g. N o n et h el ess, b ot h m et h o ds w er e f o u n d CPWroEorUcksRehodipngs hItSp:/Nc1e6ur1-3w-s0.or7g3 ACttEri bUutiRo n 4.W0oI rntekrsnahti oonpal (PCrC oBcY e4.e0).di n gs ( C E U R- W S. or g ) s uit a bl e f or s ol vi n g r a n ki n g pr o bl e m s.
tr o d u c es t h e d at as ets us e d i n t h e c urr e nt st u d y. S e cti o n 4 pr es e nts t h e s el e ct e d r a n ki n g a n d f or e c asti n g t e c h ni q u es.
E x p eri m e nt al r e s ult s ar e pr o vi d e d i n S e cti o n 5 . Fi n all y, c o n cl u di n g r e m ar k s a n d f ut ur e pl a n s ar e di s c u s s e d i n S e cti o n 6 .
3. Research data
The use of machine learning (ML) techniques for the ETA problem is discussed in [4] The authors applied artificial neural networks (ANNs) and support vector re- 3.1. Data for ranking drivers gression (SVR) to predict the time of arrival of container ships. Distance to the destination, the timestamp, geo- The available readings from a vehicle monitoring system coordinates, and weather information have been chosen that can be used to evaluate a driver’s behaviour were as features. It was shown that SVR had performed better extracted. The readings in this research cover the period than ANNs and that the weather data did not have a sig- from August 21, 2020, to January 1, 2022, and up to 398 nificant impact on estimating the time of vessel arrivals. observations representing diferent vehicles.
In the [5] study, the -Nearest neighbours (KNN), SVR, A dataset was constructed containing values for 7 atand the random forest algorithms were evaluated as meth- tributes, namely Free-rolling distance, Engine overloaded ods for predicting the arrival time of open-pit trucks. A distance, Highest gear distance, Excess idling, Overspeeding site-based approach was used as the position was only time, Extreme braking events and Harsh braking events. measured at a few discrete nodes of the route network. It was concluded that the random forest algorithm provides 3.2. Data for forecasting model the best prediction results. In this research, logistic transportation data was reviewed
Ma et al. [6] proposed a tree-based integration method and a dataset was created for the ETA forecasting models. to predict trafic accidents by using diferent data vari- The initial dataset includes 1758 observations and 13 ables. Predictions of the gradient boosting decision variables. The obtained information is from August 21, tree algorithm outperformed back propagation neural 2020 to January 24, 2022. A set of explanatory variables X, networks, support vector machines, and random forest. with vectors 1, 2, . . . , 13, is obtained. The description However, in this study, the nonlinear relationship be- of these variables is presented in Table 1. tween the influence characteristics and the predicted value was not analysed.
To improve travel time predictions, the author of [7] Table 1 study applied the combination of random forest and gra- Set of explanatory variables dient boosting regression tree (GBRT) models. The aim Variable Description Variable type was to study how reducing a large volume of raw GPS 1 Driver’s score Ordinal data into a set of feature data afects high-quality travel 2 Tour beginning country Categorical time predictions. Only travel time observations from 3 Tour ending country Categorical the previous departure time intervals were found to be 4 Number of intermediate stops Discrete tboenbeeficiuaslefdeaatusrienspauntds wwehreenrencoomotmheerndtyedpebsyothfereaault-htiomre 567 FTToouuurtrrhbbeeesggtiicnnonnuiinnnggtrydmaoynth CCCaaattteeegggooorrriiicccaaalll information (e.g. trafic flow, speed) is available. Also, 8 Vehicle height Continuous it is noted, that trees in GBRT models were found to be 9 Vehicle width Continuous consistently much shorter than those of random forest 10 Vehicle length Continuous models, leading to shorter computation times. 11 Vehicle weight Continuous
To sum up, characterizing attributes of drivers in re- 12 Hours of service breaks Continuous search are usually derivative – data obtained from vehi- 13 Planned distance Continuous cle monitoring devices represent their driving behaviour.
Since MCDM methods were found popular for conduct- Let be the factual time when the th cargo will be ing ranking procedures, two easily comparable MCDM delivered, and the planned time of delivery for the th methods will be used: TOPSIS and VIKOR. What con- cargo. Then, the deviation from the planned time of delivcerns the ETA problem, the accuracy of the ML models ery for the th cargo ∆ will be denoted as the diference tested in reviewed research was inconsistent. Therefore, between the planned and factual time of delivery: a wide variety of ML methods suitable for the problem and available data will be evaluated. Namely, decision ∆ = − , (1) tree, random forest, XGBoost, Support Vector Machine (SVM) and KNN methods, as well as an ensemble of mod- where = 1, 2, . . . , . In that case, the explanatory els, will be tested. variable is denoted as: = ∆.
(2) This variable is the goal of the forecasting problem.
The VIKOR method was introduced as one applicable technique to implement within MCDM. It focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria, and on proposing a compromise solution (one or more). The compromise ranking algorithm VIKOR has the following steps [8]: 1. Determine the best * and the worst − values of all criterion functions, = 1, 2, . . . , . If the th function represents a benefit then: * = max , − = min .
2. Compute the values and , = 1, 2, . . . , , by the relations
The basic principle of the TOPSIS method is that the chosen alternative should have the shortest distance from the ideal solution and the farthest distance from the negativeideal solution [9]. The TOPSIS procedure consists of the following steps: 1. Calculate the normalized decision matrix. The normalized value is calculated as
= √︁∑︀ =1 2 , [︂ = max * − ]︂ , * − − where are the weights of criteria, expressing their relative importance. 3. Compute the values , = 1, 2, . . . , , by the relation
= where − * − − * + (1 − ) − * − − *
, = ∑︁ * − ,
=1 * − − * = min ,
* = min , − = max ,
− = max , and is introduced as weight of the strategy of "the majority of criteria" (or "the maximum group utility"), here = 0.5. 4. Rank the alternatives, sorting by the values , and , in decreasing order. The results are three ranking lists. 5. Propose as a compromise solution the alternative (′) which is ranked the best by the measure (minimum) if the following two conditions are satisfied:
C1. "Acceptable advantage": (′′) − (′) ⩾ (8) where ′′ is the alternative with second position in the ranking list by ; = 1/( − 1); is the number of alternatives.
C2. "Acceptable stability in decision-making": Alternative ′ must also be the best ranked by or/and . Here, is the weight of the decision-making strategy "the majority of criteria".
where = 1, . . . , ; = 1, . . . , . 2. Calculate the weighted normalized decision matrix. The weighted normalized value is calculated as
= · , where = 1, . . . , ; = 1, . . . , , is the weight of the th attribute or criterion, and ∑︀
=1 = 1. 3. Determine the ideal and negative-ideal solution. * = {(max | ∈ ′), (min | ∈ ′′)}, (11) − = {(min | ∈ ′), (max | ∈ ′′)}, (12) where ′ is associated with benefit criteria, and ′′ is associated with cost criteria. 4. Calculate the separation measures, using the dimensional Euclidean distance. The separation of each alternative from the ideal solution is given as
⎯⎸ * = ⎷⎸∑︁( − *)2,
=1 where = 1, . . . , .
Similarly, the separation from the negative-ideal solution is given as
⎯⎸ − = ⎷⎸∑︁( − −)2, =1 (3) (4) (5) (6) (7)
where = 1, . . . , . 5. Calculate the relative closeness to the ideal solution. The relative closeness of the alternative with respect to * is defined as (9) (10) (13) (14) (15) * =
− * + − surpasses other ML algorithms by solving many data science problems faster and more accurately than its counterparts. Also, this algorithm has additional protection from overfitting.
The objective function to be optimized is given by (16) where is the number of iterations, (, ˆ) is the training loss function, ˆ = ∑︀
=1 is the number of trees, Ω is the regularization term, ∈ ℱ , and ℱ is the set of possible classification and regression trees.
Writing the prediction value at step as ˆ(), gives ˆ() = ∑︁ () = ˆ(−1) + (). (17) =1 Next, a tree which optimizes our objective is chosen.
() = ∑︁ (, ˆ) + ∑︁ Ω() = =1 =1 = ∑︁ (, ˆ(−1) + ()) + Ω() + ,
=1 where is a constant.
To minimize the probability of overfitting, the complexity of the tree Ω( ) is defined as (18) (19)
Decision tree is a type of supervised learning algorithm that can be used in both regression and classification problems [10]. Each node is related to an attribute, whereas the leaves of the tree represent the final solution as the result of combining values of the attributes.
The splitting process is stopped after a particular stopping criterion is met. For example, a given threshold for the minimum number of observations left in a node being reached or a given threshold for the minimum change in the impurity measure not succeeding any more by any variable can be a stopping criterion [11].
Let be the initial dataset made out of training samples with known dependent variable values. At first, the tree will be made of only a root node 1 which represents the full set of variables. The objective is to split the nodes into two decision nodes until a terminal node is reached, for example splitting into and , then splitting and into further sub-nodes until a stopping criterion is met [12].
Random forest is a ML algorithm that constructs a multitude of decision trees at training time. The main principle of constructing a random forest is that it is formed by combining solutions from binary decision trees made using diverse subsets of the original dataset and subsets containing randomly selected features from the feature set.
Constructing small decision trees that only have a few features takes up only a little of the processing time, hence the majority of such trees’ solutions can be combined into a single strong classifier.
Steps for constructing a random forest as presented in [10] are as follows: 1. First, assume that the number of cases in the training set is . Then, take a random sample of these cases, and use this sample as the training set for constructing the tree. 2. If there are input variables, specify a number < such that at each node, random variables out of the can be selected. The best split on these is used to split the node. 3. Each tree is subsequently grown to the largest extent possible and no pruning is needed. 4. Aggregate the predictions of the target trees to predict new data.
5. Finally, a decision is made by the majority rule.
XGBoost is a ML algorithm that implements frameworks based on Gradient Boosted Decision Trees [13]. XGBoost where W is a weight vector, namely, W = {1, 2, . . . , }; X is a set of training data made of number of objects, number of attributes and an associated class label ; and is a scalar constant.
Ω( ) = +
The goal of SVM is to find the maximum separating
hyperplane that would have the maximum distance between
the nearest training data objects [
WX + = 0, (21)
The distance between hyperplanes, denoted as 2/||W||, has to be maximal. Consequently, this means that ||W|| (the Euclidean norm of the vector W) has to be minimized. To simplify calculations, the Euclidean norm ||W|| can be swapped for ||W||2/2. Thus, the objective function for this optimization problem is defined as: min 1 2
W, 2 ||W|| , (WX + ) ≥ 1, = 1, . . . , , where the constraint (23) ensures that all objects from the training dataset will be positioned on the correct side of the appropriate marginal hyperplane.
The Lagrange multiplier strategy allows combining these two conditions into one: min max W, ≥0 {︃ 1
}︃ 2 ||W||2 − ∑︁ [(WX − ) − 1] .
=1 (24)
Kernel functions are used when the training dataset needs to be transformed into a higher-dimensional space due to the data being linearly inseparable.
(X, X ) = (X)(X ) , ∀X, X ∈ X. (25) In this study, the Gaussian radial basis function kernel was used: (X, X ) = e−||X−X ||2 , (22) (23) where the value is derived from the following equation: 1 ≈ MED,=1,...,(||X − X ||). (26) Here MED is the median. Usually parameter is found through trial and error.
The KNN algorithm is a method based on objects likeness
[
The Euclidean distance was used to calculate the
distance between objects.
The significance of regression in a model is usually
calculated using the coeficient of determination [
2 , 1 − 2 where 2 is a residual dispersion from a forecast model, 2 – dispersion of .
However, the adjusted coeficient of determination
2 is better suited for comparing regression models
as it avoids the inaccuracy, caused by numerous factors
in the coeficient of determination [
2 = 1 − (1 − 2) · − − −1 1 , where is the number of observations available for analysis, is the number of variables.
Moreover, statisticians are used to measuring accuracy
by computing mean square error (MSE), or its square
root conventionally abbreviated by RMSE (for root mean
square error). The latter is in the same units as the
measured variable and so is a better descriptive statistic.
Moreover, it is the most popular evaluation metric used
in regression problems. RMSE follows an assumption
that errors are unbiased and follow a normal distribution.
RMSE metric is given by [
= ⎷⎸⎸ 1 ∑︁( − )2, =1 (29) where are the observations, are the predicted values of a variable.
Moreover, the average magnitude of the forecast errors can be measured by the mean absolute error:
= 1 ∑︁ | − |. (30)
=1
In this case, the direction of errors is not being considered
[
There are various ways to improve models depending on the technique involved. The most popular way is to construct ensemble models. Once there are multiple models that produce a score for a particular outcome, they can be combined to produce ensemble scores. For example, a new score can be calculated as the average of two classifiers and then assess it as a further model. Usually, the area under the curve improves for these ensemble models. (27) (28)
procedure, first attribute weights had to be established.
Since the drivers must be ranked in compliance with at- Table 3 tribute priorities dictated by a company, their importance Score distribution with diferent weight sets was evaluated by an expert on a scale from 1 to 10. This is presented in Table 2. Thus, we get the first set of weights: where 1 = 0.09 is the weight of Free rolling distance, 2 = 0.19 is the weight of Engine overloaded distance, Excess idling and Overspeeding time, 3 = 0.13 is the weight of Highest gear distance, 4 = 0.15 is the weight of Extreme braking events, 5 = 0.07 is the weight of Harsh braking events.
However, since the importance of attributes can be biased, a baseline weight model was also tested.
Results of ranking methods. Ranking of the drivers was performed using the generated sets of weights. Criterion values, computed by TOPSIS () and VIKOR () methods, were used to rank the drivers. However, in many instances the diference between two values of the same criteria had been minute, hence the values were grouped. Values were grouped using a ten-point system.
Considering the results of diferent ranking methods presented in Table 3, the method with the most logical ranking of the drivers was confirmed to be with the VIKOR method. In addition, the first weight set should be used when creating a dataset for the forecasting models, since it would comply with the attribute priorities from the company and no significant diference was observed between the two tested sets of weights.
For improving the forecast of ETA, it was enough to forecast deviation from planned duration, because this variable had already been computed by routing service.
In that case, the goal was to forecast the deviation from planned tour duration. Overall five ML methods were tested: decision tree, random forest, XGBoost, support vector machine (SVM) and -Nearest neighbours (KNN).
Quantitative variables were normalized using min-max normalization, while the categorical variables were transformed and added to the models by replacing them with binary dummy variables.
Therefore, when applying the random selection and assignment of the set indices to the test and training sets, 75% of the dataset was assigned to the training sample and 25% to the test sample. Cross-validation was used for the selection of optimal parameters in all five models. During this procedure in the regression models, the sample data was divided into 10 groups.
Further, the optimal parameters of all models are determined: load of data. Such partial selection of a sample ˆ – of the SVM model. The adjusted coeficient of occurs once per each iteration. The maximum determination of this ensemble model resulted in 0.7672. number of repetitions was determined to be 150. Another way to form an ensemble of models is by using 4. The -Nearest neighbour model. The param- the weighted sum method. In this type of ensemble, the eter for KNN model was established to be equal to prediction value of the better model (in this case the 4. This value was selected by changing the param- random forest model) is determined to have a weighting eter value from 1 to 10 and determining which coeficient 1, that is less than 1, but not less than 0.5. parameter has the smallest RMSE value. The Eu- However, the total amount of weights must be equal clidean distance measure was used to estimate to one, therefore, the weighting coeficient of the other the distance between the points. model (SVM model) 2 shall be greater than zero, but less 5. The SVM model. The number of support vectors than 0.5. Then, the new predicted value could then be was established to be 1008 and the Gaussian radial obtained as follows: basis function kernel was used. (32) (33) (34) The equation must be met, thus (32) can be written as: ˆ = 1 · ˆ + 2 · ˆ .
1 = 1 − 2 ˆ = (1 − 2) · ˆ + 2 · ˆ .
In order to find with which weight the adjusted coefifcient of determination of the ensemble model obtains the highest value, the value of 2 was being changed from 0.01, 0.02, 0.03, and so on to 0.49. The experiment resulted in a maximum value of 2 (0.7795) when 2 was equal to 0.2. The second way of constructing an ensemble model resulted in a higher 2 than the first method, hence, the second was more suitable. Therefore, the expression of the final ensemble model was as follows: ˆ = 0.8 · ˆ + 0.2 · ˆ .
(35) The forecast graph of the created ensemble model is presented in Fig. 1. Some outliers remained poorly predicted, but the overall prediction is accurate. Metrics evaluating
The accuracy of all five constructed models was evaluated by predicting values of deviation from planned tour time for unseen test set data. The adjusted coeficient of determination 2 , RMSE, and MEA were calculated to determine and compare the suitability of the prediction models. The results are presented in Table 4. It can be seen that for all three accuracy measures, the best results for predicting test data were obtained using a random forest model, where the mean absolute diference between the predicted and actual values had been almost 684, the square root of the average squared diferences between the predicted and actual values had been 1 120.15, and the adjusted coeficient of determination had been 77.57%.
XGBoost model yielded quite similar results, where 2 had been lower by only 3.3%, the MAE error had been higher by 93.24 units and the RMSE had been higher by 90.83. The worst prediction results were obtained using KNN method, for which 2 had been less than 25%.
A possibility to improve the models by forming an ensemble model was observed, hence a decision was made to try a combination of predictions from two models: the random forest and SVM. Several combinations were made. The first method estimated the average of the forecasts of both models: ˆ = ˆ + ˆ , 2
(31) where ˆ is the predicted value of the th observation for the model ensemble, ˆ are the predicted values of the th observation of the random forest model and the created ensemble model are presented in Table 5. In comparison to the results of individual models (Table 4), higher accuracy could be observed in all three metrics of the ensemble model. Nonetheless, the improvement in accuracy was not significant: the adjusted coeficient of
We thank Tadas Motieju¯nas, Darius Ežerskis, Viktorija Naudužaitė, Donatas Šumyla and UAB Ruptela (https: //www.ruptela.com/) for cooperation and useful insights. determination was higher than the best individual model by only 0.38%, the RMSE was lower by 1.87, and MAE was lower by 0.47. In this research, in order to improve the forecast of contemporary ETA, the possibility to rank the drivers based on their behaviour data and predict deviations from planned arrival time using diferent ML methods were analysed. For this purpose, a dataset consisting of vehicle monitoring data was used for ranking the drivers with TOPSIS and VIKOR methods. It was found that the results of the VIKOR method with the company’s attribute importance weight set produced the most suitable drivers’ scores. Then, these scores were used to supplement a new dataset constructed for ML methods. Moreover, five methods: decision tree, random forest, XGBoost, SVM, KNN, were used to create the deviation from the planned tour duration forecasting model. Finally, the ensemble model based on the random forest and SVM resulted in the most accurate results (2 = 77.95%).
In the future, it is planned to continue the construction of the improved ETA prediction model by including real-world parameters that a vehicle takes into account while driving a certain route. For example, the need to stop for mandatory driving breaks or filling up would be considered.