The inverse model based multi-objective evolutionary algorithm (IM-MOEA) generates offspring by establishing probabilistic models and sampling by the model, which is a new computing schema to replace crossover in MOEAs. In this paper, an active learning Gaussian modeling based multi-objective evolutionary algorithm using population guided weight vector evolution strategy (ALGM-MOEA) is proposed. To properly cope with multi-objective problems with different shapes of Pareto front (PF), a novel population guided weight vector evolution strategy is proposed to dynamically adjust search directions according to the distribution of generated PF. Moreover, in order to enhance the search efficiency and prediction accuracy, an active learning based training sample selection method is designed to build Gaussian process based inverse models, which chooses individuals with the maximum amount of information to effectively enhance the prediction accuracy of the inverse model. The experimental results demonstrate the competitiveness of the proposed ALGM-MOEA on benchmark problems with various shapes of Pareto front.
Citation: Xiaofang Guo, Yuping Wang, Haonan Zhang. An active learning Gaussian modeling based multi-objective evolutionary algorithm using population guided weight vector evolution strategy[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 19839-19857. doi: 10.3934/mbe.2023878
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The inverse model based multi-objective evolutionary algorithm (IM-MOEA) generates offspring by establishing probabilistic models and sampling by the model, which is a new computing schema to replace crossover in MOEAs. In this paper, an active learning Gaussian modeling based multi-objective evolutionary algorithm using population guided weight vector evolution strategy (ALGM-MOEA) is proposed. To properly cope with multi-objective problems with different shapes of Pareto front (PF), a novel population guided weight vector evolution strategy is proposed to dynamically adjust search directions according to the distribution of generated PF. Moreover, in order to enhance the search efficiency and prediction accuracy, an active learning based training sample selection method is designed to build Gaussian process based inverse models, which chooses individuals with the maximum amount of information to effectively enhance the prediction accuracy of the inverse model. The experimental results demonstrate the competitiveness of the proposed ALGM-MOEA on benchmark problems with various shapes of Pareto front.
The term and concept of “tissue engineering” was officially coined over 30 years ago, in 1988, at a National Science Foundation workshop as “the application of engineering principles and methods from life sciences to a fundamental understanding of the structure-function relationships of normal and pathological mammalian tissues and the development of biological substitutes to restore, maintain or improve tissue function”. While the field of tissue engineering is relatively new, the idea of replacing one tissue by another dates back several centuries [1]. Thus, and for many years now, the replacement by implantation and transplantation of a tissue from a given site to another site in the same patient (an autograft) or in a different patient (a transplant or an allograft) has been innovative and beneficial, but both techniques present major problems. On the one hand, harvesting tissue for an autograft is expensive, painful, limited by anatomical limitations, and associated with donor site morbidity due to infection and injury. On the other hand, allografts and tissue grafts have serious constraints: limit of access to enough tissues or organs for all patients who need it, rejection by the immune system of the recipient patient, potential risks of introduction of infection or disease... [2]. It is in this context that the development of biofabrication strategies arouses considerable interest in order to develop methods, tools and products having the objectives of mimicking and replicating the anatomical and functional characteristics of human tissues.
Bone tissue is the second largest transplant tissue in the world. Millions of bone grafts (autografts and allografts) are performed each year around the world, while there is currently no satisfactory alternative to bone grafting. Traditional surgical treatments for fractures and bone defects, mainly comprising bone grafts and implantation of metal prostheses, achieve good clinical results, but these treatments also have serious drawbacks, such as infection, pain, cost. high, and the need for additional surgery. In some cases, such as bone defects, osteoporotic fractures, or bone defects/fractures in oncologic patients after radiation therapy, regeneration of bone tissue is hampered, and then requires modern strategies such as bone tissue engineering [3].
Tissue-engineering technologies involve the intimate interaction between three different components: (1) the scaffolding material that holds and cohesions cells together and forms the physical structure of tissue, i.e. acts as a model for the formation of new tissues, (2) the cells synthesizing the final tissue and (3) the signaling mechanisms (mechanical and/or chemical) that direct cells to express the desired tissue phenotype. Particular attention must be paid to the specific properties of each of these three components, in order to ensure the quality of the modified and neo-synthetized tissue and therefore the potential for clinical success when the engineered tissue is subsequently implanted into an injured site in vivo [4].
Biological and clinical evaluation of medical devices, including biomaterials, has also been implemented by ISO's ad hoc technical committee since 1988. Since then, sets of standards have been produced and are kept up to date. technological innovation in this highly biomedical field. If it is absorbable, its degradation products must also be biocompatible and not harmful. For application in a living organism, such as humans, all scaffolding materials must have very specific characteristics. First of all, to be defined as a biomaterial, the material must be biocompatible so that it can exist in harmony with the biological fluids, tissues, and cells of the host, without causing harmful effects locally or systemically. In the case of bone tissue, the scaffolding material must exhibit three fundamental bioactivities and properties: osteoinduction, osteoconduction, and osteointegration. Osteoinduction belongs to the ability to induce osteogenic differentiation of a cell that is not yet engaged [5]. In that context, an osteoinductive biomaterial can directly induce osteogenesis through the recruitment, proliferation, and differentiation of bone related stem cells such as mesenchymal stem cells. Osteoconduction refers to the ability to provide the microenvironment allowing the occurrence of in-place bone formation (osteogenesis) and bone growth [6]. Osseointegration refers to the ability of a biomaterial to elaborate direct contacts and anchoring between the exogenic material it-self and the host bone tissue, without growth of fibrous tissue at the bone-implant interface [7]. These 3 fundamental bioactivities and properties can be supported by different physical characteristics related to this specific mineralized hard material, such as stiffness and mechanical strength, viscosity, shear stress, geometry, hydrophilicity, surface charge, wettability, surface roughness and topography, porosity and pore size, permeability, mechanical stability, as well as controlled degradation rate [8]. All these parameters are crucial to encourage cell migration, adhesion, proliferation, and differentiation, but also for nutrients and oxygen transport throughout the scaffolds [9]. Another key consideration for designing a scaffold is its delivery capability through the releasing biological active agents that can induce important properties such as faster healing, antimicrobial, and antitumoral activity.
Biomaterials can be classified depending on their composition in metals (such as Fe, Mg, Zn and their alloys), ceramics (calcium phosphate ceramics such as hydroxyapatite, biphasic calcium phosphate [BCP] and tricalcium phosphate [TCP], bioactive glasses, zirconia), natural polymers (collagen, silk, chitosan, alginate, elastin, hyaluronic acid and cellulose) or synthetic polymers (such as polylactid acid [PLA], polyglycolic acid [PGA], polylactic co-glycolic acid [PLGA], poly e-caprolactone [PCL], polyethylene glycol [PEG], polybutylene terephthalate [PBT], polyethylene terephthalate [PET], polypropylene fumarate [PPF] or polyacrylic acid [PAA]), composites (defined as made of two or more substrates belonging to the same or different class of materials) and recently nanomaterials including nanoparticles [10]. All these materials can also be functionalized to improve their properties (including the three fundamental properties described above, but also to induce angiogenesis for example) [11].
The second component for bone tissue engineering belongs to the cell component where several cell types can be used to develop a bone construct, including osteoblast, embryonic stem cells (ESC), mesenchymal stem cells (MSC) and induced pluripotent stem cells (iPSC). All these cell types have largely demonstrated their ability to induce and promote and bone formation, remodeling, and healing [12].
A finally, the third part of bone tissue engineering is dedicated to signaling mechanisms that can be conveyed by the material itself, depending on its intrinsic properties and characteristics, or provided secondarily exogenously by enriching the final product with growth factors or cytokines (including TGFbeta and BMP, among others), as well as drugs [13].
At last, the recent advent and democratization of 3D printing processes, allowing the development of complex 3D structures using various biomaterials, opens up new opportunities and great flexibility in the design and production of scaffolds of different structural complexity combining adapted mechanical properties, vascularization and multicellular component [14]. In parallel, computational approaches can be carried out in order to optimize and predict the expected performances of the bone substitute produced by integrated bone tissue engineering. Finally, advances in artificial intelligence (AI), and deep learning in particular, offer the potential to improve both scientific understanding and clinical outcomes in regenerative medicine [15]. With an improved perception of how to integrate artificial intelligence into current research and clinical practice, AI offers an invaluable tool for improving patient outcomes in bone tissue engineering.
| [1] |
Y. Xue, Y. Tang, X. Xu, J. Liang, F. Neri, Multi-objective feature selection with missing data in classification, IEEE Trans. Emerging Top. Comput. Intell., 6 (2021), 355–364. https://doi.org/10.1109/TETCI.2021.3074147 doi: 10.1109/TETCI.2021.3074147
|
| [2] |
Y. Xue, B. Xue, M. Zhang, Self-adaptive particle swarm optimization for large-scale feature selection in classification, ACM Trans. Knowl. Discovery Data, 13 (2019), 1–27. https://doi.org/10.1145/3340848 doi: 10.1145/3340848
|
| [3] |
Y. Xue, X. Cai, F. Neri, A multi-objective evolutionary algorithm with interval based initialization and self-adaptive crossover operator for large-scale feature selection in classification, Appl. Soft Comput., 127 (2022), 1–14. https://doi.org/10.1016/j.asoc.2022.109420 doi: 10.1016/j.asoc.2022.109420
|
| [4] |
Y. Hu, Y. Zhang, D. Gong, Multiobjective particle swarm optimization for feature selection with fuzzy cost, IEEE Trans. Cybern., 51 (2020), 874–888. https://doi.org/10.1109/TCYB.2020.3015756 doi: 10.1109/TCYB.2020.3015756
|
| [5] |
W. Liu, A. Li, C. Liu, Multi-objective optimization control for tunnel boring machine performance improvement under uncertainty, Autom. Constr., 139 (2022), https://doi.org/10.1016/j.autcon.2022.104310 doi: 10.1016/j.autcon.2022.104310
|
| [6] |
S. Luo, X. Guo, Multi-objective optimization of multi-microgrid power dispatch under uncertainties using interval optimization, J. Ind. Manage. Optim., 19 (2023), 823–851. https://doi.org/10.3934/jimo.2021208 doi: 10.3934/jimo.2021208
|
| [7] |
R. Tanabe, H. Ishibuchi, A framework to handle multimodal multi-objective optimization in decomposition-based evolutionary algorithms, IEEE Trans. Evol. Comput., 24 (2020), 720–734. https://doi.org/10.1109/TEVC.2019.2949841 doi: 10.1109/TEVC.2019.2949841
|
| [8] |
M. Q. Li, X. Yao, What weights work for you? Adapting weights for any Pareto front shape in decomposition-based evolutionary multi-objective optimization, Evol. Comput., 28 (2020), 227–253. https://doi.org/10.1162/EVCO_A_00269 doi: 10.1162/EVCO_A_00269
|
| [9] |
T. Zhang, F. Li, X. Zhao, W. Qi, T. Liu, A convolutional neural network-based surrogate model for multi-objective optimization evolutionary algorithm based on decomposition, Swarm Evol. Comput., 72 (2022), 101081. https://10.1016/j.swevo.2022.101081 doi: 10.1016/j.swevo.2022.101081
|
| [10] |
J. Shen, P. Wang, H. Dong, J. Li, W. Wang, A multistage evolutionary algorithm for many-objective optimization, Inf. Sci., 589 (2022), 531–549. http://10.1016/j.ins.2021.12.096 doi: 10.1016/j.ins.2021.12.096
|
| [11] |
Y. Liu, Y. Hu, N. Zhu, K. Li, M. Li, A decomposition-based multi-objective evolutionary algorithm with weights updated adaptively, Inf. Sci., 572 (2021), 343–377. https://doi.org/10.1016/j.ins.2021.03.067 doi: 10.1016/j.ins.2021.03.067
|
| [12] |
P. Serafini, Simulated annealing for multi objective optimization problems, Multiple Criteria Decision Making, (1994), 283–292. https://doi.org/10.1007/978-1-4612-2666-6_29 doi: 10.1007/978-1-4612-2666-6_29
|
| [13] | Y. Jin, T. Okabe, B. Sendhoff, Dynamic weighted aggregation of evolutionary multi-objective optimization: why does it work and how?, in Proceedings of the Genetic and Evolutionary Computation Conference, (2001), 1042–1049. |
| [14] | F. Q. Gu, H. L. Liu, A novel weight design in multi-objective evolutionary algorithm, in 2010 International Conference on Computational Intelligence and Security, (2010), 137–141. https://doi.org/10.1109/CIS.2010.37 |
| [15] |
F. Gu, Y. M. Cheung, Self-organizing map-based weight design for decomposition-based many-objective evolutionary algorithm, IEEE Trans. Evol. Comput., 22 (2017), 211–225. https://doi.org/10.1109/TEVC.2017.2695579 doi: 10.1109/TEVC.2017.2695579
|
| [16] |
R. Wang, R. C. Purshouse, P. J. Fleming, Preference-inspired co-evolutionary algorithms using weight vectors, Eur. J. Oper. Res., 243 (2015), 423–441. https://doi.org/10.1016/j.ejor.2014.05.019 doi: 10.1016/j.ejor.2014.05.019
|
| [17] |
X. Yi, Y. Zhou, M. Li, Z. Chen, A vector angle-based evolutionary algorithm for unconstrained many-objective optimization, IEEE Trans. Evol. Comput., 21 (2017), 131–152. https://doi.org/10.1109/TEVC.2016.2587808 doi: 10.1109/TEVC.2016.2587808
|
| [18] |
H. Ge, M. Zhao, L. Sun, Z. Wang, G. Tan, Q. Zhang, et al., A many-objective evolutionary algorithm with two interacting processes: Cascade clustering and reference point incremental learning, IEEE Trans. Evol. Comput., 23 (2019), 572–586. https://doi.org/10.1109/TEVC.2018.2874465 doi: 10.1109/TEVC.2018.2874465
|
| [19] |
T. Liu, X. Li, L. Tan, S. Song, An incremental-learning model-based multi-objective estimation of distribution algorithm, Inf. Sci., 569 (2021), 430–449. https://doi.org/10.1016/j.ins.2021.04.011 doi: 10.1016/j.ins.2021.04.011
|
| [20] |
M. Wu, K. Li, S. Kwong, Q. Zhang, J. Zhang, Learning to decompose: a paradigm for decomposition-based multiobjective optimization, IEEE Trans. Evol. Comput., 23 (2019), 376–390. https://doi.org/10.1109/TEVC.2018.2865931 doi: 10.1109/TEVC.2018.2865931
|
| [21] |
T. Liu, X. Li, L. Tan, S. Song, A novel adaptive greedy strategy based on Gaussian mixture clustering for multiobjective optimization, Swarm Evol. Comput., 61 (2021), 1–43. https://doi.org/10.1016/j.swevo.2020.100815 doi: 10.1016/j.swevo.2020.100815
|
| [22] | M. Laumanns, J. Ocenasek, Bayesian optimization algorithms for multi-objective optimization, in Proceedings of the 7th International Conference Parallel Problem Solving from Nature, (2002), 298–307. https://doi.org/10.1007/3-540-45712-7_29 |
| [23] |
H. Karshenas, R. Santana, C. Bielza, P. Larranaga, Multiobjective estimation of distribution algorithm based on joint modeling of objectives and variables, IEEE Trans. Evol. Comput., 18 (2014), 519–542. https://doi.org/10.1109/TEVC.2013.2281524 doi: 10.1109/TEVC.2013.2281524
|
| [24] |
Q. Zhang, A. Zhou, Y. Jin, RM-MEDA: A regularity model-based multiobjective estimation of distribution algorithm, IEEE Trans. Evol. Comput., 12 (2008), 41–63. https://doi.org/10.1109/TEVC.2007.894202 doi: 10.1109/TEVC.2007.894202
|
| [25] |
R. Cheng, Y. Jin, K. Narukawa, B. Sendhoff, A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling, IEEE Trans. Evol. Comput., 19 (2015), 838–856. https://doi.org/10.1109/TEVC.2015.2395073 doi: 10.1109/TEVC.2015.2395073
|
| [26] | L. R. Farias, A. F. Araújo, IM-MOEA/D: an inverse modeling multi-objective evolutionary algorithm based on decomposition, in 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), IEEE, (2021), 462–467. |
| [27] |
J. Shen, H. Dong, P. Wang, J. Li, W. Wang, An inverse model-guided two-stage evolutionary algorithm for multi-objective optimization, Expert Syst. Appl., 225 (2023), 120198. http://doi.org/10.1016/j.eswa.2023.120198 doi: 10.1016/j.eswa.2023.120198
|
| [28] |
Z. Zhang, S. Liu, W. Gao, J. Xu, S. Zhu, An enhanced multi-objective evolutionary optimization algorithm with inverse model, Inf. Sci., 530 (2020), 128–147. http://doi.org/10.1016/j.ins.2020.03.111 doi: 10.1016/j.ins.2020.03.111
|
| [29] | X. Guo, A multi-objective decomposition based evolutionary algorithm using adaptive search, in 17th International Conference on Computational Intelligence and Security, 2021. |
| [30] |
R. Cheng, Y. Jin, M. Olhofer, B. Sendhoff, A reference vector guided evolutionary algorithm for many-objective optimization, IEEE Trans. Evol. Comput., 20 (2016), 773–791. https://doi.org/10.1109/TEVC.2016.2519378 doi: 10.1109/TEVC.2016.2519378
|
| [31] |
Q. Zhang, H. Li, MOEA/D: A multi-objective evolutionary algorithm based on decomposition, IEEE Trans. Evol. Comput., 11 (2007), 712–731. https://doi.org/10.1109/ICALT.2005.160 doi: 10.1109/ICALT.2005.160
|
| [32] |
M. Elarbi, S. Bechikh, A. Gupta, L. B. Said, Y. S. Ong, A new decomposition-based NSGA-Ⅱ for many-objective optimization, IEEE Trans. Syst. Man Cybern.: Syst., 48 (2018), 1191–1210. https://doi.org/10.1109/TSMC.2017.2654301 doi: 10.1109/TSMC.2017.2654301
|
| [33] |
J. Yuan, H. Liu, F. Gu, Q. Zhang, Z. He, Investigating the properties of indicators and an evolutionary many-objective algorithm based on a promising region, IEEE Trans. Evol. Comput., 25 (2020), 75–86. http://doi.org/10.1109/TEVC.2020.2999100 doi: 10.1109/TEVC.2020.2999100
|
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Xiaofang Guo, Yuping Wang, Haonan Zhang. An active learning Gaussian modeling based multi-objective evolutionary algorithm using population guided weight vector evolution strategy[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 19839-19857. doi: 10.3934/mbe.2023878
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