Combinatorial auction is an important type of market mechanism, which can help bidders to bid on the combination of items more efficiently. The winner determination problem (WDP) is one of the most challenging research topics on the combinatorial auction, which has been proven to be NP-hard. It has more attention from researchers in recent years and has a wide range of real-world applications. To solve the winner determination problem effectively, this paper proposes a hybrid ant colony algorithm called DHS-ACO, which combines an effective local search for exploitation and an ant colony algorithm for exploration, with two effective strategies. One is a hash tabu search strategy adopted to reduce the cycling problem in the local search procedure. Another is a deep scoring strategy which is introduced to consider the profound effects of the local operators. The experimental results on a broad range of benchmarks show that DHS-ACO outperforms the existing algorithms.
Citation: Jun Wu, Mingjie Fan, Yang Liu, Yupeng Zhou, Nan Yang, Minghao Yin. A hybrid ant colony algorithm for the winner determination problem[J]. Mathematical Biosciences and Engineering, 2022, 19(3): 3202-3222. doi: 10.3934/mbe.2022148
[1] | Kochar Khasro Saleh, Semih Dalkiliç, Lütfiye Kadioğlu Dalkiliç, Bahra Radhaa Hamarashid, Sevda Kirbağ . Targeting cancer cells: from historic methods to modern chimeric antigen receptor (CAR) T-Cell strategies. AIMS Allergy and Immunology, 2020, 4(2): 32-49. doi: 10.3934/Allergy.2020004 |
[2] | Issam Tout, Marie Marotel, Isabelle Chemin, Uzma Hasan . HBV and the importance of TLR9 on B cell responses. AIMS Allergy and Immunology, 2017, 1(3): 124-137. doi: 10.3934/Allergy.2017.3.124 |
[3] | Andrey Mamontov, Alexander Polevshchikov, Yulia Desheva . Mast cells in severe respiratory virus infections: insights for treatment and vaccine administration. AIMS Allergy and Immunology, 2023, 7(1): 1-23. doi: 10.3934/Allergy.2023001 |
[4] | Ling Wang, Shunbin Ning . “Toll-free” pathways for production of type I interferons. AIMS Allergy and Immunology, 2017, 1(3): 143-163. doi: 10.3934/Allergy.2017.3.143 |
[5] | Daniil Shevyrev, Valeriy Tereshchenko, Olesya Manova, Vladimir kozlov . Homeostatic proliferation as a physiological process and a risk factor for autoimmune pathology. AIMS Allergy and Immunology, 2021, 5(1): 18-32. doi: 10.3934/Allergy.2021002 |
[6] | Stefano Regis, Fabio Caliendo, Alessandra Dondero, Francesca Bellora, Beatrice Casu, Cristina Bottino, Roberta Castriconi . Main NK cell receptors and their ligands: regulation by microRNAs. AIMS Allergy and Immunology, 2018, 2(2): 98-112. doi: 10.3934/Allergy.2018.2.98 |
[7] | Ken S. Rosenthal, Daniel H. Zimmerman . J-LEAPS vaccines elicit antigen specific Th1 responses by promoting maturation of type 1 dendritic cells (DC1). AIMS Allergy and Immunology, 2017, 1(2): 89-100. doi: 10.3934/Allergy.2017.2.89 |
[8] | James Peterson . Affinity and avidity models in autoimmune disease. AIMS Allergy and Immunology, 2018, 2(1): 45-81. doi: 10.3934/Allergy.2018.1.45 |
[9] | Michael D. Caponegro, Jeremy Tetsuo Miyauchi, Stella E. Tsirka . Contributions of immune cell populations in the maintenance, progression, and therapeutic modalities of glioma. AIMS Allergy and Immunology, 2018, 2(1): 24-44. doi: 10.3934/Allergy.2018.1.24 |
[10] | Caterina Marangio, Rosa Molfetta, Erisa Putro, Alessia Carnevale, Rossella Paolini . Exploring the dynamic of NKG2D/NKG2DL axis: A central regulator of NK cell functions. AIMS Allergy and Immunology, 2025, 9(2): 70-88. doi: 10.3934/Allergy.2025005 |
Combinatorial auction is an important type of market mechanism, which can help bidders to bid on the combination of items more efficiently. The winner determination problem (WDP) is one of the most challenging research topics on the combinatorial auction, which has been proven to be NP-hard. It has more attention from researchers in recent years and has a wide range of real-world applications. To solve the winner determination problem effectively, this paper proposes a hybrid ant colony algorithm called DHS-ACO, which combines an effective local search for exploitation and an ant colony algorithm for exploration, with two effective strategies. One is a hash tabu search strategy adopted to reduce the cycling problem in the local search procedure. Another is a deep scoring strategy which is introduced to consider the profound effects of the local operators. The experimental results on a broad range of benchmarks show that DHS-ACO outperforms the existing algorithms.
We are witnessing a rapid advancement in immunotherapy, in particular adoptive T-cell immunotherapy, against specific cancers over the past decade. Currently, adoptive T-cell immunotherapy comprises of three different classes through the use of tumor-infiltrating lymphocytes (TILs), chimeric antigen receptor (CAR)-and T-cell receptor (TCR)-engineered T cells [1]. While TILs are obtained through the isolation from tumor mass, the latter two methods obtain T cells through genetic engineering. Both CAR-and TCR-redirected systems result in the form of antigen-specific T cells, which would permit the immune system to confer an adequate anti-tumor immune response that maybe not present naturally [1].
Several published articles on the distinction between TCR-and CAR-engineered T-cell systems are available (please read review [2] in particular). TCR is an αβ heterodimer receptor, naturally expressed on the T-cell surface, which binds to a specific peptide-major histocompatibility complex/MHC unit. TCR associates with CD3 molecules (γ, δ, ε and ζ chains) to provide intracellular signaling domains, which is a prerequisite for a T cell to confer an immune response. In addition, the presence of either co-receptor CD4 or CD8 supports the responsiveness of a T cell to be activated by TCR binding to as few as one peptide-MHC unit. This sensitive, yet specific system allows T cells to physiologically target intracellular antigens in a form of peptide-MHC complexes [2]. The CAR refers to a synthetic construct typically comprising a single-chain antibody variable fragment, an extracellular domain/hinge, a transmembrane domain, one or more intracellular signaling domains (e.g. CD28 or 4-1BB) and cytoplasmic immunoreceptor tyrosine activation motifs derived from CD3-ζ chain [3]. Less commonly, the CD3-ζ chain is substituted with the γ chain of FcεRI or the CD3-ε chain [4]. The CAR system can target cell surface antigens independent of MHC. Transformed cells, such as cancerous cells, usually express a particular cell surface antigen at high density, hence these kinds of target cells can be recognized and eliminated by the CAR-engineered T cells [2]. Due to the pronounced differences between the CAR and TCR systems (as shown in Figure 1), it is indeed difficult to directly compare these two systems. Nonetheless, it is fair to state that CAR system has more potential to be utilized in a wide population, since it does not face any MHC restriction. On the other hand, TCR is a more specific system than CAR due to its capability to recognize and respond to as few as only one particular peptide-MHC complex [2].
As mentioned above, both CAR and TCR systems are currently being explored as potential treatment targets in different cancers. While the clinical efficacy of CAR-engineered T cells against solid tumors is still limited, partly due to the local immunosuppressive tumor environment, it has been demonstrated that CAR treatment against CD19 antigen (expressed by B cells) resulted in complete remission in several patients suffering from B-cell malignancies [5,6,7,8]. Despite its efficacy, CAR therapy, however, is associated with several side effects. In general, it could cause "the cytokine release syndrome" because of the systemic release of pro-inflammatory cytokines, e.g. TNF-α and IL-6, at high levels [9]. In particular, CD19-specific CAR therapy has been reported to result in B-cell aplasia that prompts for exogenous administration of immunoglobulin [2]. On the other hand, trials using TCR-engineered T cells demonstrated some success in treating both solid and hematological tumors [2]. However, current TCR-engineered T cells have been developed to target tumor-associated antigens (e.g. MAGE-A3 or NY-ESO-1), which are actually self antigens perse [10]. This implies that TCR-generated T cells could cross-react to similar peptide-MHC complexes in heathy tissue, although are presented at very low levels, resulting in severe, sometime lethal adverse events [11,12]. Taken together, despite these two systems are potentially efficacious in treating certain cancers, their safety profiles are still of concern and they need to be addressed and properly rectified before they can be routinely used in the clinical setting.
In addition, due to the complex process to produce a specific type of CAR-or TCR-engineered T cells per patient, there is a cautious remark questioning the ability of patients or public health system to pay substantial costs incurred by these modes of treatment. It is forecasted that the price ranges of CAR-or TCR-engineered T cells are between $120,000 and $300,000 per patient [13,14]. This estimated price seriously challenges the likelihood to implement these modes of treatment in the clinical setting [13]. Therefore, any creative solution to reduce the incurred costs, e.g. converting the engineered T cells from a specific patient-customized item to a mass-produced item [13], will be crucial in order to support and sustain the economic viability of these novel therapeutic modes.
Functional T-cell responses are required to control HBV and HCV replication, as well as to eliminate viral infection [15,16]. Therefore, both CAR and TCR systems have been studied the context of HBV and HCV infection as well. The published viral epitopes, targeted by CAR and TCR-engineered T cells, are summarized in Table 1. With respect to HCV infection, both systems have been extensively studied in vitro, i.e. by targeting HLA-A*02:01-restricted epitopes within HCV NS3 or NS5A protein, as well as HCV E2 glycoprotein in the TCR and CAR systems, respectively [17,18,19,20]. Both systems demonstrated their efficacy in controlling HCV replication in vitro with a low level of cytotoxicity. Nonetheless, subsequent in vivo and clinical studies are required to confirm whether these efficacies observed in vitro can be replicated without a profound risk of morbidity or mortality. Another hindrance is that potent antiviral drugs to cure HCV-infected patients are already available on the market [21], hence questioning the necessity to develop adoptive T-cell immunotherapy against chronic HCV infection.
System | HBV | HCV |
CAR | S domain of HBs antigen [22] | e137 of HCV/E2 glycoprotein [18] |
TCR | HLA-A*02:01-restricted HBs183-191 [14,24] | HLA-A*02:01-restricted NS31073-1081 [17,19,20] |
HLA-A*02:01-restricted HBs370-379 [23,24] | HLA-A*02:01-restricted NS5A1992-2000 [17,20] | |
HLA-A*02:01-restricted HBc18-27 [23,24] | ||
HLA-C*08:01-restricted HBs171-80 [24] |
Lack of potent anti-HBV drugs in contrast, has accelerated studies on adoptive T-cell immunotherapy. A research group led by Ulrike Protzer uses CAR that targets HBV envelope protein and has tested this system in a HBV-transgenic mouse model. This group demonstrated that CAR-engineered T cells were able to control HBV replication with a transient liver damage in vivo. In addition, their study showed that the presence of HBs antigens in murine sera did not interfere with the functionality of HBV-specific CAR-engineered T cells [22]. However, it is noteworthy that the levels of HBs antigen in murine sera (~1,000–1,200 IU/mL) correspond only to the levels observed in the low-replicate phase of chronic Hepatitis B [22]. This implies that it is elusive yet on whether CAR-engineered T cells can be functional in patients with higher levels of HBs antigen. As an alternative, the HBV-specific TCR-engineered T-cell research, led primarily by Antonio Bertoletti's group, is focusing on targeting certain MHC-restricted epitopes within viral antigens, e.g. HBV surface or core antigen. This group has demonstrated that TCR-engineered T cells are also able to control HBV replication in both cell lines and xenograft mice [14,23].
Taken together, both CAR-and TCR-engineered T cells have merits to be further developed as a potential treatment tool against chronic HBV infection. However, both methods are associated with a risk of significant liver inflammation and consequently, liver damage. Therefore, extensive studies are required to provide sufficient evidence in order to support the efficacy and safety of these treatment modes for patients with chronic HBV infection.
It has been acknowledged that chronic viral hepatitis contributes to the majority of primary hepatocellular carcinoma/HCC cases [25]. In line with the primary usage of adoptive T-cell therapy against cancers, this mode of treatment has a potential utility for the treatment of HBV-or HCV-associated HCC.
It is important to point out that a high frequency of HBV DNA integration is observed in the genome of HBV-associated HCC cells, resulting in the expression of HBV antigens by tumor cells [26]. This allows the usage of TCR-engineered T cells to treat HBV-associated HCC. Unlike self antigens, HBV antigens are not found in healthy tissues. Hence, these viral antigens theoretically can serve as better target antigens in certain HCC cases. However, since non-cancerous but HBV-infected hepatocytes also express HBV antigens, HBV-specific TCR-engineered T cells could attack those infected hepatocytes. This potentially could cause severe liver damage.
To address this concern, Bertoletti's group decided to treat a liver-transplanted patient who developed extrahepatic HCC metastasis with HBV-DNA integration, as the first use of HBV-specific TCR-engineered T cells in a clinical setting [27]. The patient importantly exhibited HBV surface antigen restricted by HLA-A*02:01 (i.e., HBs183-191 epitope), only in tissues with the extrahepatic HCC metastasis. Hence, the metastatic tissue could be attacked by HBV-specific TCR-engineered T cells with a significant reduced risk of damaging healthy liver tissue. Indeed, this group demonstrated the clinical potential and safety of using HBV-specific TCR-engineered T cells by choosing a suitable patient [27]. This finding still needs to be validated in clinical studies using large number of patients. Nonetheless, this milestone study suggests that the adoptive T-cell therapy can be used against a selected group of HBV-associated HCC cases, such as to prevent or treat HCC recurrence in liver-transplanted patients with HBV-positive HCC [28]. In addition, this research group recently modified its TCR engineering technology from the viral vector-based to mRNA electroporation-based method [14]. This TCR mRNA electroporation method is, arguably, a promising technology [14] due to its successful rate of engineering T cells (approximately half of the engineered T cells were endowed with antigen-specific functionality), its better safety profile (because of the transient functionality of engineered T cells) and its much reduced costs (approximately $30,000 per patient because of the less complexity and effort to engineer T cells). This improved technology, if proven, would sustain the economic viability of developing and implementing HBV-specific TCR-engineered T cells for clinical use.
In contrast, HCV as an RNA virus does not integrate with the host genome. Therefore, despite a study demonstrated the utilization of HCV-specific TCR-engineered T cells against HCV-associated HCC in cell lines and xenograft mice [29], it will be difficult to select a suitable group of HCV-associated HCC patients in order to be treated with this treatment mode.
We are entering a new exciting era where adoptive T-cell immunotherapy is extensively studied against viral hepatitis-associated liver cancer. Based on the evidence presented in this review, we are optimistic and feel that the adoptive T-cell immunotherapy, at least in a form of TCR-engineered T cells, could serve as a novel alternative yet effective treatment for a selected group of HBV-associated HCC patients.
No fund or grant was received for this article.
Both authors are also employees of Nutricia Research and therefore declare potential conflicts of interest.
[1] |
S. J. Rassenti, V. L. Smith, R. L. Bulfin, A combinatorial auction mechanism for airport time slot allocation, Bell J. Econ., 13 (1982), 402–417. https://doi.org/10.2307/3003463 doi: 10.2307/3003463
![]() |
[2] | K. Xu, Y. Zhang, X. Shi, H. Wang, Y. Wang, M. Shen, Online combinatorial double auction for mobile cloud computing markets, in IEEE 33rd International Performance Computing and Communications Conference, (2014), 1–8. https://doi.org/10.1109/PCCC.2014.7017103 |
[3] |
T. G. Chetan, M. Jenamani, S. P. Sarmah, Two-stage multi-attribute auction mechanism for price discovery and winner determination, Trans. Eng. Manage., 66 (2019), 112–126. https://doi.org/10.1109/TEM.2018.2810510 doi: 10.1109/TEM.2018.2810510
![]() |
[4] |
S. Wang, S. Qu, M. Goh, M. Wahab, H. Zhou, Integrated multi-stage decision-making for winner determination problem in online multi-attribute reverse auctions under uncertainty, Int. J. Fuzzy Syst., 22 (2019), 2354–2372. https://doi.org/10.1007/s40815-019-00757-0 doi: 10.1007/s40815-019-00757-0
![]() |
[5] |
W. Fontanini, P. A. Ferreira, A game-theoretic approach for the web services scheduling problem, Expert Syst. Appl., 41 (2014), 4743–4751. https://doi.org/10.1016/j.eswa.2014.02.016 doi: 10.1016/j.eswa.2014.02.016
![]() |
[6] |
D. H. Kim, S. A. Kazmi, A. Ndikumana, A. Manzoor, W. Saad, C. S. Hong, et al., Distributed radio slice allocation in wireless network virtualization: matching theory meets auctions, IEEE Access, 8 (2020), 494–732. https://doi.org/10.1109/ACCESS.2020.2987753 doi: 10.1109/ACCESS.2020.2987753
![]() |
[7] |
A. K. Ray, M. Jenamani, P. K. Mohapatra, Supplier behavior modeling and winner determination using parallel mdp, Expert Syst. Appl., 38 (2011), 4689–4697. https://doi.org/10.1016/j.eswa.2010.08.044 doi: 10.1016/j.eswa.2010.08.044
![]() |
[8] |
S. De Vries, R. V. Vohra, Combinatorial auctions: a survey, INFORMS J. Comput., 15 (2003), 284–309. https://doi.org/10.1287/ijoc.15.3.284.16077 doi: 10.1287/ijoc.15.3.284.16077
![]() |
[9] |
M. Rekik, S. Mellouli, Reputation-based winner determination problem for combinatorial transportation procurement auctions, J. Oper. Res. Soc., 63 (2012), 1400–1409. https://doi.org/10.1057/jors.2011.108 doi: 10.1057/jors.2011.108
![]() |
[10] |
W. Zhong, K. Xie, Y. Liu, C. Yang, S. Xie, Multi-resource allocation of shared energy storage: a distributed combinatorial auction approach, IEEE Trans. Smart Grid, 11 (2020), 4105–4115. https://doi.org/10.1109/TSG.2020.2986468 doi: 10.1109/TSG.2020.2986468
![]() |
[11] |
M. H. Rothkopf, A. Pekeč, R. M. Harstad, Computationally manageable combinational auctions, Manag. Sci., 44 (1998), 1131–1147. https://doi.org/10.1287/mnsc.44.8.1131 doi: 10.1287/mnsc.44.8.1131
![]() |
[12] |
X. Li, S. Ma, Multi-objective memetic search algorithm for multi-objective permutation flow shop scheduling problem, IEEE Access, 4 (2016), 2154–2165. https://doi.org/10.1109/ACCESS.2016.2565622 doi: 10.1109/ACCESS.2016.2565622
![]() |
[13] | Z. Lu, Y. Zhou, J. K. Hao, A hybrid evolutionary algorithm for the clique partitioning problem, IEEE Trans. Cybernetics, (2021). |
[14] |
M. Aïder, O. Gacem, M. Hifi, A hybrid population-based algorithm for the bi-objective quadratic multiple knapsack problem, Expert Syst. Appl., 191 (2022), 116238. https://doi.org/10.1016/j.eswa.2021.116238 doi: 10.1016/j.eswa.2021.116238
![]() |
[15] |
Q. Zhou, J. K. Hao, Q. Wu, A hybrid evolutionary search for the generalized quadratic multiple knapsack problem, Eur. J. Oper. Res., 296 (2022), 88–803. https://doi.org/10.1016/j.ejor.2021.04.001 doi: 10.1016/j.ejor.2021.04.001
![]() |
[16] | X. Li, X. Zhang, M. Yin, J. Wang, A genetic algorithm for the distributed assembly permutation flowshop scheduling problem, in 2015 IEEE Congress on Evolutionary Computation (CEC), (2015), 3096–3101. https://doi.org/10.1109/CEC.2015.7257275 |
[17] |
Y. Zhou, X. Liu, S. Hu, Y. Wang, M. Yin, Combining max-min ant system with effective local search for solving the maximum set k-covering problem, Knowl. Based Syst., 239 (2021), 108000. https://doi.org/10.1016/j.knosys.2021.108000 doi: 10.1016/j.knosys.2021.108000
![]() |
[18] |
Ș. Öztürk, R. Ahmad, N. Akhtar, Variants of artificial bee colony algorithm and its applications in medical image processing, Appl. Soft Comput., 97 (2020), 106799. https://doi.org/10.1016/j.asoc.2020.106799 doi: 10.1016/j.asoc.2020.106799
![]() |
[19] |
M. Dorigo, L. M. Gambardella, Ant colony system: a cooperative learning approach to the traveling salesman problem, IEEE Trans. Evol. Comput., 1 (1997), 53–66. https://doi.org/10.1109/4235.585892 doi: 10.1109/4235.585892
![]() |
[20] |
X. Zhang, X. Li, J. Wang, Local search algorithm with path relinking for single batch-processing machine scheduling problem, Neural Comput. Appl., 28 (2017), 313–326. https://doi.org/10.1007/s00521-016-2339-z doi: 10.1007/s00521-016-2339-z
![]() |
[21] |
M. Li, J. K. Hao, Q. Wu, Learning-driven feasible and infeasible tabu search for airport gate assignment, Eur. J. Oper. Res., 2021 (2021). https://doi.org/10.1016/j.ejor.2021.12.019 doi: 10.1016/j.ejor.2021.12.019
![]() |
[22] |
Z. Lu, J. K. Hao, U. Benlic, D. Lesaint, Iterated multilevel simulated annealing for large-scale graph conductance minimization, Inform. Sci., 572 (2021), 182–199. https://doi.org/10.1016/j.ins.2021.04.102 doi: 10.1016/j.ins.2021.04.102
![]() |
[23] |
F. Glover, Tabu search-part i, ORSA J. Comput., 1 (1989), 190–206. https://doi.org/10.1287/ijoc.1.3.190 doi: 10.1287/ijoc.1.3.190
![]() |
[24] |
Y. Zhou, J. Li, Y. Liu, S. Lv, Y. Lai, J. Wang, Improved memetic algorithm for solving the minimum weight vertex independent dominating set, Mathematics, 8 (2020), 1155. https://doi.org/10.3390/math8071155 doi: 10.3390/math8071155
![]() |
[25] |
P. V. Silvestrin, M. Ritt, An iterated tabu search for the multi-compartment vehicle routing problem, Comput. & Oper. Res., 81 (2017), 192–202. https://doi.org/10.1016/j.cor.2016.12.023 doi: 10.1016/j.cor.2016.12.023
![]() |
[26] |
L. Xing, Y. Liu, H. Li, C. C. Wu, W. C. Lin, X. Chen, A novel tabu search algorithm for multi-agv routing problem, Mathematics, 8 (2020), 279. https://doi.org/10.3390/math8020279 doi: 10.3390/math8020279
![]() |
[27] |
B. Vangerven, D. R. Goossens, F. C. Spieksma, Winner determination in geometrical combinatorial auctions, Eur. J. Oper. Res., 258 (2017), 254–263. https://doi.org/10.1016/j.ejor.2016.08.037 doi: 10.1016/j.ejor.2016.08.037
![]() |
[28] |
M. Kaleta, Network winner determination problem, Arch. Control Sci., 28 (2018). https://doi.org/10.24425/119077 doi: 10.24425/119077
![]() |
[29] |
N. Remli, A. Amrouss, I. El Hallaoui, M. Rekik, A robust optimization approach for the winner determination problem with uncertainty on shipment volumes and carriers' capacity, Trans. Res. Part B: Meth., 123 (2019), 127–148. https://doi.org/10.1016/j.trb.2019.03.017 doi: 10.1016/j.trb.2019.03.017
![]() |
[30] |
X. Qian, S. C. Fang, M. Huang, X. Wang, Winner determination of loss-averse buyers with incomplete information in multiattribute reverse auctions for clean energy device procurement, Energy, 177 (2019), 276–292. https://doi.org/10.1016/j.energy.2019.04.072 doi: 10.1016/j.energy.2019.04.072
![]() |
[31] |
X. Qian, F. T. Chan, M. Yin, Q. Zhang, M. Huang, X. Fu, A two-stage stochastic winner determination model integrating a hybrid mitigation strategy for transportation service procurement auctions, Comput. Ind. Eng., 149 (2020), 106703. https://doi.org/10.1016/j.cie.2020.106703 doi: 10.1016/j.cie.2020.106703
![]() |
[32] |
C. W. Lee, W. P. Wong, J. Ignatius, A. Rahman, M. L. Tseng, Winner determination problem in multiple automated guided vehicle considering cost and flexibility, Comput. Ind. Eng., 142 (2020), 106337. https://doi.org/10.1016/j.cie.2020.106337 doi: 10.1016/j.cie.2020.106337
![]() |
[33] | Y. Fujishima, K. Leyton-Brown, Y. Shoham, Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches, in IJCAI, 99 (1999), 548–553. |
[34] | N. Nisan, Bidding and allocation in combinatorial auctions, in Proceedings of the 2nd ACM Conference on Electronic Commerce, (2000), 1–12. https://doi.org/10.1145/352871.352872 |
[35] | K. Leyton-Brown, Y. Shoham, M. Tennenholtz, An algorithm for multi-unit combinatorial auctions, in Aaai/iaai, (2000), 56–61. |
[36] |
T. Sandholm, S. Suri, Bob: Improved winner determination in combinatorial auctions and generalizations, Artif. Intell., 145 (2003), 33–58. https://doi.org/10.1016/S0004-3702(03)00015-8 doi: 10.1016/S0004-3702(03)00015-8
![]() |
[37] |
O. Günlük, L. Ladányi, S. De Vries, A branch-and-price algorithm and new test problems for spectrum auctions, Manag. Sci., 51 (2005), 391–406. https://doi.org/10.1287/mnsc.1040.0332 doi: 10.1287/mnsc.1040.0332
![]() |
[38] |
L. F. Escudero, M. Landete, A. Marín, A branch-and-cut algorithm for the winner determination problem, Decis. Support Syst., 46 (2009), 649–659. https://doi.org/10.1016/j.dss.2008.10.009 doi: 10.1016/j.dss.2008.10.009
![]() |
[39] | H. H. Hoos, C. Boutilier, Solving combinatorial auctions using stochastic local search, in Aaai/iaai, (2000), 22–29. |
[40] | Y. Guo, A. Lim, B. Rodrigues, Y. Zhu, Heuristics for a bidding problem, Comput. Oper. Res., 33 (2006), 2179–2188. |
[41] | D. Boughaci, B. Benhamou, H. Drias, Stochastic local search for the optimal winner determination problem in combinatorial auctions, in International Conference on Principles and Practice of Constraint Programming, Springer, (2008), 593–597. |
[42] | N. Wang, D. Wang, Model and algorithm of winner determination problem in multi-item e-procurement with variable quantities, in The 26th Chinese Control and Decision Conference (2014 CCDC), (2014), 5364–5367. https://doi.org/10.1109/CCDC.2014.6852222 |
[43] | M. B. Dowlatshahi, V. Derhami, Winner determination in combinatorial auctions using hybrid ant colony optimization and multi-neighborhood local search, J. AI Data Min., 5 (2017), 169–181. |
[44] |
D. Boughaci, B. Benhamou, H. Drias, A memetic algorithm for the optimal winner determination problem, Soft Comput., 13 (2009), 905. https://doi.org/10.1007/s00500-008-0355-3 doi: 10.1007/s00500-008-0355-3
![]() |
[45] |
H. Zhang, S. Cai, C. Luo, M. Yin, An efficient local search algorithm for the winner determination problem, J. Heuristics, 23 (2017), 367–396. https://doi.org/10.1007/s10732-017-9344-y doi: 10.1007/s10732-017-9344-y
![]() |
[46] |
G. Lin, W. Zhu, M. M. Ali, An effective discrete dynamic convexized method for solving the winner determination problem, J. Comb. Optim., 32 (2016), 563–593. https://doi.org/10.1007/s10878-015-9883-9 doi: 10.1007/s10878-015-9883-9
![]() |
[47] |
G. Lin, Z. Li, A hybrid binary harmony search algorithm for solving the winner determination problem, Int. J. Innovative Comput. Appl., 10 (2019), 59–68. https://doi.org/10.1504/IJICA.2019.100547 doi: 10.1504/IJICA.2019.100547
![]() |
[48] | H. C. Lau, Y. G. Goh, An intelligent brokering system to support multi-agent web-based 4/sup th/-party logistics, in 14th IEEE International Conference on Tools with Artificial Intelligence, (2002), 154–161. |
[49] | K. Leyton-Brown, M. Pearson, Y. Shoham, Towards a universal test suite for combinatorial auction algorithms, in Proceedings of the 2nd ACM Conference on Electronic Commerce, (2000), 66–76. https://doi.org/10.1145/352871.352879 |
[50] |
M. López-Ibáñez, J. Dubois-Lacoste, L. P. Cáceres, M. Birattari, and T. Stützle, The irace package: Iterated racing for automatic algorithm configuration, Oper. Res. Perspect., 3 (2016), 43–58. https://doi.org/10.1016/j.orp.2016.09.002 doi: 10.1016/j.orp.2016.09.002
![]() |
System | HBV | HCV |
CAR | S domain of HBs antigen [22] | e137 of HCV/E2 glycoprotein [18] |
TCR | HLA-A*02:01-restricted HBs183-191 [14,24] | HLA-A*02:01-restricted NS31073-1081 [17,19,20] |
HLA-A*02:01-restricted HBs370-379 [23,24] | HLA-A*02:01-restricted NS5A1992-2000 [17,20] | |
HLA-A*02:01-restricted HBc18-27 [23,24] | ||
HLA-C*08:01-restricted HBs171-80 [24] |
System | HBV | HCV |
CAR | S domain of HBs antigen [22] | e137 of HCV/E2 glycoprotein [18] |
TCR | HLA-A*02:01-restricted HBs183-191 [14,24] | HLA-A*02:01-restricted NS31073-1081 [17,19,20] |
HLA-A*02:01-restricted HBs370-379 [23,24] | HLA-A*02:01-restricted NS5A1992-2000 [17,20] | |
HLA-A*02:01-restricted HBc18-27 [23,24] | ||
HLA-C*08:01-restricted HBs171-80 [24] |