Abstract
The analytical hierarchical process (AHP) is a multi-criteria, decision-making process that has demonstrated to be of a high utility to achieve complex decisions. This work presents a method to apply it in grupal decisions, where the weights that each user assigns to the criteria are different and private. A combination of consensus process and gradient ascent is used to reach a common agreement that optimizes the utility of the decision using the information exchanged in the local neighborhood exclusively.
The AHP problem is modeled through a multilayer network. Each one of the criteria are negotiated by consensus with the direct neighbors on each layer of the network. Furthermore, each node performs a transversal gradient ascent and corrects locally the deviations from the personal decision to keep the best option.
The process locates the global optimal decision, taking into account that this global function is never calculated nor known by any of the participants. If there is not a global optimal decision where all the participants have a not null utility, but a set of suboptimal decisions, they are automatically divided into different groups that converges into these suboptimal decisions.
Keywords
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Johansson, B., et al.: Subgradient methods and consensus algorithms for solving convex optimization problems. In: Proceedings of IEEE CDC 2008, pp. 4185–4190 (2008)
Zanella, F., et al.: Newton-raphson consensus for distributed convex optimization. In: Proceedings of IEEE CDC-ECC 2011, pp. 5917–5922 (2011)
Zanella, F., et al.: Asynchronous newton-raphson consensus for distributed convex optimization. In: Proceedings of IFAC NecSys 2012 (2012)
Zanella, F., et al.: Multidimensional newton-raphson consensus for distributed convex optimization. In: Proceedings of ACC 2012, pp. 1079–1084 (2012)
Askari-Sichani, O., Jalili, M.: Large-scale global optimization through consensus of opinions over complex networks. Complex Adapt. Syst. Model. 1(1), 11 (2013)
Boccaletti, S., Bianconi, G., Criado, R., del Genio, C., Gómez-Gardeñesi, J., Romance, M., Sendiña-Nadalj, I., Wang, Z., Zanin, M.: The structure and dynamics of multilayer networks. Phys. Rep. 544, 1–122 (2014)
Cai, K., Ishii, H.: Average consensus on arbitrary strongly connected digraphs with dynamic topologies. In: Proceedings of ACC 2012, pp. 14–19 (2012)
Cavalcante, R., Rogers, A., Jennings, N.: Consensus acceleration in multiagent systems with the chebyshev semi-iterative method. In: Proceedings of AAMAS 2011, pp. 165–172 (2011)
Elhage, N., Beal, J.: Laplacian-based consensus on spatial computers. In: AAMAS, pp. 907–914 (2010)
Frasca, P., Carli, R., Fagnani, F., Zampieri, S.: Average consensus on networks with quantized communication. Int. J. Robust Nonlin. 19(16), 1787–1816 (2009)
Hu, H.X., et al.: Group consensus in multi-agent systems with hybrid protocol. J. Franklin Inst. 350(3), 575–597 (2013)
Ishizaka, A., Labib, A.: Review of the main developments in the analytic hierarchy process. Expert Syst. Appl. 38(11), 14336–14345 (2011)
Ji, Z., Lin, H., Yu, H.: Leaders in multi-agent controllability under consensus algorithm and tree topology. Syst. Cont. Lett. 61(9), 918–925 (2012)
Yuan, K., Ling, Q., Yin, W.: On the convergence of decentralized gradient descent. Technical report. Report 13–61, UCLA CAM (2014)
Lancichinetti, A., Fortunato, S.: Consensus clustering in complex networks. CoRR abs/1203.6093 (2012)
Matei, I., Baras, J.: Performance evaluation of the consensus-based distributed subgradient method under random communication topologies. IEEE Sig. Proc. 5(4), 754–771 (2011)
Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE TAC 49(9), 1520–1533 (2004)
Pedroche, F., Rebollo, M., Carrascosa, C., Palomares, A.: On the convergence of weighted-average consensus. CoRR arxiv:1203.6093 [math.OC] (2013)
Pereira, S., Pages-Zamora, A.: Consensus in correlated random wireless sensor networks. IEEE Sig. Proc. 59(12), 6279–6284 (2011)
Salazar-Ramirez, N., Rodríguez-Aguilar, J.A., Arcos, J.L.: Robust coordination in large convention spaces. AI Commun. 23, 357–372 (2010)
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This work is supported by the PROMETEOII/2013/019 and TIN2015-65515-C4-1-R projects of the spanish government.
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Rebollo, M., Palomares, A., Carrascosa, C. (2016). Decentralized Group Analytical Hierarchical Process on Multilayer Networks by Consensus. In: Demazeau, Y., Ito, T., Bajo, J., Escalona, M. (eds) Advances in Practical Applications of Scalable Multi-agent Systems. The PAAMS Collection. PAAMS 2016. Lecture Notes in Computer Science(), vol 9662. Springer, Cham. https://doi.org/10.1007/978-3-319-39324-7_16
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DOI: https://doi.org/10.1007/978-3-319-39324-7_16
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