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ARTICLE   Open Access    

An evolutionary game theory-based machine learning framework for predicting mandatory lane change decision

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  • Mandatory lane change (MLC) is likely to cause traffic oscillations, which have a negative impact on traffic efficiency and safety. There is a rapid increase in research on mandatory lane change decision (MLCD) prediction, which can be categorized into physics-based models and machine-learning models. Both types of models have their advantages and disadvantages. To obtain a more advanced MLCD prediction method, this study proposes a hybrid architecture, which combines the Evolutionary Game Theory (EGT) based model (considering data efficient and interpretable) and the Machine Learning (ML) based model (considering high prediction accuracy) to model the mandatory lane change decision of multi-style drivers (i.e. EGTML framework). Therefore, EGT is utilized to introduce physical information, which can describe the progressive cooperative interactions between drivers and predict the decision-making of multi-style drivers. The generalization of the EGTML method is further validated using four machine learning models: ANN, RF, LightGBM, and XGBoost. The superiority of EGTML is demonstrated using real-world data (i.e., Next Generation SIMulation, NGSIM). The results of sensitivity analysis show that the EGTML model outperforms the general ML model, especially when the data is sparse.
  • Pancreatic cancer (PC) is among the most lethal malignancies, and its mortality closely parallels its morbidity. PC is estimated to be the second leading cause of cancer deaths in the next decade, with incidence increasing rapidly[1,2]. Surgical pancreatectomy remains the only curative approach for PC. Unfortunately, the majority of patients are unresectable at the time of diagnosis due to extensive local spread and metastasis[3,4]. PC is an atypical disease whose symptoms are easily confused with other noncancerous gastrointestinal symptoms, including nausea, abdominal pain, weight loss, and jaundice, leading to later medical consultations. In addition, the pancreas is an easily overlooked organ (16 cm × 6 cm × 2 cm) hidden behind the stomach and duodenum, and pancreatic cancer holds few blood vessels compared to other gastrointestinal cancers, making PC insensitive to imaging detection, such as computed tomography (CT) and magnetic resonance imaging (MRI)[5]. Large-scale screening programs can effectively reduce the disease burden in various gastrointestinal cancers, including esophageal cancer and colorectal cancer. However, there are no noninvasive diagnostic methods that facilitate early diagnosis of population-based PC[69]. This fact sheds light on the necessity for discovering a novel powerful diagnostic approach with higher compliance for PC in the early stages of development.

    The human body encompasses trillions of indigenous microbes, including eukaryota, bacteria, and archaea. Microbiota are a collection of microorganisms that live within/on the human body, and the human microbiome refers to the collective genome encoded by the microbiota[10,11]. Body sites such as the skin, oral cavity, stomach, bladder, vaginal cavity, nasal cavity, and lungs host rich microbial communities; among them, the gastrointestinal tract harbors the greatest density of microbiota, which means the gut microbiota receive the most attention. Bacterial analysis is the main focus when mentioning the microbiota unless otherwise specified. Recently, facilitated by the advancement of high-throughput 16S rRNA sequencing and whole-genome shotgun metagenomic technology, we can gain a glimpse into microbial diversity and abundance[12,13]. Accumulating studies have suggested that the human microbiota plays a vital role in human health, both in physiological and pathological conditions. Given that the microbiota is associated with a variety of diseases, its analysis may help in disease diagnosis, prognosis, prevention, and therapy[1419]. Among several sample sources that can reflect the fluctuation of the human microbiota, such as intestinal mucosa and secretions, stool, and oral saliva are undoubtedly the most noninvasive and accessible means. It has been reported that diagnostic models based on discriminating bacterial species from oral or fecal samples show high sensitivity and specificity in various malignancies, including hepatocellular carcinoma and colorectal cancer[2022]. Further studies reveal that dysbiosis of the gut microbiota participates in carcinogenesis via abnormal metabolites or immune modulation. There are also articles mentioning the relationship between gut microbiota and PC, which provides a basis for the diagnostic value of gut microbiota in PC. Farrell et al. compared oral microbial composition between PC patients and matched healthy controls via Human Oral Microbe Identification Microarray (HOMIM). They identified 16 species/clusters, which showed a significantly different frequency between the two groups[23]. Similarly, Michaud et al. compared antibodies against oral bacteria between 405 PC patients and 416 matched controls and showed that individuals expressing higher levels of antibodies against Porphyromonas gingivalis (P. gingivalis) have a twofold higher risk of PC than those with lower levels of antibodies[24]. In addition to HOMIM and antibodies, there are various methods to investigate the microbial composition, including the long-lasting gold standard, 16S rRNA sequencing[25]. Based on next-generation sequencing technology, several studies aimed to reveal the entirety of the genetic information contained in a sample from PC patients and looked to discriminate bacteria as a diagnostic biomarker for PC[2640].

    Considering the possibility of human microbiota serving as a noninvasive diagnostic tool in the screening of PC, we sought to systematically review the studies revealing different microbial compositions between PC patients and controls and the possible use of the models established on discriminated taxa for the early diagnosis of PC. Given the significant variations between different detection methods for the microbial community, this systematic review focuses only on articles using 16S rRNA sequencing.

    The aim of this systematic review was to collect all original research articles that evaluated the possibility of gut microbiota, measured by 16S rRNA sequencing, as a noninvasive prognostic tool for PC. The research was performed in accordance with procedures recommended by the Cochrane Collaboration.

    A comprehensive literature search for eligible articles was performed in PubMed, Cochrane Library, Embase, and Web of Science up to 20 November, 2024. The search approach followed the combinations of the terms 'pancreatic cancer', 'pancreatic ductal adenocarcinoma', 'pancreatic adenocarcinoma', 'gut', 'fecal', 'stool', 'oral', 'salivary', 'microbial', 'microbiome', and 'microbiota'. Relevant reviews were screened to seek missing studies. Titles and abstracts were screened to remove duplicates. This systematic review was limited to English-language articles only.

    The articles that met all following terms were included in this review: assessed the gut microbial community in oral or fecal samples from PC patients compared with healthy controls, used 16S rRNA sequencing, and found several discriminated bacteria as outcomes. Studies were removed if they were published as letters or case reports, as they failed to provide enough data for the present review. Studies examining fungi or viruses in PC patients were excluded because they did not share the same sequencing method with bacteria. Articles focused on specific bacterial species, such as Helicobacter pylori, were also removed because several meta-analyses related to this topic have been published. The reviewers screened the studies based on the inclusion criteria independently, and disagreements were discussed to resolve the differences.

    Two reviewers independently retrieved the articles. The basic information extracted from the articles was summarized as: study characteristics, population characteristics, and methodologic characteristics. The study characteristics were as follows: first author, publication year, country, publication type, and study type. The population and methodologic characteristics were displayed in terms of sample size, age, sex, body mass index, smoking status, sample source, temperature for storage, measurement method, diversity assessment, and administration of antibiotics or probiotics. To minimize biases, a quality assessment was conducted following the Newcastle–Ottawa Scale (NOS)[41], which is based on three components: the selection of study groups, comparability, and ascertainment of exposure/outcome. Two independent reviewers scored the NOS on major aspects of risk and applicability assessment.

    The search process is displayed in a PRISMA flow diagram, as shown in Fig. 1. A total of 80 papers were retrieved from PubMed, the Cochrane Library, Embase, and the Web of Science. Following a thorough screening of their full titles and abstracts, 18 reviews or meta-analyses were excluded. The full-text articles were further examined and those that did not meet all the inclusion criteria were excluded. Fourty-seven papers were excluded due to the following reasons: use of invasive methods to obtain samples (n = 5), and not being human studies (n = 10); lack of controls (3); not pancreatic cancer (26); other detection methods (3). Finally, 15 further studies were ultimately included.

    Figure 1.  Flowchart.

    Table 1 displays the characteristics of the 15 studies included in our review published between 2013 and 2024. Among the 15 studies, five originated from China, four were from the USA, another two were from Israel and Japan, and one was from Iran and Germany. The majority of studies were published as journal articles, and only two were conference proceedings. Only one of the studies was designed as a prospective study, while the remaining studies were case–control studies. The NOS score ranged from 6 to 8 in the included studies.

    Table 1.  Study characteristics.
    Study Country Publication type Study type NOS score
    Fan et al., 2018[26] USA Journal article Prospective cohort 8
    Torres et al., 2015[31] USA Journal article Controlled 8
    Olson et al., 2017[29] USA Journal article Pilot 7
    Lin et al., 2013[34] USA Conference proceedings Pilot 7
    Lu et al., 2019[28] China Journal article Controlled 8
    Vogtmann et al., 2019[32] Iran Journal article Controlled 8
    Ren et al., 2017[30] China Journal article Controlled 8
    Half et al., 2019[27] Israel Journal article Controlled 8
    Half et al., 2015[33] Israel Conference proceedings Pilot 6
    Kartal et al., 2022[35] Germany Journal article Case–control 6
    Chen et al., 2023[36] China Journal article Controlled 7
    Hashimoto et al., 2022[38] Japan Journal article Controlled 8
    Sono et al., 2024[39] Japan Journal article Controlled 7
    Zhao et al., 2024[37] China Journal article Controlled 8
    Yang et al., 2023[40] China Journal article Controlled 6
    NOS, Newcastle-Ottawa Scale. USA, United States of America.
     | Show Table
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    The population characteristics are described in Table 2. The sample size of the included studies ranged between 28 (13 PC) in the smallest study by Lin et al., and 732 (361 PC) in the largest study by Fan et al. To increase the specificity of the diagnostic taxa, four reviews included other pathological conditions, such as pancreatitis and nonalcoholic fatty liver disease, in the control group rather than healthy individuals only. The majority of journal articles were able to provide necessary demographic information such as age, gender, and body mass index. The sample type included an oral wash, saliva, tongue coat, and stool, which were all obtained by noninvasive methods. Half of the studies emphasized that samples were stored at −80 °C before analysis. It is recognized that the administration of antibiotics, probiotics, and prebiotics may affect gut microbiota. All the case–controlled journal articles limited antibiotic usage when enrolled. Smoking status, a well-known risk factor for PC, also plays a role in gut microbiota analysis, as mentioned in only four articles. Although all these articles adopted 16S rRNA sequencing, hypervariable regions vary with different papers including V3–V4, V4–V5, and V3–V5, while several articles did not mention the hypervariable regions they chose for analysis. Six articles assessed both α-diversity and β-diversity in the analysis, the Simpson index and the Shannon index were the most used as an outcome of α-diversity, and β-diversity is mainly represented by the principal coordinate analysis of weighted and unweighted UniFrac distances. The above description is shown in Table 3.

    Table 2.  Population characteristics.
    Study Sample size Age % male BMI % smoking
    PC Control PC Control PC Control PC Control PC Control
    Fan et al., 2018[26] 361 371 68.5 68.3 57.1 57.1 57.3 49.9
    Torres et al., 2015[31] 8 100
    (other disease 78 HC 22)
    71.1 60.7
    (other cancers)
    75.0 50.0
    Olson et al., 2017[29] 40 97
    (IPMN 39; HC 58)
    < 70, 64.0%; ≥ 70, 35.0% < 70, 42.0%; ≥ 70, 59.0% (IPMN); < 70, 81.0%;
    ≥ 70, 19.0% (HC)
    53.0 56.0 (IPMN); 40.0 (HC) Normal 38.0%; abnormal 61.0% Normal 36.0%;
    abnormal 64.0% (IPMN); normal 43.0%;
    abnormal 57.0% (HC)
    44.0 46.0 (IPMN); 31.0 (HC)
    Lin et al., 2013[34] 13 15
    (pancreatitis 3 HC 12)
    Lu et al., 2019[28] 30 25 50.8 ± 5.3 48.2 ± 6.0 70.0 80.0 22.5 ± 1.2 22.6 ± 1.6
    Vogtmann et al., 2019[32] 273 285 < 70, 63.7%;
    ≥ 70, 36.3%
    < 70, 67.4%; ≥ 70, 32.6% 60.4 46.0 Normal 57.5%; abnormal 42.5% Normal 46.3%;
    abnormal 53.7%
    30.5 25.6
    Ren et al., 2017[30] 85 57 56.0 (33.0–78.0) 52.0 (43.0–67.0) 55.3 63.2 22.7 (19.5–26.0) 23.2 (18.5–27.1)
    Half et al., 2019[27] 30 35
    (NAFLD 16; PCL 6 HC 13)
    68.9 ± 6.2 51.0 ± 10.8 (NAFLD);
    66.0 ± 15.3 (PCL);
    59.0 ± 8.7 (HC)
    53.3 75.0 (NAFLD);
    83.3 (PCL); 46.2 (HC)
    Half et al., 2015[33] 15 15
    Kartal et al., 2022[35] 57 79 (HC 50 CP 29)
    Chen et al., 2023[36] 40 54 (HC 50 CP 15)
    Hashimoto et al., 2022[38] 5 68 70.0−89.0 54.0 40.0 42.6
    Sono et al., 2024[39] 30 18 63.7 63.0 53.3 66.7 22.0 24.5 36.7 88.9
    Zhao et al., 2024[37] 29 9 67.6 ± 10.8 30.5 ± 6.8 58.6 33.3 22.4 ± 2.9 20.8 ± 1.5
    Yang et al., 2023[40] 44 50 47.7 22.4 ± 2.8
    /, no related information; BMI, body-mass index; HC, healthy control; IPMN, intraductal papillary mucinous neoplasms; NAFLD, non-alcoholic fatty liver disease; PCL, pre-cancerous lesions. Notes: * It was a prospective study including two large population-based cohorts whose BMI was described in Median or mean.
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    Table 3.  Methodologic characteristics.
    Study Sample Temperature
    for storage
    Measurement
    method
    Diversity assessment Antibiotics Probiotic or
    prebiotic
    α-diversity β-diversity
    Fan et al., 2018[26] Oral wash −80 °C 16S V3–V4 Shannon, Simpson PCoA
    Torres et al., 2015[31] Saliva −80 °C 16S Chao1 ANOSIM Not in 2 wk
    Olson et al., 2017[29] Saliva 16S V4–V5 NP Shannon, Inverse Simpson NA Not in 30 d
    Lin et al., 2013[34] Oral wash 16S
    Lu et al., 2019[28] Tongue coat 16S V3–V4 Shannon, Simpson, inverse Simpson, Obs, Chao 1, ACE PCoA Not in 8 wk Not in 8 wk
    Vogtmann et al., 2019[32] Saliva −70 °C 16S V4 Observed SVs, Shannon, Faith's PD PCoA
    Ren et al., 2017[30] Stool −80 °C 16S V3–V5 Shannon, Simpson, Chao 1 PCoA Not in 8 wk Not in 8 wk
    Half et al., 2019[27] Stool −80 °C 16S Shannon PCoA Not in 8 wk
    Half et al., 2015[33] Stool 16S ANOSIM
    Kartal et al., 2022[35] Stool and saliva −80 °C 16S V4 Shannon, Simpson Unweighted TINA index
    Chen et al., 2023[36] Fecal and saliva −80 °C 16S V3–V4 Chao1, Shannon observed species, and PD whole tree PCoA Not in 4 wk Not in 4 wk
    Hashimoto et al., 2022[38] Stool and saliva −80 °C 16S Shannon PCoA Not in 6 months Not in 6 months
    Sono et al., 2024[39] Stool and saliva 16S V3–V4 Observed features, Shannon BrayeCurtis dissimilarity QIIME 2
    Zhao et al., 2024[37] Stool −80 °C 16S V3–V4 Chao 1 Acex, Shannon Simpson Sobs i Coverage Mothur software Qiime Not in 8 wk Not in 8 wk
    Yang et al., 2023[40] Stool −80 °C 16S Chao 1 Shannon PCoA
    −, no related information. d, day; wk, week.
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    Bacterial taxonomic levels are described in Table 4. Combining studies that investigated samples from the oral cavity, six phyla were significantly different between PC patients and healthy controls, including Fusobacteria, Bacteroidetes, Firmicutes, Actinobacteria, Verrucomicrobia, and Proteobacteria. In addition, the abundance of Firmicutes and Proteobacteria was found to differ significantly in at least two studies, and they shared the same changing directions in different articles. However, there were some contradictory findings in the phyla Bacteroidetes and Fusobacteria. Fan et al. found that the phylum Fusobacteria was associated with decreased PC risk (OR = 0.94), while the phylum Bacteroidetes was associated with a higher risk of PC (OR = 1.01)[26]. Their findings were inconsistent with the results from Lu et al., whose findings suggested that PC patients presented a higher abundance of Fusobacteria and a lower abundance of Bacteroidetes than healthy controls[28]. However, the results from Fan et al. were in agreement with the findings from a European cohort containing 405 PC patients and 416 matched controls[24], in which higher antibody levels from Fusobacteria in prediagnosis blood were associated with reduced PC risk. At the genus level, 19 taxa were found to be significantly different between PC patients and healthy controls in five studies: Leptotrichia, Alloprevotella, Bacteroides, Porphyromonas, Aggregatibacter, Neisseria, Streptococcus, Haemophilus, Corynebacterium, Fusobacterium, Actinomyces, Rothia, Solobacterium, Oribacterium, Campylobacter, Atopobium, Parvimonas, Paraprevotella, and Lachnospiraceae G7. Among these identified genera, Bacteroides was found to be higher in PC, while Porphyromonas, Aggregatibacter, Neisseria, and Haemophilus were lower in PC when compared with controls in at least two articles. All five genera were found to change in the same direction between different studies. Nevertheless, there was an inconsistency between articles, such as the genus Leptotrichia that was found by Torres et al.[31] and by Lu et al.[28] to be more abundant in PC patients, while Fan et al.[26] found the genus Leptotrichia to be associated with decreased PC risk (OR = 0.87). This inconsistency may be explained by different experimental designs and various types of published articles.

    Table 4.  Discriminating taxa.
    Study Bacteria taxonomic level
    Phylum Class Order Family Genus
    Fan et al., 2018[26] Bacteroidetes (↑) SR1[C-1] (↑) Fusobacteriales (↓) Leptotrichiaceae (↓) Alloprevotella, Porphyromonas gingivalis, and Aggregatibacter actinomycetemcomitans (↑)
    Fusobacteria (↓) Fusobacteria (↓) Leptotrichia (↓)
    Torres et al., 2015[31] Firmicutes (↑) Leptotrichia Bacteroides (↑)
    Proteobacteria (↓) Porphyromonas Aggregatibacter Neisseria (↓)
    Olson et al., 2017[29] Firmicutes (↑) Bacilli (↑) Lactobacillales (↑) Streptococcaceae (↑) Streptococcus (↑)
    Proteobacteria (↓) Gammaproteobacteria; Betaproteobacteria (↓) Pasteurellales Neisseriales (↓) Pasteurellaceae Neisseriaceae (↓) Haemophilus Neisseria (↓)
    Lin et al., 2013[34] Bacteroides (↑)
    Corynebacterium Aggregatibacter (↓)
    Lu et al., 2019[28] Firmicutes, Fusobacteria and Actinobacteria (↑) Leptotrichiaceae, Fusobacteriaceae, Actinomycetaceae, Lachnospiraceae, Micrococcaceae, Erysipelotrichaceae, and Campylobacteraceae (↑) Leptotrichia, Fusobacterium, Actinomyces, Rothia, Solobacterium, Oribacterium, Campylobacter, Atopobium, and Parvimonas (↑)
    Bacteroidetes (↓) Prevotellaceae, Pasteurellaceae, and Porphyromonadaceae (↓) Porphyromonas, Haemophilus, and Paraprevotella (↓)
    Vogtmann et al., 2019[32] Enterobacteriales (↑) Enterobacteriaceae, Bacteroidaceae, Staphylococcaceae (↑) Lachnospiraceae G7 (↑)
    Haemophilus (↓)
    Ren et al., 2017[30] Bacteroidetes (↑) Prevotella, Veillonella, Klebsiella, Selenomonas, Hallella, Enterobacter, and Cronobacter (↑)
    Firmicutes and Proteobacteria (↓) Gemmiger, Bifidobacterium, Coprococcus, Clostridium IV, Blautia, Flavonifractor, Anaerostipes, Butyricicoccus, and Dorea (↓)
    Half et al., 2019[27] Bacteroidetes (↑) Bacteroidia; Verrucomicrobiae; Clostridia Bacteroidales; Verrucomicrobiales; Clostridiales Porphyromonadaceae; Verrucomicrobiaceae; Clostridiaceae1 Odoribacter, Akkermansia (↑)
    Firmicutes (↓) Clostridiumsensustricto1 (↓)
    Half et al., 2015[33] Bacteroidetes Verrucomicrobia (↑) Sutterella, Veillonella, Bacteroides, Odoribacter, and Akkermansia (↑)
    Firmicutes and Actinobacteria (↓)
    Kartal et al., 2022[35] Veillonella atypica, Fusobacterium, nucleatum/hwasookii, Alloscardovia, omnicolens (↑) Romboutsia timonensis, Faecalibacterium, rausnitzii, Bacteroides, coprocola, Bifidobacterium, and bifidum (↓)
    Chen et al., 2023[36] Bacteroidetes (↑) Veillonella, Peptostreptococcus, Akkermansia, Parvimonas, Solobacterium, Olsenella, and Escherichia-Shigella (↑)
    Firmicutes (↑)
    Proteobacteria (↑)
    Verrucomicrobia (↑)
    Hashimoto et al., 2022[38] Actinomyces, Lactobacillus, Streptococcus, and Veillonella (↑)
    Anaerostipes (↓)
    Sono et al., 2024[39] Firmicutes (↑) Streptococcus (↑)
    Proteobacteria (↓) Neisseria (↓)
    Zhao et al., 2024[37] Moraella, Sphingomonas Oxalobacteriae
    Yang et al., 2023[40] Firmicutes, Bacteroidetes, Proteobacteria, and Actinobacteria (↑) Streptococcus, Lactobacillus, and Bifidobacterium (↑)
     | Show Table
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    Based on nine studies focusing on fecal samples, six phyla differed between PC patients and controls. It seems that these nine articles came to some consensus at the phylum level, which all found that Bacteroidetes was significantly more abundant in PC patients than in healthy controls, while Firmicutes was less abundant in PC patients. Two of these articles were conducted by Half et al.[27], whose results were somewhat consistent in some genera, such as Odoribacter and Akkermansia. The comparison is mainly performed between articles from Ren et al.[30] and Half et al.[27] Unlike at the phylum level, there were extensive differences that distinguished PC patients from controls at the genus level between the papers from China and Israel, with almost no overlap. Ren et al. reported that PC patients had significantly higher levels of Prevotella, Veillonella, Klebsiella, Selenomonas, Hallella, Enterobacter, and Cronobacter, as well as lower levels of Gemmiger, Bifidobacterium, Coprococcus, Clostridium IV, Blautia, Flavonifractor, Anaerostipes, Butyricicoccus, and Dorea. The inconsistency is probably driven by a difference in methodology as well as population features, including host genetics and lifestyle.

    Five articles established diagnostic models based on the discriminated bacteria derived from their analysis[27,28,30,36,40]. The area values under the receiver operator characteristic curve (AUC) in these five studies were very similar to each other, ranging from 0.802 to 0.927. The details are displayed in Table 5. Based on a sample from the tongue coat, Lu et al. developed a model based on the combination of Fusobacterium, Leptotrichia, and Porphyromonas, with high sensitivity (0.771) and specificity (0.786) to discriminate patients with PC from controls[28]. Ren et al.[30] and Half et al.[27] focused on fecal analysis and established a diagnostic model with values of 0.859 and 0.769 for sensitivity and 0.667 and 0.8 for specificity, respectively. Based on fecal flora, Chen et al.[36] and Yang et al.[40] developed diagnostic models with values of 0.916 and 0.927, respectively, but did not provide sensitivity and specificity.

    Table 5.  Diagnostic models.
    Study Models Sensitivity Specificity AUC
    Lu et al., 2019[28] Fusobacterium, Leptotrichia, and Porphyromonas 0.771 0.786 0.802
    Ren et al., 2017[30] Based on the 40 genera 0.859 0.667 0.842
    Half et al., 2019[27] Based on discriminating taxa 0.769 0.8 0.825
    Chen et al., 2023[36] Random forest 0.916
    Yang et al., 2023[40] Random forest 0.927
    AUC, area under the receiver operator characteristic curve.
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    Fifteen studies examining the difference in the microbial community between PC patients and controls were included in the present systematic review. Although very limited comparisons were allowed due to the great heterogeneity between these studies, there existed an optimistic conclusion that microbial analysis holds the potential to provide a novel diagnostic tool for the early detection of PC.

    It has been reported that the majority of humans may share a 'core microbiota'[42], which has evolved with humans for thousands of years and participates in physiological activities such as nutrient absorption and immune regulation. It is also undoubted that human microbiota may be affected by various external factors, including geographic location, ethnicity, lifestyle, and medications[11,12]. Differences in host location have been reported to be the strongest phenotypic determinant with microbiota variations in humans with similar ancestry[43]. Therefore, the geographical differences of the included articles contribute to inevitable heterogeneity in this systematic review. In addition, there are mutual regulations between microbiota and smoking status or diabetes[14,44], which are also recognized as risk factors for PC. There were limited included articles that described the conditions of smoking or diabetes in detail. Finally, the administration of antibiotics, probiotics, and prebiotics has a crucial impact on the microbiota. Although five journal articles excluded individuals who had taken antibiotics within an indicated period, the majority of the articles failed to provide information about probiotic or prebiotic issues. The sample size, a highly relevant factor in statistical strength, varies from 28 to 732 people in the papers included in this report. Compared with small sample sizes, studies with large sample sizes potentially represent better credibility in the results. Among the nine studies, there was only one prospective evaluation based on two large cohorts. The variations in study design and sample size also led to heterogeneity between articles.

    The present research focused on studies that investigated the microbial community based on 16S rRNA sequencing, whose protocols are divergent between articles. The variations in sample handling, variable regions, sequencing depth, and sequencing platform resulted in significant methodological heterogeneity in the present review.

    In addition to 16S rRNA sequencing, detection methods for microbes include plasma antibody analysis, enzyme-linked immunosorbent assay, quantitative polymerase chain reaction, and microbe identification microarray[4547]. Combining the results of different techniques and populations, there are two promising microbes involved in PC development, P. gingivalis and Leptotrichia. Periodontal disease is an acknowledged risk factor for PC[48]. Furthermore, P. gingivalis is a major pathogen responsible for periodontal disease[49], and it was found to be increased in PC by multiple articles. Torres et al.[31] and Fan et al.[26] found that P. gingivalis differed significantly between PC and controls. Moreover, Michaud et al. found that a higher level of antibodies against P. gingivalis was associated with an increased risk of PC. Further studies have revealed that P. gingivalis promotes PC carcinogenesis by producing PAD enzymes, which induce mutations in P53 or KRAS or initiate Toll-like receptor (TLR) signaling pathways, which are critical in PC development[47,50]. Fan et al.[26], Torres et al.[31], and Lu et al.[28] found that Leptotrichia differed between PC and controls despite inconsistent directions. Leptotrichia, known as an opportunistic pathogen involved in periodontal disease, is associated with a decreased risk of PC by Fan et al.[26], and Torres et al.[31] are regarded as a protective bacterium for PC[51,52]. In addition, Torres et al. suggested a relatively high ratio of Leptotrichia to Porphyromonas in PC patients. However, further investigation is needed to reveal their role in pancreatic cancer development[31].

    P. gingivalis and Leptotrichia, along with their metabolic products, contribute to the development of pancreatic cancer through multiple mechanisms. Here are the possible mechanisms: P. gingivalis can induce inflammation by releasing lipopolysaccharides (LPS) and other virulence factors, thereby triggering an immune response. This includes the activation of Toll-like receptors (TLRs) on pancreatic cells and immune cells, leading to the secretion of pro-inflammatory cytokines (such as IL-1β, IL-6, TNF-α)[53]. P. gingivalis and Leptotrichia produce short-chain fatty acids (SCFAs) and other metabolites during carbohydrate fermentation. While some SCFAs can be protective, elevated levels may contribute to the activation of pro-inflammatory pathways[54]. Enzymes produced by P. gingivalis (such as gingipains) and Leptotrichia can degrade extracellular matrix components and epithelial cells. Damage inflicted on pancreatic tissues can stimulate further inflammation and repair processes[55]. Both bacteria can modulate the adaptive immune response, leading to reduced efficacy in tumor cell recognition. For example, P. gingivalis can induce the polarization of macrophages toward an M2 phenotype, which is immunosuppressive, and stimulate regulatory T cells (Tregs)[56].

    A single bacterium fails to show powerful diagnostic ability in early PC detection, and obvious diagnostic models based on multiple bacteria have better performance. As reported in the study by Zheng et al.[20], the multibacterial model based on 30 optimal microbial markers identified from East China can also discriminate hepatocellular carcinoma independently in Northwest China and Central China. The AUC was 80.64% (95% CI 74.47% to 86.80%) for early HCC diagnosis in the discovery phase, which was relatively stable in two validation phases, with values of 76.80% (95% CI 67.90% to 85.70%) and 79.20% (95% CI 67.40% to 90.90%) between early HCC and controls[20]. Yu et al. established a diagnostic model from fecal metagenomes, which can distinguish colorectal cancer from controls with an AUC of 84% in China. Moreover, the AUC values are 72% and 77% when validated in France and Australia, respectively[57]. These studies suggest the possibility of universal bacterial models in discerning gastrointestinal cancers from healthy controls even with microbial variations from geographical and population differences. The analysis by Torres et al. of salivary microbial profiles supports prior work suggesting that salivary microbial communities of patients diagnosed with pancreatic cancer are distinguishable from salivary microbial communities of healthy patients or patients with other diseases, including non-pancreatic cancers[31]. At the phylum level, pancreatic cancer patients tended to have higher proportions of Firmicutes and lower proportions of Proteobacteria. The most striking difference between the microbial profiles of pancreatic cancer patients and other patient groups was in the ratio of the bacterial genera Leptotrichia and Porphyromonas. The LP ratio had been identified as a potential biomarker from a preliminary analysis and an analysis of the full dataset found significantly higher LP ratio in pancreatic cancer patient saliva than in other patients. Based on a sample from the tongue coat, Lu et al.[26] developed a model based on the combination of Fusobacterium, Leptotrichia, and Porphyromonas, with high sensitivity (0.771) and specificity (0.786) to discriminate patients with PC from controls. Zhao's study indicated that pancreatic cancer can significantly increase the species richness and diversity of gut microbes in patients[37]. The dominant species of gut microbes in pancreatic cancer and healthy people are Bacteroides and Lachnospira. The study by Yang et al. demonstrated significant differences in intestinal microbiome composition between PC patients and healthy people, and found that the intestinal microbial richness of PC patients was higher, and the Streptococcus content was significantly increased[40]. Through LEfSe, RF analysis and verified by ROC curve, it was found that it had important discrimination ability in the PC group.

    At the same time, none of them performed independent validation in different geographic regions, which limits the reliability of the multibacterial model. Nevertheless, these studies indicate that a noninvasive strategy for the early diagnosis of PC may be achieved by microbiota-targeted biomarkers, which need further investigation in a larger population and cross-regional validation.

    The association between the microbiota and PC is widely recognized. However, whether it is a causal relationship and the mechanisms contributing to these observations remain elusive. Emerging studies have moved into the field of elucidating mechanisms by which the microbiota influences the initiation and progression of PC.

    According to the present studies, the microbiota may impact PC development through local and/or remote means. The pancreas, which used to be considered a sterile organ, harbors its own microbial environment, at least under pathological conditions[58]. Considering that the pancreas gland is directly connected to the gastrointestinal tract via a pancreatic duct in the duodenum, it appears possible that some microorganisms directly translocate to the pancreatic parenchyma through the pancreatic duct. The relatively higher prevalence of PCH (pancreatic head carcinoma) than PCB (pancreatic body and tail carcinoma) may provide feasible evidence for this hypothesis due to the closer anatomical location of the pancreatic head to the duodenum[59,60]. In addition, oral gavage of Bifidobacterium pseudolongum leads to the presence of the bacterium in the pancreas in a mouse model of PC[61]. Another alternative hypothesis is explaining how microbiota gain access to the pancreas; it is based on mesenteric lymph and/or mesenteric venous drainage[62]. The gut microbiota is an important component of the gut barrier, and disturbance of the microbiota may induce dysfunction of the gut barrier. The microbes may migrate into pancreatic parenchyma as a consequence of intestinal barrier damage and lymphatic dysfunction, which is caused by dysbiosis. The pancreatic microbiota, especially the intratumoral microbiota, may affect the prognosis and therapeutic efficacy of pancreatic cancer. Riquelme et al. compared tissue microbiota between long-term survival and short-term survival PC patients by 16S rRNA sequencing and found a significant difference in diversity and dominant taxa between them. Patients with a higher abundance of Pseudoxanthomonas-, Streptomyces-, Saccharopolyspora-, Bacillus clausii in tumor tissues presented with long survival, suggesting the importance of pancreatic microbiota in prognosis prediction[63]. Geller et al. found the presence of γ-proteobacteria in pancreatic tumors, probably induced via gemcitabine resistance, owing to gemcitabine degradation by γ-proteobacteria products, such as cytidine deaminase[64]. In addition, Pushalkar et al. also suggested that the intratumoral microbiota influences the response to immunotherapy[61]. These findings indicate the potential of microbial modulation as adjuvant therapy in PC treatment.

    It is well-established that chronic inflammation is paramount for PC initiation and progression[65]. Chronic pancreatitis, a typical condition of pancreatic inflammation, as well as diabetes and obesity, which may cause systematic inflammation, are risk factors for PC. The microbiota plays a critical role in the development of chronic pancreatitis[66], diabetes, and obesity, by which microbes indirectly impact PC tumorigenesis. Furthermore, an increased abundance of LPS-producing bacteria has been observed in a variety of gastrointestinal malignancies, including pancreatic cancer. Ren et al. found that LPS-generating bacteria, such as Prevotella, Hallella, and Enterobacter, were enriched in fecal samples from PC patients[30]. Lipopolysaccharide (LPS), a major microbe-specific molecular compound localized in the outer membrane of gram-negative bacteria may be recognized by Toll-like receptors (TLRs), which are expressed in immune cells. The combination of LPS and TLR activates multiple downstream proinflammatory pathways, including the NF-κB/MAPK signaling pathway, which plays an important role in inflammation[6769]. The microbiota exerts a carcinogenic impact by maintaining an inflammatory environment.

    The immunosuppressive microenvironment is an essential feature of pancreatic cancer. Recently, immune therapy of PC has attracted much attention despite the limited response thus far[61]. The microbes have a dual impact on malignancies. On the one hand, bacterial ablation improves the efficacy of checkpoint-targeted immunotherapy, which suggests the immune-suppressive effect of microbiota; on the other hand, antibiotic administration limits the effectiveness of PD-1 therapy, which indicates that microbes may provoke cancer immunity[7073]. Although an intact gut microbiota is essential for the maturation of the immune system, the absence of microbiota may lead to hypoplastic lymphoid organs and immune cells. Some microbes are responsible for innate and adaptive immune suppression in tumorigenesis by the interaction between LPS and TLRs. The binding and activation of TLRs, including TLR7, TLR9, and TLR5[61,74,75] , via bacterial products maintain an immune-suppressive microenvironment by T cells and another lymphocyte inactivation as a consequence of the macrophage M2-like phenotype. Riquelme et al. found that the gut microbiome can affect immune cell infiltration in pancreatic tumors, and microbiota from long-term surviving patients may induce a strong antitumor immune response[63].

    Diabetes and obesity, as the systemic inflammatory status mentioned above, are also the two most common metabolic diseases worldwide. Considering the essential role of gut microbiota in the digestion and metabolism of nutrients, the gut microbiota is regarded as an intermediate key linking metabolic disorders and pancreatic cancer. Ren et al. found that the abundance of butyrate-producing bacteria, including Coprococcus, Clostridium IV, Blautia, and Flavonifractor, decreased in the stool of PC patients, suggesting that gut microbiota may affect PC development through metabolites[30]. Butyrate is a short-chain fatty acid (SCFA) derived from the fermentation of fiber by gut microbiota and has shown an antitumor effect in various malignancies. Butyrate can help maintain the integrity of the gut barrier by providing an energy source for intestinal epithelial cells and inhibiting microbe translocation by gut leakage[76,77]. In addition, butyrate plays an essential role in multiple cancerous activities by regulating epigenetic processes, including proliferation, differentiation, apoptosis, and invasion.

    It is estimated that approximately 10-20% of malignancies are attributed to infectious factors. Several specific microbes have been identified as carcinogenic pathogens, such as Helicobacter pylori in gastric cancer and HPV in cervical cancer. However, no specific pathogen has been found to be the causative agent for PC[78,79]. Accumulating epidemiological studies suggest a close relationship between H. pylori, hepatitis virus, and PC despite still controversy between studies[8083]. In addition, some articles highlight the importance of fungi in the carcinogenesis of PC. Aykut et al. found that pancreatic cancer tissue harbors 3,000-fold increased fungi compared with healthy tissue, especially Malassezia spp. Administration of amphotericin B to eliminate fungi may delay the progression and invasion of PC in mouse models[84]. Further research suggested that glycans on the fungal wall may bind and activate mannose-binding lectin (MBL) and then drive the complement system cascade, which is necessary for oncogenic progression.

    The development of pancreatic cancer is a long-term process that develops through several histopathological facets, including the following: chronic inflammation, pancreatic intraepithelial neoplasia, and finally pancreatic cancer[85]. The microbiota may play a key role in the entire process from chronic pancreatitis to precancerous conditions, even to pancreatic cancer. A qualified diagnostic model can distinguish PC patients from confusing diseases such as other gastrointestinal malignancies rather than healthy individuals only. Four studies included in this review have considered this and recruited pancreatitis, NAFLD, and IPMN patients as controls[27,29,31]. Although independent articles explain the relationship between chronic pancreatitis or IPMN and microbiota, a comparative model from a homogeneous region and population is still needed to establish a more qualified diagnostic model for pancreatic cancer with higher specificity.

    The present study had several limitations. First some of the sample sizes of the articles included were small, with only 13 individuals in some disease groups, which is mainly due to the low rate of pancreatic cancer incidence. Secondly, not all medical records had randomized controls, furthermore, the specimen sites studied in the individual articles differed, which may have led to a bias in the measured flora.

    This systematic-based review on limited existing human studies, supporting the possibility of microbiota analysis, searched for a useful noninvasive diagnostic tool in PC detection. The variations in study design and population, methodological characteristics between studies, as well as the influence of region, drugs, and diet on the microbiota led to heterogeneity in this systematic review. Therefore, future studies with larger sample sizes and controlled covariates are needed for a better understanding of the relationship between microbiota and PC, as well as several different diseases.

  • Not applicable.

  • The authors confirm contribution to the paper as follows: draft manuscript preparation: Zhang Y, Du H; manuscript reviewed and editing: Chen H. All authors reviewed the results and approved the final version of the manuscript.

  • The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

  • The authors declare that they have no conflict of interest.

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  • Cite this article

    XU S, LI M, ZHOU W, ZHANG J, WANG C. 2024. An evolutionary game theory-based machine learning framework for predicting mandatory lane change decision. Digital Transportation and Safety 3(3): 115−125 doi: 10.48130/dts-0024-0011
    XU S, LI M, ZHOU W, ZHANG J, WANG C. 2024. An evolutionary game theory-based machine learning framework for predicting mandatory lane change decision. Digital Transportation and Safety 3(3): 115−125 doi: 10.48130/dts-0024-0011

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An evolutionary game theory-based machine learning framework for predicting mandatory lane change decision

Digital Transportation and Safety  3 2024, 3(3): 115−125  |  Cite this article

Abstract: Mandatory lane change (MLC) is likely to cause traffic oscillations, which have a negative impact on traffic efficiency and safety. There is a rapid increase in research on mandatory lane change decision (MLCD) prediction, which can be categorized into physics-based models and machine-learning models. Both types of models have their advantages and disadvantages. To obtain a more advanced MLCD prediction method, this study proposes a hybrid architecture, which combines the Evolutionary Game Theory (EGT) based model (considering data efficient and interpretable) and the Machine Learning (ML) based model (considering high prediction accuracy) to model the mandatory lane change decision of multi-style drivers (i.e. EGTML framework). Therefore, EGT is utilized to introduce physical information, which can describe the progressive cooperative interactions between drivers and predict the decision-making of multi-style drivers. The generalization of the EGTML method is further validated using four machine learning models: ANN, RF, LightGBM, and XGBoost. The superiority of EGTML is demonstrated using real-world data (i.e., Next Generation SIMulation, NGSIM). The results of sensitivity analysis show that the EGTML model outperforms the general ML model, especially when the data is sparse.

    • Mandatory lane change (MLC) refers to the behavior that the driver must change the current lane to the expected lane in some places due to traffic regulations or his/her driving needs. MLC usually occurs in expressway weaving areas, on and off ramps, and the entrance to intersections. Compared with discretionary lane changing (DLC, e.g., the lane changing behavior taken by the drivers to improve the current driving environment), MLC is more likely to cause traffic oscillations, which have a negative impact on traffic efficiency and safety[1,2]. Therefore, analyzing, modeling, and predicting mandatory lane-changing behavior is important for improving road traffic safety and efficiency.

      In the past decade, there has been a rapid increase in research on lane change modeling, especially on mandatory lane change decision (MLCD) prediction[35]. MLCD models can be categorized into two types, physics-based models and machine-learning models. Early physics-based MLCD models started from the classic rule-based models (e.g., Gipps[6], MITSIM[7], MOBIL[8]), and utility-based models[9], which imitated human drivers' activities towards lane-changing. However, challenging function expressions and complicated parameters make these models more difficult to calibrate and validate. The lane-changing process involves dynamic interaction between drivers, that is, one driver pays the cost (e.g., speed, space) and the other driver benefits from it (e.g., acceleration, lane change). Game theory (GT), one of the most frequent applications of simulating the process of human competitive and cooperative behaviors, can better describe the interaction between drivers. Thus, there have been many MLCD models integrated with GT[10,11], which are at the forefront of MLCD research. Evolutionary Game Theory (EGT) presents the objective of dynamically describing the competition and cooperation between human. MLCD models based on EGT can explain the progressive cooperative interactions of drivers. The parameters in the physics-based models have physical meaning, so the model is highly interpretable. However, the models only include a subset of the significant factors of MLCD and ignore the rest of the potential factors, so the prediction accuracy is low. Machine learning (ML) models focus on learning lane-changing behavior from vehicle-related data (e.g., dynamic and trajectory data). Due to the complexity of influencing factors of MLCD, ML models are gradually being applied to MLCD modeling[12,13]. In addition, the effect of the driving style on MLCD was also considered in the modeling process[14]. In general, the prediction accuracy of MLCD by ML models is high, but the models have high requirements on data quality and quantity, and low robustness. Besides, the model lacks interpretability, in other words, the model cannot explain how the driving behavior evolves as traffic environment changes.

      Recently, modeling methods that combine physics-based models and machine learning models are gaining popularity in balancing prediction accuracy and the interpretability in the engineering field[15,16]. In machine learning models' loss functions, physics information is usually encoded as governing equations, physical constraints, or regularity terms. In the field of traffic, the application of this method is not extensive enough, and it is currently limited to traffic state prediction and car-following (CF) behavior modeling. Shi et al. utilize a neural network to encode the traffic flow model for traffic state estimation[17]. They observed that the proposed Physics-informed Deep learning (PIDL) approach has the capability of making precise and timely TSE even with sparse input. Yuan et al. transformed the physical knowledge in the traditional car-following model into a physical regularize of multivariate Gaussian processes to predict the drivers' car-following behaviors[18]. The results demonstrated that the proposed method outperforms the previous methods in estimation precision. Mo et al.[19] designed a physics-informed deep learning car-following model (PIDL-CF) architecture and utilized two neural network models: ANN and LSTM to further validate the generalization of the PIDL method. The results showed the superior performance of physics- informed methods over those without physical information. Masmoudi et al. propose an autonomous vehicle following framework that involves using leading vehicle detecting based on You Look Once version 3 (YOLOv3) and implementing vehicle following using reinforcement learning-based algorithms[20]. This method, which combines physical models with machine learning, shows considerable advantages in terms of effectiveness. In all, physics-informed methods can overcome the challenges of training data-hungry machine learning models, particularly arising from limited data and imperfect data (e.g., missing data, outliers, noisy data).

      To obtain a more predictive and explainable MLCD model that can depict the driving behavior of the interacted drivers with different driving styles, this study is aimed to develop an evolutionary game theory-based machine learning model (EGTML). The model prediction result is output by the machine learning model which is informed by the EGT-based physics model. The main contributions of this paper are as follows:

      (1) Design an EGTML architecture to model the mandatory lane change decision of multi-style drivers, which combines the physics-based model (data efficient and interpretable) and the machine learning model (high prediction accuracy).

      (2) Demonstrate the generalization of EGTML methods by using four different ML methods: ANN, RF, LightGBM, and XGBoost. The results showed that EGTML holds the potential to maintain high prediction accuracy and enhance the data-efficiency of training by incorporating physical knowledge.

      (3) Demonstrate the superiority of EGTML on real-world data. The results showed that the proposed hybrid paradigm outperforms the general machine learning model across various training data, especially when the data is sparse.

    • Since there are significant differences in driving behaviors of drivers with different styles, it is necessary to accurately model the lane-changing behaviors of drivers with different styles. This paper established a multi-style driver clustering model based on the Gaussian mixture model (GMM)[21].

    • Gaussian mixture model (GMM) is a linear combination of multiple single Gaussian models. If the d-dimensional vector x obeys the Gaussian mixture distribution, its probability density function is defined as:

      fM(x)=ki=1αi×f(xμi,Σi) (1)

      where, αi is the mixing coefficient, f(xμi,Σi) is the probability density function of the i-th Gaussian distribution, its equation is as follows:

      f(xμi,Σi)=1(2π)d2|Σ|12EXP[12(xμi)TΣ1i(xμi)] (2)

      where, μi is the d-dimensional mean vector, Σi is the d × d-dimensional covariance matrix. The main parameters of GMM are {(ai,μi,Σi)i=1,2,,k}. The Expectation-Maximum (EM) algorithm[22] is the common solution algorithm to obtain the optimal parameters. The EM algorithm continuously updates the parameters in the iterative process until the termination condition is satisfied.

    • During the operation of the vehicle by different styles of drivers, the operating parameters of the vehicle are different, which are intuitively reflected in the changes in parameters such as speed and acceleration[23]. The vehicle operating parameters can be obtained from the vehicle trajectory data. To consider the impact of the traffic operation state on drivers, define the ratio of vehicle speed to the space average speed as the speed ratio r to replace speed, the calculation formula is as follows:

      ri=vi¯vs (3)
      ¯vs=ni=1vin (4)

      where, ¯vb is the space average speed, n is the number of vehicles, and vi is the speed of ith vehicle. Based on the speed ratio r and the acceleration a, the driving style feature vector is constructed {E(r),VAR(r),E(a)}. The feature vector is brought into the GMM and the EM algorithm is used to obtain the optimal model parameters. Then, the vehicles are divided into k-clusters, corresponding to different driving styles.

    • Here, Evolutionary Game Theory (EGT)[24] is used to analyze the mandatory lane-changing decision game and predict the decision-making of game players. Dynamic analysis is used to solve the stable solution of the evolving system and predict the decision-making of the game participants. Two significant contents of EGT are shown as follows.

    • ESS is a strategy that enables the evolving system to reach a stable state, which is equivalent to Nash equilibrium in traditional game theory. Combined with the theory of biological evolution, ESS can be regarded as a process of survival of the fittest. Assuming that in a certain group, if the mutation of an individual can help the individual better adapt to the environment, the proportion of the mutation will increase, and the group can survive better. So, the mutation is the ESS of the group. In the MLCD game system, ESS is the decision made by drivers in the stable state.

    • 'Replication' refers to individuals following a better strategy, and the replicator dynamics equation indicates the rate of change in the proportion of individuals. The replicator dynamic equation is the differential equation defined as follows:

      dxidt=xi[u(si,x)u(s,x)] (5)

      where, si is the i-th strategy of the individual strategy set xi is the probability that the individual chooses the strategy si at time t, u(si, x) is the expected payoff when the individual chooses the strategy si, and u(s, x) is the average expected payoff of all strategy sets of the individual.

      As shown in Fig. 1, there are two players in the mandatory lane-changing decision game, the lane-changing vehicle (SV) and the vehicle behind it in the target lane (TB). According to the driving style of SV and TB, the MLCD game can be divided into different categories. First, SV signals the lane-changing request to TB. Second, TB responds by accelerating to refuse to yield or decelerating to yield. Finally, SV decides whether to lane change or not according to the response of TB.

      Figure 1. 

      The schematics of lane-changing.

    • SV and TB are the participants of the system, and the strategy set of SV is {Lane change, Do not lane change}, and the strategy set of TB is {Yield, Do not yield}. According to the different strategy combinations of SV and TB, the system will reach different stable states.

      The game process of the lane-change decision is shown in Fig. 2. Based on efficiency (i.e., speed loss), safety, and, accessibility (i.e., lane-changing demand), construct the payoff matrix for MLCD, which is shown in Table 1. P and Q denote the payoffs for SV and TB, respectively.

      Table 1.  The payoff matrix for MLCD.

      Game players SV
      Lane change No lane change
      TB Yield P11 : α1TTC + β1L P21 : −β1L
      Q11 : α2TTC − β2Δv Q21 : −β2Δv
      No yield P12 : −α1TTC P22 : −β1L
      Q12 : β2Δv − α2TTC Q22 : β2Δv

      Figure 2. 

      The game process of the lane-changing decision.

      Specifically, the efficiency payoff of TB is mainly reflected in the speed loss Δv caused by deceleration and yielding, and the payoff factor is β2. For the payoff of lane-changing demand, the distance of SV to the end of MLC L is used to represent the payoff of lane-changing demand, and the factor is β1. Time-To-Collision (TTC)[25] is used to represent the safety payoff between SV and TB, and the factors of SV and TB are α1 and α2 respectively. TTC refers to the time when the front and rear vehicles collide under the condition that the relative speed of the front and rear vehicles remain unchanged. It can be calculated as follows:

      TTC={yi1(t)yi(t)12(li1+li)vi(t)vi1(t)vi(t)>vi1(t)+vi(t)vi1(t) (6)

      where, yi(t), vi(t) and li represent the position, speed and length of the rear vehicle, yi-1(t), vi-1(t), and li-1 represent the position, speed, and length of the front vehicle. α1, α2, β1, and β2 are all in the range of (0,1) and satisfy α1 + β1 = 1 and α2 + β2 = 1.

    • SV and TB cannot take the optimal decision at the beginning of the game, so they must combine their own and each other's decisions, and eventually make the optimal decision through a game period and bring the system to a stable state. This optimal decision combination is the Evolutionarily Stable Strategy (ESS)[24].

      Suppose the probability of SV taking lane-changing behavior is x1, the probability of drivers taking yielding behavior is x2. The expected payoffs of SV and TB can be calculated.

      The expected payoff of SV taking lane-changing behavior is:

      W1=Ax2+C(1x2) (7)

      The expected payoff of SV not taking lane-changing behavior is:

      W2=Ex2+G(1x2) (8)

      The expected payoff of SV is:

      WSV=W1x1+W2(1x1) (9)

      The expected payoff of TB taking yielding behavior is:

      w1=Bx1+F(1x1) (10)

      The expected payoff of TB not taking yielding behavior is:

      w2=Dx1+H(1x1) (11)

      The expected payoff of TB is:

      wTB=w1x2+w2(1x2) (12)

      During the driving process, drivers will abandon low-payoff strategies and adopt high-payoff strategies. Therefore, x1 and x2 will change over time and satisfy the following equations:

      FSV(x1,x2)=dx1/dt=x1[W1WSV] (13)
      fTB(x1,x2)=dx2/dt=x2[w1wTB] (14)

      SV and TB cannot take the optimal decision at the beginning of the game, so they must combine their own and each other's decisions, through a period of game, and finally make the optimal decision, so that the system can reach a stable state. Assuming that at the beginning of the game, the probability of SV taking lane-changing behavior is x01, and the probability of TB taking yielding behavior is x02. Then, x01 changes to x11 according to Eqn (13), and x02 changes to x12 according to Eqn (14). After several iterations of this cycle, the system finally reaches a stable state, at this time, (xn1,xn2) is the stable point of the system, and the strategy combination is the ESS. When the system reaches a stable state, x1 and x2 satisfy the following equation:

      {x1(1x1)[(A+GCE)x2+CG]=0x2(1x2)[(B+FDF)x1+FH]=0x1,x2[0,1] (15)

      The four definite solutions of the equation are (0,0), (0,1), (1,0), (1,1), and another is (HFB+HDF,GCA+GCE). Not all of the above solutions can make the system reach a stable state. When the system reaches a stable state, the payoff function reaches the maximum value, so the stability analysis of solutions can be transformed into the problem of solving the maximum value of the function. For each solution, the dynamic equation is 0, so a solution satisfying the first derivative of the dynamic equation is less than 0 is a stable solution of the system. Therefore, the stable solution needs to satisfy the following equation:

      {FCV(x)=(12x1)[(A+GCE)x2+CG]<0fTB(x)=(12x2)[(B+HDF)x1+FH]<0 (16)

      Calculating the value of the first derivative of the dynamic equation at each solution, the results are as shown in Table 2.

      Table 2.  Stability analysis of equilibrium solution.

      (x1, x2) FCV(x) fTB(x) Stability
      (0, 0) C-G F-H Determined by the payoff matrix
      (0,1) A-E H-F
      (1,0) G-C B-D
      (1,1) E-A D-B
      (HFB+HDF,GCA+GCE) 0 0 Unstable solution

      Therefore, the set of stable solutions of the system is {(0,0), (0,1), (1,0), (1,1)}, and the corresponding set of ESS is {(Do not lane change, Do not yield), (Do not lane change, Yield), (Lane change, Do not yield), (Lane change, Yield)}. The stable solution of the system is determined by the payoff matrix. Finally, EGT-based MLCD is determined by the payoff matrix and the initial values of x1 and x2 according to the identified decisions. Assuming the stable solution of the system is (1,0), then solve the ESS of the system and calculate the values of x1 and x2 to determine the lane-changing decision of SV. The evolution path of the system is shown in Fig. 3.

      Figure 3. 

      Schematic diagram of the evolution of the probability.

      In this case, SV has a greater payoff by lane-changing, but TB tends to choose not to yield, the players compete for the road resources and the ESS is (Lane change, No yield).

    • Whether SV changes the lane or not depends not only on the probability of SV lane-changing, but also the probability of TB yielding, but also on whether the lane-changing safety criteria are satisfied[26]. Because TTC can reflect the relative motion trend and collision possibility between the front and rear vehicles, it is utilized to formulate the lane-changing safety criteria and shown as follows:

      TTCTFTTCminTF,TTCTBTTCmin TB (17)

      where, TTCTF and TTCTB are between SV and TF, TB, TTCminTF and TTCminTB are constraints.

    • Only when the probability of SV lane-changing and the probability of TB yielding are both greater than 0.5 and the lane-changing safety criteria is satisfied, the model outputs YEGT = 1, indicating SV lane changing, otherwise, the model outputs YEGT = 0, indicating SV no lane changing. The EGT-based physics model is as follows:

      YEGT={1p1>0.5,p2>0.5,TTCTF>TTCminTF,TTCTB>TTCminTB0otherwise (18)
    • According to the PIDL architecture proposed by Mo et al.[19], the EGTML model consists of two elements: a machine-learning model and an EGT-based physics model. Both models take the feature vector X as input and the lane-changing decision Y as output. The output of the EGTML model is the output of the ML model, and the output of the EGT-based model is the physical knowledge of ML model, which provides constraints for the output of the ML model. Figure 4 illustrates the structure of the EGTML model.

      Figure 4. 

      Structure diagram of EGTML.

    • In previous MLCD models, the features such as speed, acceleration, and speed difference are generally selected. But the traffic state information contained in these features is not comprehensive to fully describe the complex interaction between SV and surrounding vehicles (i.e., front vehicle on the target lane TF, behind vehicle on the target lane TB, front vehicle on the current lane CF, behind vehicle on the current lane CB). This paper comprehensively considered the safety indicators TTC, and finally determined 24 features to construct the feature vector X as the input of the EGTML model, as shown in Table 3.

      Table 3.  Features of the EGTML model.

      Symbol Meaning Unit
      VOV, VOF, VOB, VTP, VTH The speed of the vehicle m/s
      AOV, AGF, ACB, ATF, ATB The acceleration of the vehicle m/s2
      ΔVCF, ΔVCB, ΔVTF, ΔVTB The speed difference between vehicles m/s
      GCF, GCB, GTF, GTB The gap between vehicles m
      TTCCF, TTCCB, TTCTF, TTCTB The TTC between vehicles s
      L The distance of SV to the end of MLC m
      ¯vs Space average speed m/s
    • The observation dataset is a set of state-decision pairs {X,ˆY}, where the observed state is the feature vector X, and the identified decision is ˆY, where ˆY=1 indicates lane change and ˆY=0 indicates no lane change. In addition to the observation dataset, the collocation dataset needs to be defined. The collocation dataset is a set of state-decision pairs {X,YBGT}, where the observed state is the feature vector X, and the collocation decision Ytar  is the lane-changing decision predicted by EGT-based physics model for the observed state. According to a certain training-test split ratio, observation dataset is divided into two subsets. One subset and the collocation dataset constitute the training dataset, and the other subset is used for model testing. The process of the split dataset is shown in Fig. 5.

      Figure 5. 

      Relationship between observation and collocation dataset.

    • After the dataset is divided, the loss function of the model needs to be defined. The loss function consists of two parts, one of which is the difference between the identified decision and the predicted decision of the machine learning model (i.e., the data difference), and another is the difference between the predicted decision of EGT-based model and the machine learning model. (i.e. the physics difference). Specifically, the AUC value is used to evaluate the difference. The loss function is defined as follows:

      Lossθ=αAUCc+(1α)AUCo (19)

      where, α is the weight that balances the contributions made by the data difference and physics difference.

    • The trained EGTML can be used to predict the test dataset. Precision (P), recall (R), and accuracy (A) are used to evaluate the prediction performance of the EGTML model. The indexes are defined as follows:

      P=TPTP+FP (20)
      P=TPTP+FP (21)
      A=TP+TNTP+FP+TN+FN (22)
    • The model training process of EGTML consists of two processes, EGT-based model parameter calibration and machine-learning model parameter optimization. The training process is shown in Fig. 6. The EGT-based model parameter calibration problem can be written as the following optimization problem:

      Figure 6. 

      Training process of EGTML.

      minλObj=1NoNoi=1|YiphyˆYi|2i=1,,N0 s.t. Yiphy=fλ(^Xi|λ),λΛ (23)

      where, λ are the parameters of the EGT-based model, N0 is the number of observed data, YiEOH is the ith predicted decision by the EGT-based model ˆYi is the ith identified decision Λ is the feasible domain of the parameters, representing the physical range of each parameter. The objective function obj calculates the difference between the predicted decision of the EGT-based model and the identified decision in MSE form. The smaller the objective function, the closer the model result is to the observed result.

      After the parameter calibration of the EGT-based model, using Eqn (19) to calculate the loss between the predicted decision of the ML model and the predicted decision of the EGT-based model, the identified decision, respectively, to obtain the loss of EGTML. The Adam algorithm is used to minimize the loss until the algorithm obtains the optimal parameter θ.

    • The performance of the EGTML model is validated using the real-world data, US-101 dataset in the Next Generation SIMulation (NGSIM) dataset[27]. The collection section of the US-101 dataset was the southbound section of the US-101 Freeway in Los Angeles, California, USA. The length of the road section was 640 m, including five mainline lanes, an on-ramp, an off-ramp, and a distribution lane. The five mainline lanes from the inner lane to the outer lane were numbered sequentially from lane 1 to lane 5, the distribution lane is lane 6, the on-ramp and off-ramp are lane 7 and lane 8. The trajectory data in US-101 is the original unfiltered data, and there were outliers and measurement errors, which will affect the training and validation of the model. Therefore, the moving average method is used to smooth the position, speed, and acceleration of the vehicle to improve the data quality and reduce error interference[28] .

      The continuous data in the dataset is then binned to enhance the robustness and reduce the risk of model overfitting. In the US-101 data collection section, there were a lot of mandatory lane-changing behaviors in lane 5 and lane 6. Five hundred and eighty six samples were extracted and the start and end times of each sample were identified. When the lateral speed was greater than 0.2 m/s, there was a tendency to move laterally into an adjacent lane within 1 s, which was defined as the start time. When the lateral speed was less than 0.2 m/s and the lateral position remained stable within 1 s, this was defined as the end time[29]. Lateral refers to the direction perpendicular to the direction of the lane. Taking vehicle No. 20 as an example, the identification of the start and end time of lane-changing is shown in Fig. 7. After identifying the start time and the end time, the trajectory data of 5 s before the start time and the entire lane-changing process is selected to simplify the dataset.

      Figure 7. 

      Identification of the start and end time of vehicle No. 20. Diagram of (a) lateral position, (b) lateral speed.

    • The number of cluster centers of GMM was defined as 2, and the drivers on lane 5 and lane 6 were divided into two data subsets, corresponding to conservative drivers, and aggressive drivers respectively. The number of aggressive drivers was 616, accounting for 37.84%, and the number of conservative drivers was 1,012, accounting for 62.16%. Overall, both the average acceleration and the variance of speed ratio of aggressive drivers were larger than those of the conservative drivers. The distribution of sample eigenvalues are shown in Fig. 8. It can be seen that both the average acceleration and the variation of speed ratio of aggressive drivers are larger than those of the conservative drivers.

      Figure 8. 

      Distribution of sample eigenvalues. (a) Speed ratio mean - Speed ratio variance; (b) Speed ratio variance - Acceleration mean.

    • According to the driving style of SV and TB, the MLCD game can be divided into the following four categories: Category 1 is the aggressive SV and aggressive TB. Category 2 is the aggressive SV and conservative TB. Category 3 is the conservative SV and aggressive TB. Category 4 is the conservative SV and conservative TB. Using observation data to calibrate the EGT-based model parameters for four categories. For the payoff factors, in the range of (0,1), with a step size of 0.01, all the parameter combinations were traversed to optimize Eqn (23), and the calibration results are shown in Table 4. The definition of each parameter is described above. The 85th percentile TTCTF and TTCTB were chosen as the calibrated values for TTCminTF and TTCminTB to ensure the safety performance of most vehicles.

      Table 4.  The calibration of parameters.

      Category 1 2 3 4
      α1 0.98 0.99 0.96 0.97
      β1 0.02 0.01 0.04 0.03
      α2 0.8 0.9 0.8 0.85
      β2 0.2 0.1 0.2 0.15
      TTCminTF 6.25 6.25 6.25 6.25
      TTCminTB 6.25 6.25 6.25 6.25

      After parameter calibration, the payoff matrix was calculated and the evolution with time of the probability of lane-changing and yielding for each of the four MLC categories calculated by replicator dynamic equations and was plotted in Fig. 9.

      Figure 9. 

      Evolution diagram of probability of lane-changing and yielding. (a) Category 1 (Aggressive SV - Aggressive TB); (b) Category 2 (Aggressive SV - Conservative TB); (c) Category 3 (Conservative SV - Aggressive TB); (d) Category 4 (Conservative SV - Conservative TB).

      In Fig. 9a & c, the probability of SV lane-changing increased over time, while the probability of TB yielding decreased at first and then increased gradually, implying that there may be an obvious competition between two drivers at the beginning of the game when TB is aggressive. Compared to aggressive SV, when SV is conservative, the intensity and duration of the competition was comparatively lower.

      In Fig. 9b & c, the probability of SV lane-changing increases more rapidly, while the probability of TB yielding increases directly. That is, conservative TB tends to yield to SV during the game.

    • The prediction performance on the test dataset of the EGTML model was evaluated by precision (P), recall (R), and accuracy (A). Widely-used ML models (i.e., ANN, RF, LightGBM, and XGBoost) were applied to construct the EGTML model.

      ANN[30]: Artificial neural network (ANN) is a computational model that consists of several processing elements that receive inputs and deliver outputs based on their predefined activation functions.

      RF[31]: Random Forest (RF) is an ensemble learning method for classification that operates by constructing a multitude of decision trees during the training process. The output of the RF is the class selected by most trees.

      LightGBM[32]: LightGBM is an improvement of gradient ascending algorithm (GBDT) in efficiency and scalability, which incorporates two innovative techniques: Gradient-based One-Side Sampling (GOSS) and Exclusive Feature Bundling (EFB).

      XGBoost[33]: XGBoost is a scalable, distributed gradient-boosted decision tree (GBDT) that provides parallel tree boosting.

      The evaluation of different ML models is shown in Table 5. The ROC curves, and PR curves are shown in Fig. 10. It can be seen that the EGTML models using different ML models all have good prediction performances, among them, the LightGBM performs the best.

      Table 5.  The evaluation of different ML models.

      Index ANN RF LightGBM XGBoost
      P 0.775 0.855 0.833 0.871
      R 0.963 0.931 0.944 0.933
      A 0.795 0.832 0.865 0.847

      Figure 10. 

      The ROC curves, and PR curves of different ML models. (a) ROC curves; (b) PR curves.

    • After applying the best performing ML model (i.e., LightGBM), the distribution of longitudinal Lane Change Decision position output from EGTML (EGT-LightGBM) and LightGBM, as well as the identified decisions (i.e., ground truth), were plotted and are shown in Fig. 11 by MLC game categories.

      Figure 11. 

      Distribution of longitudinal Lane Change Decision position. (a) Category 1 (Aggressive vs Aggressive); (b) Category 2 (Aggressive vs Conservative); (c) Category 3 (Conservative vs Aggressive); (d) Category 4 (Conservative vs Conservative).

      Category 1 (Aggressive vs Aggressive): In Fig. 11a, it can be seen that the distribution of output from EGTML is more similar than that from the pure ML model. This result is also confirmed by the KL divergence gained from pure ML and ground truth (i.e., 0.271) as well as from EGTML and ground truth (i.e., 0.231). According to Fig. 11a, the competition between two aggressive drivers may increase the difficulty of MLC, which leads to the discrete distribution of lane change positions.

      Category 2 (Aggressive vs Conservative): KL divergence from EGTML (i.e., 0.081) is lower than that from ML (i.e., 0.098). In Fig. 11b & c, because conservative drivers tend to yield to aggressive drivers during the game, more aggressive drivers can finish their MLC earlier than that in Category 1.

      Category 3 (Conservative vs Aggressive): KL divergence from EGTML (i.e., 0.145) is lower than that from ML (i.e., 0.172). According to the low intensity and duration of the competition from conservative SV and aggressive TB in Fig. 9c, the difficulty of MLC for conservative drivers is higher than that of Category 4 (i.e., the distribution of lane change positions in Category 4 is more centralized).

      Category 4 (Aggressive vs Conservative): Both the tendency of distribution in Fig. 11d and KL divergency (i.e., 0.036 > 0.029) demonstrate that EGTML has a better performance in the prediction of MLCD. Because the tendency of evolution probability of SV and TB in Fig. 9d is similar to that in Fig. 9b, a comparable trend of the output distribution is also displayed between Fig. 11d & b.

      In summary, EGTML can learn the knowledge of evolutionary game theory and capture the game interactions between multi-style drivers in different game scenarios, which improves the interpretability of traditional ML.

    • EGT-LightGBM was used for testing the parameter sensitivity of EGTML.

      Firstly, to show that the advantages of the EGTML model persist across different numbers of training data, different numbers of training data wer randomly selected and the prediction performances evaluated on the test dataset. The results are shown in Fig. 12a, where the x-axis is the number of training data, and the y-axis is the prediction accuracy. As can be seen, the overall performance of the EGTML model is better than the traditional ML model and the EGT-based model even with the variability of the training data. The difference with the former shrinks and the difference with the latter increases as the training data increases. This phenomenon is similar to the results shown by PINN-CF[19].

      Figure 12. 

      The performance of EGTML. (a) Varying numbers of training data; (b) varying α.

      Secondly, to analyze the influence of the weight α on the EGTML model, the model is trained by the value of α from 0 to 1 with a step size of 0.1. Then, the performance of the trained model is evaluated on the same test dataset. The results are shown in Fig. 12b, the x-axis is the value of α, and the y-axis is the prediction accuracy. As can be seen, when the value of α is 0.1, the performance of the EGTML model is optimal.

    • This paper develops an evolutionary game theory-based machine learning mandatory lane change decision model (EGTML). The prediction result is output by the machine learning model which is informed by the EGT-based physical model. This modeling framework holds the potential to maintain high prediction accuracy and enhance the data efficiency of training by incorporating physical knowledge. The generalization of the EGTML method is further validated using four machine learning models: ANN, RF, LightGBM, and XGBoost, and the superiority of EGTML is demonstrated on the NGSIM dataset. Applying the best-performing EGT-LightGBM, and LightGBM to test the parameter sensitivity of EGTML, the results show that the EGTML model outperforms the general ML model, especially when the data is sparse.

      To the best of our knowledge, this paper is the first-of-its-kind that employs a hybrid paradigm where a physics-based model is encoded into a machine learning model for mandatory lane-changing decision prediction. Thus, there are still a lot of unresolved research questions. This work will be extended in several directions. (1) More advanced physics-based MLCD models will be encoded into ML models, which may hold the potential to capture more complex lane-changing behaviors. (2) A systematic simulation procedure should be developed for testing the proposed EGTML model and identifying the best physics-based models by deriving some key metrics (e.g., collision rate, conflicting distribution).

    • The authors confirm contribution to the paper as follows: conceptualization, methodology, draft manuscript preparation: Xu S; software: Xu S, Li M; data curation: Li M; visualization, investigation: Li M, Zhou W, Zhang J; supervision, project administration, funding acquisition: Wang C. All authors reviewed the results and approved the final version of the manuscript.

    • Data will be made available upon reasonable request to the corresponding author.

      • This research was supported by the National Key R&D Program of China (2023YFE0106800), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX24_0100).

      • The authors declare that they have no conflict of interest. Chen Wang is the Editorial Board member of Digital Transportation and Safety who was blinded from reviewing or making decisions on the manuscript. The article was subject to the journal's standard procedures, with peer-review handled independently of this Editorial Board member and the research groups.

      • Copyright: © 2024 by the author(s). Published by Maximum Academic Press, Fayetteville, GA. This article is an open access article distributed under Creative Commons Attribution License (CC BY 4.0), visit https://creativecommons.org/licenses/by/4.0/.
    Figure (12)  Table (5) References (33)
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    XU S, LI M, ZHOU W, ZHANG J, WANG C. 2024. An evolutionary game theory-based machine learning framework for predicting mandatory lane change decision. Digital Transportation and Safety 3(3): 115−125 doi: 10.48130/dts-0024-0011
    XU S, LI M, ZHOU W, ZHANG J, WANG C. 2024. An evolutionary game theory-based machine learning framework for predicting mandatory lane change decision. Digital Transportation and Safety 3(3): 115−125 doi: 10.48130/dts-0024-0011

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