1. Introduction with the Literature Review
Suburban railways play or should play an important role in agglomerations as the main means of transport connecting the core with the surroundings. Significant numbers of lines, journeys, and seats can affect the choice of means of transport. This creates environmentally friendly travel. Modeling the use of suburban railways should take into account two main aspects: (a) rail operations and (b) cooperation in the transport system. A suburban railway works similarly to all other railways. It is slightly closer to metro systems due to high frequency, while being unlike long-distance rail due to higher stop density and lower speeds. Therefore, the typical problems of planning rail operations should be taken into account. There are numerous studies on these problems.
Table 1 contains the list of publications analyzed in this paper concerning the considered problems and heuristic tools. In [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24], researchers address the problems related to railway modeling, and the authors of [
25,
26,
27,
28] consider the demand side of transport systems. It is worth noting that [
29], discussed below, does not exist in the table because of its review character. In [
30,
31,
32,
33,
34,
35,
36,
37], researchers address the problems of integration in a suburban transport system. Sources [
38,
39] show directions for future research, and sources [
40,
41,
42,
43] contain important definitions (they were not added to the table). In [
44,
45,
46,
47,
48,
49,
50,
51,
52,
53], authors present different tools used to solve some problems (partially not as transportation problems, but with methodologies inspiring the method presented here). The tools are discussed in
Section 2.
Sometimes the problems classified in
Table 1 are more complex. Dong et al. [
7] integrate the planning of train stops with the timetable, and Yan et al. [
2] integrate the timetable with route planning. Wang et al. [
12] and Zhao et al. [
19] combine train timetables and rolling stock. Zhang et al. [
16] integrate train timetables and track maintenance scheduling.
The above characterized examples illustrate the offer (supply side of the transport system). On the other hand, the result in the form of passenger flow (demand side of the transport system) was taken into account, inter alia, in: Xiao et al. [
25], Shen et al. [
26], Wu et al. [
27], and Liu et al. [
28]. These works include passenger flow as a direct result of modeling or simulation. In many studies, passenger flow is a factor influencing the modeled parameters, such as train schedules.
Rail is not the only means of transport in suburban areas. The railway is or should be one of several integrated components that work together at different levels. Access to rail should be improved by means of “complementary tools or means of transport”, forming a “delivery system” that includes local buses, private cars including car sharing, bicycles including rental, etc. It is important to optimize local systems, create nodes, and integrate tariffs and cost coordination. The importance of coordination studies is shown by a review by Liu et al. [
29], who identified 135 papers on these topics. Further problems are related to the developing autonomy of vehicles. Examples of studies from recent years concerning cooperation in transport systems are presented in
Table 1 ([
25,
26,
27,
28]).
Many parameters were taken into account in the models presented above. For example, Ahmed et al. [
6] collect 27 input parameters, including: average travel speed, train headway, number of stations, spacing between stations, etc. The number of input parameters in Dong et al. [
7] is 21 and includes, inter alia: the number of passengers arriving at the station, the number of trains, etc. A specific parameter is “passenger satisfaction” or “dissatisfaction” (Hickish et al. [
3], Satoshi et al. [
22], Stead et al. [
34], Shen et al. [
26]). Shen et al. [
26] formulate nine elements creating passenger satisfaction: direction and guidance, cleanliness and comfort, speediness and convenience, safety and security, ticket service, equipment and facilities, staff service, information distribution, and convenient facilities for passengers.
Specific review studies (Liu et al. [
29], Tang et al. [
38]) formulate directions for future research. Integration with various planning activities is important. Data quality, data limitations or imperfections, uncertainty, and passenger behavior should be carefully considered. Modeling analyses should be more complex and include, inter alia, multi-objective optimization, multi-agent systems, and negotiations. Comprehensive and more flexible approaches will pay off.
All the parameters presented above affect the use of suburban railways. However, not only the “physical” ones (easy to identify and measure), such as speed or numbers, are important. Other parameters that are more difficult to identify and have a “psychological” aspect should also be taken into account. Lopez and Farooq [
39] state that “
transportation data are shared across multiple entities using heterogeneous mediums”. Such data vary on certain days (not only working days and holidays, but some typical working days may also differ in passenger flow depending on weather, accidents, and random factors). The influence of bounded rationality and unbounded uncertainty is significant (Khisty and Arslan [
40]). Similar problems are discussed by Li et al. [
41] and Wu et al. [
27]. They wrote that the assumption of rational passenger behavior is not correct. Taking into account the behavior of passengers requires the use of advanced and unconventional tools in modeling. Tools inspired by nature and social behavior are called “artificial intelligence” (AI) or “heuristics” (in a broader sense, not just as an optimization tool).
The main research goal of this paper is to create a new algorithm (NOAH) not as an optimization tool but as a method of observation of selected datasets. The reason for this is the problems with the identification of the close set of important factors and with the collection and selection of the data. Known and used methods have other assumptions. The proposed algorithm allows us to find new and nonobvious connections between the factors (these are not correlations in the strictly mathematical sense). Assumptions to create an algorithm will be formulated after the presentation of the heuristics (
Section 2). The rest of this paper is organized as follows:
Section 3 presents the new algorithm, and
Section 4 shows an example of its application (with the description of the case study area,
Section 4.1; collection of factors,
Section 4.2; and two experiments,
Section 4.3 and
Section 4.4). The last two sections contain a discussion and conclusions.
2. Heuristics as Inspirations from Nature
The term “heuristics” will be used here in a broader, philosophical sense, as defined by Kahneman [
42]: “a heuristic is a mental shortcut that our brains use that allows us to make decisions quickly without having all the relevant information”. In more “technical” literature, this concept or tool is often referred to as “computational intelligence” or “artificial intelligence”. Regardless of the name, such tools are very popular and efficient in solving many problems, including modeling railways. Many tools developed in the last few decades can be considered “heuristics”. Tang et al. [
38] identify 139 articles from the last decade on the use of heuristics in railway systems.
The third column in
Table 1 presents tools used to solve the collected problems. Most of them are heuristics. An element inspired by nature, especially simulated human or animal behavior, is important. New developments in “metaheuristics” and their applications are presented by Lau et al. [
43]. They evoke, among others, a new method called “flying elephants” (Xavier and Xavier [
44]), which shows interesting and intriguing assumptions and solutions.
Some studies include more than one tool, including Yang et al. [
35], who compared the effectiveness of GA and MINLP. The set in
Table 1 contains only selected sources from a very large database. The selection focuses on methods dedicated to railway modeling or on tools that will be inspirations for the method formulated in this paper. Specifically, these are relatively new studies using PSO, SCO, BCO, SOM, blockchain, multiagent, or BBO methods. For example, Zheng et al. [
21] used the earlier concept of Simon [
54], biogeography-based optimization, to analyze emergency railway wagon scheduling. Similarly, Hua et al. [
51] used the Nakamoto blockchain concept [
55] for intelligent control on heavy haul railways.
Summarizing the above description, the conditions for a new model of suburban railway use are summarized below. Railways function in the transport system, and cooperation with other modes of transport is necessary. We may collect a large amount of data, but we do not know the significance (impact) of each individual piece of information. There are many factors that influence the use of suburban rail, and their impacts may vary from day to day. Passenger behavior (including the choice of means of transport) is not rational. We should consider bounded rationality and unbounded uncertainty. The modeled object (railway in the transport system) is variable. The “optimal” solution probably does not exist; rather, we are looking for an “acceptable” solution. An acceptable solution contains a set of factors that are realizable and make economic sense. The results from the model can support the decision-making process—for example, when choosing a specific option, planning system development, etc. It is desirable to use a dedicated metaheuristic in the new model. SOM, multiagent, and blockchain elements inspire certain assumptions about the new proposal. In particular, solutions based on animal or human behavior will be useful for creating a new modeling tool.
So, the new model (algorithm) should be allowed to compare different data with higher or lower complexity to show potential sets of them. It will be possible to analyze both the existing (observed) data as well as more theoretical values. The process of comparison should be flexible and based on partially random procedures. The assumptions collected above can be realized using a specific heuristic. A novel heuristic will be proposed based on the specific behaviors of monkeys.
3. The NOAH Concept Based on the Behavior of Monkeys
A novel tool created here and called “NOAH” (Nest of Apes Heuristic) is inspired by the social behavior of groups of monkeys. Numerous studies and publications have been devoted to groups of monkeys from different monkey species—such as diana (Decellieres et al. [
56]), vervet (Gareta Garcia et al. [
57]), capuchin (Leca et al. [
58]), gelada (Miller et al. [
59]), or colobus (Wikberg et al. [
60])—which create various nests with specific social behaviors. Colobus monkeys create specific “social networks” based on interactions [
60]. A visualization (model) of such a network is presented in
Figure 1 (part b). Diana monkeys form specific relationships called “dear-enemy” or “nasty-neighbor” depending on the type of habitat [
56]. Distributed leadership has been observed in the nests of white-faced capuchins [
58]. All members can initiate a group movement, and many members recruit followers. Wild female vervets adapt their maneuvering to different pressures [
57]. They are characterized by rapid social plasticity and flexible changes in care patterns (described by the authors as “Machiavellian-like”—this “human” analogy is important here). Miller et al. [
59] identify leaders in gelada nests under the influence of out-of-group paternity. The behavior of such species has been compared with other primates and has been linked to human mating systems, including behaviors jealousy (Scelza et al. [
61]) and reproductive strategies (Scelza et al. [
62]). The implications presented by Miller et al. in [
59] refer to the “weirdness” of various human populations described by Heinrich et al. [
63]. WEIRD here is an acronym standing for western, educated, industrialized, rich, and democratic. The authors conclude that not all human groups can be characterized as above. Other classified groups have different social behaviors. Therefore, their description should assume specific and partially unknown parameters.
Hypothetically and in accordance with the heuristic methods described in
Section 2, the behaviors presented above can be used in an algorithm (NOAH) that can describe not only groups of animals, but also technical systems containing parameters (factors) related to human behavior (like choice of transport means). Especially useful can be changeable leadership in the nest and the behaviors of followers. The parameters will be associated with “monkeys”—individuals in the nest that change their behavior (monkey position) according to specific procedures including leader creation, observations by followers, importance and hierarchy of individuals, dynamic changes in the nest, etc.
Changes to the nest will modify individuals (factors) before the algorithm stops. It will be possible to analyze and observe different sets of parameters (monkeys), their interactions, and their correlations. NOAH does not specify an optimal solution but shows possible datasets for comparison. It helps in choosing one or more. The operation of NOAH is very similar to the SOM (self-organized maps) concept, the stages of the blockchain, or the multiagent concept. A graphical representation of the exemplary methods is shown in
Figure 1. Part (a) of this figure shows an SOM-like network, part (b) shows the colobus monkey nest described earlier, and part (c) shows the monkey nest and interactions between leaders (big black spots) and followers (little black spots) according to the NOAH concept.
Important for the application of NOAH in selected problems is the selection of parameters (factors) and their conversion into “monkeys”. Initially, the selection of parameters is made by an “expert” with the use of all of the available data. After the algorithm is stopped, the re-conversion procedure will follow. These elements will be described in
Section 4 with a specific example. The basic and theoretical aspects of NOAH are presented here. Each monkey has a specific position in the nest that is variable. The monkey position values are limited to a range of 0 to 1 as defined by the procedures in NOAH.
A specific set of terms, parameters, and symbols used in NOAH is defined herein.
Nest (seat, habitat) is a set of individuals (representing factors in the model).
Position of the monkey in the nest, Mn, is a key variable in the algorithm. Each monkey changes its position in the nest, assuming the role of a leader or follower (representing variable values of factors and their importance in the model).
Steps (iterations) of changes in the nest, starting from zero, i = 0, are successive periods with a specific nest state (monkey position, i.e., factor values). The steps will continue until the socket is stable (will not change). See stopping criteria.
Importance of an individual,
In, is a random variable indicating the subjective position of the monkey in the nest. The scope of this variable is determined by Formula (1).
Hierarchy of an individual,
Hn: This is a variable indicating a more objective position of the individual in the nest, assuming an actual value of
Mn, a random importance
In, a moderated followers coefficient
L, and a number of steps
i. The hierarchy is calculated using Formula (2).
Followers coefficient (influence of leaders),
L: This determines the time and efficiency of the algorithm (it should be precisely defined in accordance with the specification of the modeled problem). Its impact increases in subsequent iteration steps—see Formula (2).
L values should oscillate around 1–3 (see example in
Section 4).
Random hierarchy modifiers,
Rn: These are used to modify the position of the monkey going to the next step of changes in the nest. The modifiers depend on the value of the hierarchy, taking into account the defined range of hierarchy modifiers according to Formula (3).
Range of hierarchy modifiers,
Rmin and
Rmax: This also determines the runtime and efficiency of the algorithm; the
Rmin value should be negative and the
Rmax value positive (see example in
Section 4).
NOAH works according to the algorithm shown in
Figure 2. The position of the monkey in the next step is calculated using Formula (4). The position is changed taking into account the values of random hierarchy modifiers with the restrictions determined by Formula (5).
The progressing steps create a changeable nest with individuals who change their positions. That means the changeable values of factors are considered in the model. The leaders (factors with higher importance) are identified, observed, and analyzed. The whole nest (set of all factors) can be analyzed too. The algorithm heads to the nest stability, which means reducing the changes in the monkey’s position during the steps. The tempo of such stabilization depends on the value of the followers coefficient and the range of hierarchy modifiers. However, specific stopping criteria are formulated. In each step the following “decisions measures” are calculated:
M as the sum of all
Mn,
I as the sum of all
In,
H as the average from all
Hn, and
R as the average of all
Rn. Consideration of these measures in the aspect of stopping criteria is shown in the example in
Section 4.
The next steps of the algorithm create a changing nest with individuals of different positions. This refers to changes in the value of the factors included in the model. Leaders (factors of greater importance) are identified, monitored, and analyzed. The entire nest (set of all factors) can also be analyzed. The algorithm aims at nest stability, which means reducing the changes in the monkey’s position during steps. The pace of such stabilization depends on the value of the followers coefficient and the range of hierarchy modifiers. Specific stopping criteria have been formulated. At each step, the following “decision measures” are calculated:
M as the sum of all
Mn,
I as the sum of all
In,
H as the average of all
Hn, and
R as the average of all
Rn. The inclusion of these measures in terms of the stopping criteria is illustrated in the example in
Section 4.
5. Discussion
Table 6 summarizes the important data for all factors. The minimum, maximum, reference (actual), and final values from both experiments are shown. The reference values correspond to the observed (measured) situations. Measurements and data collection were performed in the spring of 2022. The minimum and maximum values are calculated or assumed according to physical conditions or other possibilities. For example, “percentage of spaces occupied” (
F4) can of course vary between 0 and 100%, and “parking volume on PR” (
F7) can vary between 0 and 100, the upper limit being the actual number of parking spaces in all of the considered locations. The “cost” (
F10) could vary from PLN 4.6 to 12.0, which results from the comparison of various fees in the considered journeys between the origin and the destination; “travel times” (
F12–
F14) oscillate between values obtained from measurements or calculated taking into account the possible speeds.
The values obtained in the experiments depend on the values of the parameters adopted in the algorithm: the followers coefficient (L) and the range of hierarchy modifiers (Rmin, Rmax). These values may vary depending on the specifics of the problem under consideration (e.g., depending on a number of factors) and should be tested in the experimental phase of the research. Finally, the values were selected—L = 1.5, Rmin = −0.3 and Rmax = 0.3—as the best according to the decision measure change process. The impact of the abovementioned parameters on the results of NOAH requires further research and will be explored in the future.
The factors values obtained from the experiments should be analyzed as a complex set of parameters. In both experiments, sufficient numbers of trips (F1) and stops (F5) were identified in relation to the values of the other factors. These values led to an intuitive decrease in the number of passengers during the day (F2). Comparing these values with the stable number of residents (F6), there is a need to increase the role of the delivery system. The delivery system is represented here by factors including cars in PR (F7) and passengers arriving from correlated forms of public transport (F8). The travel cost (F10) should be lower. The conditions tested above also show a lower number of journeys by means that compete with rail, both with private cars (F16) and buses (F15).
Some results differ in both experiments. Because the first experiment starts with the “average” values of the factors, the results are close to the middle between the minimum and the maximum. This shows the potential NOAH effect but is not of practical use. The results of the second experiment are more realistic and allow you to judge the real conditions. The maintenance of a clear difference between the travel time of rail travel and those of competitive forms is particularly visible. The results show the possibilities of further use of the constructed methodology and algorithm. For example, it is possible to test other numbers of residents (F6) or numbers of departures (F1). It is also possible to test different values of the minimum and maximum factors. They should allow the modeling of various conditions in the suburban rail system and the observation of correlations between all factors. Initial values of the abovementioned parameters should be carefully collected. This limitation requires further work to be overcome.
The obtained results correspond with actual topics involved in the interdisciplinary field of sustainable urban planning and transport development. Significantly, connection with heuristics used in analyses of transportation and railway systems [
64,
65] occurred. This aspect shows the potential of the proposed algorithm and methodology to be developed in other studies not only connected with railway systems and not only in transportation engineering.
6. Conclusions
The parameters describing a suburban rail system have different characteristics. The set of possible factors is not precisely defined, and the data collection process has specific problems. Some data are incomplete, while others contain errors. The influence of each selected factor and its importance are not fully understood. Therefore, modeling and analysis of suburban rail systems requires specific methods that also take into account human behavior. Here, heuristics as a holistic tool can help in the analysis of possible correlations between factors, as well as be helpful in the decision-making process. The novel method presented here allows using an open set of data. The factors could be different and somewhat “chaotic” at first sight (as in the presented experiments). This is the key innovation in analyses of “technical systems” like the suburban railways considered here.
The main advantage of the proposed method is the creation of the possibility to observe various sets of data and their interactions without precise knowledge about the influence of a specific factor on the result. The data (describing the transportation systems) depend partially on human decisions. For example, the choice of the mode of transport could be a reaction to the behaviors of other people (neighbors, social media groups). So, an individual can observe and copy leaders as a follower. The use of the specific transport means influencing the number of passengers or parking volume in PR has some uncertainties and could be modeled using heuristics.
NOAH, which is inspired by the behavior of groups of monkeys, especially taking into account dynamic changes in leadership, is likely to be useful in specific technical problems where physical parameters (such as the number of departures or stops) are compared with human decisions moderated by travel time, prices, etc. The basic definitions, the procedures, the algorithm, and the potential application of NOAH are illustrated in simple examples with a relatively small set of factors. The NOAH algorithm modifies the values of factors in a heuristic way and shows possible solutions that could be introduced in reality. This method created originally by the author is quite similar to swarm intelligence algorithms (like PSO and ACO) but contains new elements based on specific behaviors of monkeys which were described in
Section 3.
Strict comparison of this new method with others is not possible because of the other goals of those methods. The heuristics search mainly for optimal solutions. NOAH can compare factors, not showing the best result. This is an intentional assumption representing the difficulty of evaluation of data by an individual person. Thus, the evaluation of the effectiveness of the proposed method is difficult, especially in the present stage of research. The study introduced in one of the Polish agglomerations will be continued and should formulate remarks to modify selected elements of the transport system (e.g., number of departures or cost) with the observation of changes in other factors. When the obtained results are similar to the model, NOAH will be effective.
The presented material introduces the new algorithm by showing its procedures that can allow for its use in similar problems. This could test obtained assumptions and improve procedures in the future. Future works should contain influence analyses of the parameters adopted in the algorithm (the followers coefficient and the range of hierarchy modifiers), other (broader) sets of factors, and comprised studies in other areas. The NOAH method could be also used for other problems where incomplete and different data make observations of technical systems difficult.