Multi-Criteria-Based Optimization Model for Sustainable Mobility and Transport

: This paper deals with problems of freight transport sustainability from the perspective of four key factors: greenhouse gas production, fossil fuel dependence, congestion, and accident rates. It is based on the results of the FreightVision project, in which the author participated as a researcher and member of the design team. The aim was to develop a set of 35 recommendations to serve as a tool for European Union decision-making in transport policy matters at the highest level. The developed measures were prioritized, and a list of individual recommendations was drawn up according to their potentials. Then, the set of measures was processed using multi-criteria analysis tools, and these results were compared with the original list using comparative analysis to identify differences between the two approaches. The contribution of this work is the development of a methodology for evaluating the trafﬁc measures according to their priorities and, at the same time, the veriﬁcation of the empirical results thus obtained with the results that were the output of the mathematical processing. This work ﬁlls a research gap in a similar problem area by working with speciﬁc measures systematically developed for the purposes of analysis; these results are used to formulate recommendations for the European Commission whose policy decisions should lead to an increased level of freight transport sustainability


Introduction
Transport policy has been an integral part of the European Union's common policy for over thirty years. In addition to the opening of transport markets and the creation of a trans-European transport network, the European Commission is seriously addressing the model of "sustainable mobility", particularly in the area of the steady increase in greenhouse gas emissions from the transport sector, a factor which poses a serious threat to the achievement of the stated objectives of improving air quality. Transport policy is supported by Article 4(2) (g) and Title VI of the Treaty on the Functioning of the European Union [1]. Since the entry into force of the Treaty of Rome on 1 January 1958, member states have focused on a common transport policy, one of the first areas to be addressed jointly, and have begun to make efforts to shape it. The basic priority was the creation and opening of a common transport market and free environment for the provision of transport services [2]. At the same time as the opening of the transport market, an environment of competition is emerging in the field of individual modes of transport and multimodal transport. At the same time, national laws, regulations, and administrative measures relating to the technological, social, and fiscal environment in which transport services are provided are being harmonized, a process that is becoming increasingly important [3]. The volumes of goods and passengers transported have been steadily increasing due to the results of the opening and liberalization of transport markets and the EU internal market, the formal abolition of borders, price reductions, and technological innovation [4]. However, an economically successful and dynamic transport sector must also face some serious threats, especially those related to the environment, and therefore the "sustainability model" is becoming increasingly important [5].
Despite the efforts made, the European transport policy faces many sustainability challenges. The transport sector accounts for around a quarter of the total man-made greenhouse gas emissions in the European Union. Moreover, transport is the only EU sector whose greenhouse gas emissions have increased since 1990. For this reason, the article "Towards a unified European transport area" contained in the White Paper recommends a target of a 20% reduction in transport emissions (excluding international maritime transport) between 2008 and 2030 and a reduction of at least 60% between 1990 and 2050. Additionally, a 40% reduction in emissions from international maritime transport between 2005 and 2050 is recommended. The 2001 White Paper states that it is realistic to increase the use of low-carbon fuels in air transport by 40% by 2050 while reducing the number of conventionally fuelled cars by 50% by 2030 and phasing them out completely by 2050 [6].
This work deals with the problems of reaching a sustainable freight transport system. Sustainable development must take into account three dimensions: economics, environment, and society; therefore, this problem includes a lot of different aspects [7,8]. With respect to European freight transport, these aspects are of various levels of importance because freight transport has a limited impact on some of them. Therefore, this work focuses on a subset of sustainability aspects currently considered the most critical ones with respect to the sustainable European transport system because their development is still not clearly sustainable [9]. Moreover, they were explicitly mentioned in the mid-term review of the European Commission's 2001 White Paper on Transport. These aspects are greenhouse gas (GHG) emissions, dependence on fossil fuels, fatalities, and congestion. However, the goal of the work represents recommendations to the Directorate-General for Energy and Transport on how sustainable development can be achieved for these four criteria without negatively impacting the other sustainability criteria [10,11].
As for unsustainable development with respect to GHG Emissions, the environmental aspect of European transport (within the scope of the EU-27 member states) was unsatisfying in the past. In Europe, transport's GHG Emissions (expressed in CO 2 equivalents) increased between 1995 and 2020 by 17% (European Commission 2020), whereas Europe's total emissions were reduced (-6%). Therefore, transport's share increased from 16% to 19.5%. Within this timeframe, GHG Emissions decreased in all sectors except the transport sector (European Environment Agency 2021).
The major problem is given by dynamic development caused partly by a strong freight transport performance (in tonne-kilometers) increase of 38% which was higher than passenger transport growth (25% pkm-passenger kilometers) and even moderately higher than economic growth (36% of gross domestic product). The technical improvements in freight transport were lower than the transport demand increase. If freight transport continues to have very strong growth rates in the future and will not be decoupled from GDP growth, there is definitely a sustainability problem considering the IPCC's (Intergovernmental Panel on Climate Change) reports on risks involved with GHG Emissions.
In the case of unsustainable development with respect to fossil fuel share in 2020, Europe's import dependency on oil was 82.6% (European Commission 2020). Transport's dependence on oil was about 95% (European Commission 2021). As oil seems to be a finite natural source, one of the main questions is when this source will be exhausted. The term "Peak Oil" refers to the maximum rate of production of oil in any area under consideration. There are different opinions on when this point in time will be reached (or already has been reached), but this work looks at a timeframe from the present until 2050-there seems to be a high consensus that peak oil will be reached before then. However, considering that sustainable development should "ensure that it meets the needs of the present without compromising the ability of future generations to meet their own needs" (United Nations 1987), the current transport is apparently not sustainable with respect to energy usage.
As for unsustainable development with regard to road fatalities in 2020, Europe's road transport system caused 54.318 fatalities. In addition, 1,512,643 people were injured in road accidents (European Commission 2021). Although very strong improvements in road safety have been made in past decades, further improvements are needed for a sustainable transport system. The White Paper's (European Commission 2001) goal to reduce the number of road fatalities by 50% between 2000 and 2025 will fail mainly due to the EU enlargement (EU-15 member countries could reduce the number of road fatalities by 42.7% between 2000 and 2025, but the EU-27 member countries could reduce this number by only 29.1%).
In the case of unsustainable development with respect to traffic congestion, there are different numbers on the costs of road traffic/transport congestion varying between 0.7% and 1.8% of the GDP which is generally considered as being too high. Therefore, congestion represents a major economic sustainability aspect causing time losses and increased vehicle emissions, as well as negative impacts on European competitiveness [6].
The objective of this work is to provide policy recommendations for sustainable development focusing on these four described sustainability criteria. Especially, it should answer the following two research questions: -What should be the politically agreed-upon reduction targets for 2050 for these four sustainability criteria? -What should be done by transport policymakers to reach these targets?
Both the questions are answered by proposing an "Action Plan" which is the main result of this work.

Groundwork for Multi-Criteria and Comparative Analysis
In the process of compiling the forecasts, visions, and scenarios, 35 policy measures were identified that could affect the freight transport sector with respect to the four criteria examined-greenhouse gas emissions, fossil fuel dependence, congestion, and accidents. These measures relate to road, rail, inland and maritime shipping, the supply chain, energy suppliers, and fleet providers. The analysis of these measures includes practice (experience) and feasibility; potential impact on the four selected sustainability criteria; arguments for and against; research, technology development and transport policy aspects; key milestones; and conclusions [12].
The identified areas include research and technological development as well as transport policy measures; the managing body is represented by the European Commission's Directorate for Energy and Transport, and the solved problems include a sustainable European transport system. The measures are identified and divided into the following categories: road transport, rail transport, inland and maritime shipping, supply chain, energy suppliers, and fleet providers [13].

Decision-Making Criteria for Key Factors and Weighting
As a rule, determination of criterion weights usually represents an initial step in parsing of a multi-criteria variant analysis model. Further, the information obtained by one of procedures (ranking method and scoring method) is used for determining the preference relationships between the variants depending on the objectives of the overall analysis. The used methods can be used for quantification of a verbal expression of variant scores. Both the methods use determination of criterion weights from ordinal information on criteria preferences and work with ordinal criterion preference information assuming that a solver is able and willing to express the importance of each criterion by assigning ordinal numbers to each criterion or by comparing all pairs of criteria to determine which criterion of the current pair is more important than the other [14]. In both cases, it is acceptable to designate two or more criteria as equivalent ones.
The ranking method is mainly used to determine the weights of criteria when several experts assess their importance. Each of them ranks the criteria from the most to least important. The most important criterion will be given n points (n is the number of criteria), the second most important n − 1 points, and so on, until the least important criterion receives only 1 point. If the criteria are of equal importance, they will be scored according to their average ranking. The weight of each criterion is determined by adding the points received from all experts and dividing them by the total number of points the experts distributed among all criteria. This ensures the sum of the weights of all criteria is equal to 1 [15].
In general, if the j-th criterion is scored with b points (by a single value or by a sum of values in the case of multiple expert evaluations) its weight is calculated on the basis of the relation: This formula normalizes the preference information of the criteria; hence, the procedure is called normalization of criterion weights.
In determination of weights from cardinal information about the preferences of criteria, the scoring method assumes the user is able and willing to determine not only the order of importance of the criteria but also the ratio of importance between all pairs of criteria.
The importance of each of the options under the given criterion is expressed by a certain number of points on a specified scoring scale. Decimal numbers may be used, and multiple criteria may be assigned the same point value. This method is also used for calculating the weights of the criteria in a similar way to the ranking method when more than only one expert evaluates the criteria. Each expert scores each criterion with a certain number of points, the more important the criterion, the more points it receives (using a scale of 0 to 10, the criterion may have a score of 0 from an expert who considers it completely unimportant and 10 points from an expert who considers it absolutely important). This scale for scoring can be also expressed graphically using a line segment. On this line segment, the positions of each criterion are plotted against the ends of the line to indicate the highest and lowest preference. The calculation of the weights from the scores is carried out in the same way as in the case of the ranking method. The values of the weighting vector are normalized according to Equation (1), where b j is the sum of all the points from individual experts given to the j-th criterion.
However, it should be considered whether it is always appropriate to fix the range of the scale at the beginning of the evaluation. This procedure is possible when the solver has a clear idea from the beginning how important the different criteria are for the evaluation of the variants. Then, it is most appropriate to assign the most important criterion the highest possible score, the least important criterion the lowest possible score, and to place all other criteria on a given scale, taking into account not only the scores of these two criteria but also the scores of the other previously placed criteria. It is also possible to proceed in such a way that, in a first step, we carry out a kind of estimation of the scores of the criteria, which we then reassess and remove any discrepancies. Another option is the procedure where we assign criteria scores according to indices with only the order of importance of the first criterion being fixed. Thus, the true extent of the scale will be known only after the evaluation of the last criterion in the set of all criteria [16].
Saaty's method is used to weigh criteria when only one expert is evaluating them. This is a quantitative pairwise comparison method for criteria. A nine-point scale is used to rate pairwise comparisons of criteria (1-equivalent criteria i and j; 3-weakly preferred criterion i over j; 5-strongly preferred criterion i over j; 7-very strongly preferred criterion i over j; 9-absolutely preferred criterion i over j) and intermediate levels (values 2, 4, 6, and 8) can be used. The expert compares each pair of criteria and writes the magnitudes of the preferences of the i-th criterion with respect to the j-th criterion in the Saaty's matrix S = (s ij ): s ij weights of individual criteria If both the i-th and the j-th criterion are equivalent then s ij = 1, if the i-th criterion is weakly preferred over the j-th one then s ij = 3, if the i-th criterion is strongly preferred over the j-th criterion then s ij = 5, if the i-th criterion is strongly preferred then s ij = 7, if the i-th criterion is absolutely preferred then s ij = 9. If the j-th criterion is preferred over the i-th criterion, the inverted values are written into the Saaty's matrix (s ij = 1 /3 for weak preference; s ij = 1 /5 for strong preference; etc.). The square matrix is of nan order as well as reciprocal (i.e., s ij = 1/s ij ) and actually expresses an estimate of the proportions of the weights of the i-th and j-th criteria. All values on the main diagonal of the Saaty's matrix are always number one (each criterion is equivalent to itself). The elements of this matrix are usually not perfectly consistent, i.e., they do not apply s hj = s hi × s hj . for all h, i, j = 1, 2, . . . , n. In the case of a matrix V = (v ij ), whose elements would be the actual weight quotients (v ij = v i /v j ), the above condition would be valid for the elements of this matrix. The degree of consistency is measured, for example, by the consistency index defined by the Saaty's matrix as: where I s is consistency index, I max is the largest eigenvalue of the Saaty's matrix, and n is the number of criteria. The Saaty's matrix is considered as sufficiently consistent when I s < 0.1. The weights v j could be estimated from the condition that the matrix S should have a difference as small as possible from the matrix V. In the usual sense, this would mean minimizing the sum of squares of deviations of the identical elements of these two matrices. To calculate them, it would then be necessary to solve the optimization model: under the condition ∑ n j=1 v j = 1. Where s ij are weights of individual criteria, and v i and v j are criteria. This is a non-convex quadratic programming model that can be computationally complicated [10].
The selection of a suitable set of criteria allows a simple and transparent evaluation of the different options. Quantitative criteria allow easier processing than qualitative criteria. For example, it will be much more difficult to evaluate the process of applying traffic regulations than tabular information on progressive distance-based charging. However, in the context of complexity, use of qualitative criteria cannot always be avoided [17].
Then, the weights are assigned to each criterion in the selected set to determine their priorities. The weighting methods are classified according to the preference information among the criteria available to the expert group. The FreightVision project expert group consisting of Helmreich, Mattila, Antikainen, Hansen, and Malinovský assigned the following weights to the criteria of the key factors which are arranged in the following Tables 1-4 [18]. The technology of ecologically clean trucks 3   The weighting was based on the following aspects: practice and feasibility, business perspective, and potential impact on sustainability criteria (rating scale: -3, strong negative impact; 0, no impact; and +3, strong positive impact). The far-right column shows the averages of the potential values.
Afterwards, the priority ratings assigned to each measure by the members of the expert group were divided into three categories: not recommended, important, and very important. This classification reflects the experience and ideas of the team members and can serve as one of the decision support tools for the European Commission in transport policy matters.
However, it is not the only solution and, therefore, further analyses should be carried out, such as a comparative analysis of these results with the results of the multi-criteria analysis of options, which is the subject of the next section.

Multi-Criteria Analysis of Variants
Multi-criteria decision-making models depict decision problems in which the consequences of a decision are assessed according to multiple criteria. Multi-criteria characterize almost every decision situation. Considering multiple criteria in evaluation introduces difficulties into problem-solving and conflicts arise from the general controversy of criteria. Indeed, if all criteria pointed to the same solution, only one of them would be sufficient to choose the most appropriate decision. The purpose of the models in these situations is either to find the "best" option according to all considered aspects, to exclude ineffective options, or to organize the set of options. Approaches to multi-criteria decision-making vary according to the nature of the set of options or admissible solutions. According to the method of specification, two groups of such models can be distinguished-multi-criteria variant evaluation models specified using a finite list of variants and their rankings according to each criterion and multi-criteria optimization models with a set of variants with infinitely many elements expressed by means of constraints and the evaluation of each variant is given by individual criterion functions.
The theory and model of multi-criteria variant analysis deals with the problems of how to select one or more variants from a set of admissible variants and recommend them for implementation. The decision maker should proceed as objectively as possible in the selection of alternatives and, for this purpose, the apparatus of various procedures and methods of analysis of alternatives is used. Sometimes, it is possible to separate the person of the task assignor from the person of the task solver (analyst). This procedure has its advantages and disadvantages. The advantage is that the analyst is rarely interested in the outcome of the decision and therefore acts as objectively as possible. The disadvantage may be that the analyst is not familiar with all the details of the task which could not be captured by the model when the task was assigned. Therefore, although the result may be a recommendation of what is objectively the "best" option, in practice, another option that, for example, ranked in the second order could be better, especially with small differences in the values of the aggregate decision criterion. In multi-criteria variant analysis (or ranking) models, a finite (discrete) set of m variants is given which are ranked according to n criteria. The goal is to find the variant that is ranked best overall according to all criteria, the compromise variant, or to rank the variants from best to worst or to eliminate inefficient variants. Options are concrete decision options, the subject of their own decision-making, and they are feasible and not logical nonsense. Options must be carefully selected to be achievable and to be a suitable solution. The options are then evaluated against each of the criteria. A criterion is an aspect of the evaluation of options and can be qualitative or quantitative [19].
Multi-criteria analysis (evaluation) of variants represents a complex of methods from the field of operational research whose purpose is supporting decision-making processes based on post-judgment of given variants (criteria) described by sets of elements representing multiple sub-criteria that may conflict with each other [20]. This analysis is intended especially for supporting complex decision-making, where individual variants need to be assessed according to a larger number of aspects.
The multi-criteria decision process is usually described by two types of components. The first group includes the set of variants, the set of evaluation criteria, and the set of links between the criteria and the variants (allowing the definition of the evaluation function), and the second group includes the selection method (allowing the formulation/construction of the multi-criteria mathematical model). For a multi-criteria mathematical model, the input needs to be defined in terms of additional information not yet included in the model due to impossibility of their explicit description [21]. Usually, the most common form of this additional information is a set of subjective preferences of the decision maker defined over a set of stated criteria.
The main objective was to establish a set of recommendations for the European Commission concerning the identified problems of freight transport in the EU transport area which have been prioritized by the FreightVision expert group, of which I was a member, under four main criteria/key factors: greenhouse gas production, dependence on fossil fuels, congestion, and fatalities. The contribution of this work represents the elaboration of a comparative analysis of the results determined by the group of experts with the results obtained by means of multi-criteria analysis over the variants (key criteria) after their assignation to certain weights (so-called modified Metfessel distribution) and the justification of their differences. Multi-criteria analysis of variance was chosen as the scoring method.
The composition of the model of the multi-criteria evaluation of variants was carried out as follows: The list of variants The list of evaluation criteria C = {c 1 , c 2 , . . . c n } (6) where v i are variants, and c i are evaluation criteria. All variants v i , i = 1, 2, . . . n form a vector of criterion values (y i1 , y i2 , . . . y ik ). Based on this vector, the model of the multi-criteria analysis of variants described by a criterion matrix is created.
The intention of the analysis is to find the optimal variant (set of variants) achieving the best score within the given selection criteria.
According to the methodological description presented above, a multi-criteria analysis was carried out using the scoring method; results were compared with the significance of the mentioned 35 recommendations (stated as "potentials" in Tables 1-4) determined on the basis of heuristic analyses carried out by the FreightVision expert group without using mathematical methods.
Four key factors (greenhouse gas production, fossil fuel dependence, congestion, and accident rates) were chosen as the criteria for the multi-criteria analysis. Weights were assigned to the criteria using a heuristic method. They determine the weight vector → W (0.42; 0.35; 0.12; 0.11) as follows: GHG production (0.42); dependence on fossil fuels (0.35); congestion (0.12); accident rate (0.11).
By uniting Tables 1-4 in the Excel spreadsheet, a comprehensive structure of all 35 measures for all four key criteria was created with assigned weights, and the weighted totals (Table 5) for each measure were automatically calculated according to the formula: where X . . . weighted total, − x i . . . average of given measure, w i . . . weight of given key factor.
The calculated weighted totals for each measure are described and discussed in the following section.

Evaluation of Multi-Criteria Analysis Results
The overview given below (Table 6) contains potentials calculated on the basis of weighted values determined by the FreightVision experts group. The potentials shown indicate the importance of individual measures that should be taken into account in future planning and decision-making by the European Commission in the context of EU transport policy. The higher the value of a potential (weighted total), the higher the priority of a specific measure.  For better transparency, the data from the table has been arranged in the following diagram ( Figure 1). For better transparency, the data from the table has been arranged in the following diagram ( Figure 1).
The calculated weighted totals for each measure for all criteria used as inputs can be found in the following graph ( Figure 1).  The calculated weighted totals for each measure for all criteria used as inputs can be found in the following graph ( Figure 1).
Both the table and chart of potentials for each measure serve as tools for a quick assessment of the priorities that should guide transport policy decision-making at the highest level.

Comparative Analysis
While the results of the multi-criteria analysis are of good quality due to the experience of the group of experts who organized the measures and the weights they assigned to them, they are nevertheless affected by the presence of the human factor. For this reason, it is interesting to carry out a comparative analysis of these results with the results of the criterion analysis of the variants described and carried out in Section 2.3.
The following table (Table 7) integrates the results of the recommendations for individual measures carried out by the members of the expert group (columns titled "not recommended", "important", and "very important") ( Table 5) and the results of the multicriteria analysis based on the weighted sums of the potentials of the individual measures (column MCA) ( Table 6). The analytical table shows that the results obtained by these two different methods differ significantly in some cases. For example, in the case of the measure "Fossil fuel taxation", the experts rated it as moderately important while the calculation in the multi-criteria analysis corresponds to the highest level of importance [22].
One other option for how to improve the common output of both methods would be the creation of compromise (averaged) results of both approaches or the use of a neural network-based algorithm. This area could be the subject of further research.

Action Plan
The Action Plan aims to achieve a sustainable transport system by moving towards a scenario defined by a set of measures (EC recommendations). Policy actions should therefore aim to influence and determine the development of key characteristics (factors). Policy actions are therefore evaluated according to their impact on key factors, i.e., not according to their impact on the characteristics set against the sustainability criteria. This can be achieved by matching the most effective policy measures to each key characteristic.
In the framework of this work, 35 policy measures to influence the freight transport system in the EU have been identified and analyzed. Two different policy areas have been brought together in this exercise, which are synergistic but usually treated separately: research (RTD) and transport policy. The reason why these aspects are not usually discussed together is to some extent organizational. These two policy areas are usually handled by different ministries or departments in the member states. In addition, the staff in the ministries have different backgrounds and experience, as R&TD people usually have a technological background, whereas staff in transport ministries have mainly a legal background. However, these areas are combined here because the challenges are so challenging that they cannot be addressed in only one of these two areas. Therefore, an integrated approach has been taken, combining the development of new technologies with relevant policy criteria. Under this approach, the following options are available: if the appropriate technology is developed, policy criteria can set the right framework for the market, so that price and other market signals will drive the rapid deployment of innovative technologies. In addition, policy criteria can provide incentives for faster development of innovative technologies necessary to address the challenges in the long-distance freight sector. The main objective of this approach is therefore an action plan that optimally links research and technological development policy and transport policy.
The Action Plan is a combination of R&TD and transport policy tasks for each of the most effective policy actions, taking into account each of the key characteristics. The Action Plan was composed of the following two steps: the selection of the most effective policy actions and the identification of tasks for the selected policy actions.

Conclusions
The comparative analysis of the importance of the individual recommendations of the FreightVision Expert Group (columns titled "not recommended", "important", and "very important") and the weighted totals representing the importance levels of these measures obtained by the multi-criteria analysis (MCA) carried out by the scoring method shows that the importance levels of the measures obtained by the two methods differ considerably in a number of cases. This can be justified by the manifestation of the human factor where the process of determining significance by a group of experts is influenced by the different experiences and perceptions of the individual members, which may be influenced by different interests, ideas, and also by the country of origin, as individual regions may differ considerably in relation to each recommendation. Then, the construction of the vector of weights will influence levels of significance that generate resulting values that differ from those obtained without the use of mathematical methods.
It could also be a subject for further research to model a set of significance levels for individual measures using different configurations of the weight vector → W and to analyze the projection of changes in the weight values of certain criteria onto individual measures [23].
Sustainability problems are mainly caused by road transport and will have to be addressed there. In short: policy will not achieve a sustainable freight transport system unless the focus is on improvements in road transport. This focus will not only be positive for road transport-it will increase the pressure to achieve a sustainable road transport system. The impact on the rail and inland waterway systems is difficult to predict. If road transport succeeds in achieving the objectives defined in this paper, and thus becomes increasingly sustainable and able to maintain its economic competitiveness, then other modes will find it difficult to increase their market shares, while at the same time creating reasons to invest in public infrastructure. There is a certain risk associated with this future development, particularly for rail transport. In the event that the recommended measures for road transport cannot be maintained, this will present an opportunity for rail transport. However, this can only be exploited if clear objectives are set and the consequences for both road and rail are defined.
In addition to its original purpose, i.e., to perform a multi-criteria analysis in order to formulate policy recommendations for the European Commission, this work can also serve as a basis for future research and further studies in the field of freight transport development in relation to other key factors or in other regions of the world.