A Decentralized Approach to Solve Group AHP with Agreements by Consensus
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.
KeywordsComplex networks Consensus Gradient descent Analytical hierarchical process Agreement
This work is supported by the PROMETEOII/2013/019 and TIN2015-65515-C4-1-R projects of the spanish government.
- 1.Johansson, B., et al.: Subgradient methods and consensus algorithms for solving convex optimization problems. In: Proceedings of IEEE CDC 2008, pp. 4185–4190 (2008)Google Scholar
- 2.Zanella, F., et al.: Newton-Raphson consensus for distributed convex optimization. In: Proceedings of IEEE CDC-ECC 2011, pp. 5917–5922 (2011)Google Scholar
- 3.Zanella, F., et al.: Asynchronous newton-Raphson consensus for distributed convex optimization. In: Proceedings of IFAC NecSys 2012 (2012)Google Scholar
- 4.Zanella, F., et al.: Multidimensional newton-Raphson consensus for distributed convex optimization. In: Proceedings of ACC 2012, pp. 1079–1084 (2012)Google Scholar
- 7.Cai, K., Ishii, H.: Average consensus on arbitrary strongly connected digraphs with dynamic topologies. In: Proceedings of ACC 2012, pp. 14–19 (2012)Google Scholar
- 8.Cavalcante, R., Rogers, A., Jennings, N.: Consensus acceleration in multiagent systems with the Chebyshev semi-iterative method. In: Proceeding of AAMAS 2011, pp. 165–172 (2011)Google Scholar
- 9.Elhage, N., Beal, J.: Laplacian-based consensus on spatial computers. In: AAMAS, pp. 907–914 (2010)Google Scholar
- 12.Ishizaka, A., Labib, A.: Review of the main developments in the analytic hierarchy process. Expert Syst. Appl. 38(11), 14336–14345 (2011)Google Scholar
- 14.Lancichinetti, A., Fortunato, S.: Consensus clustering in complex networks. CoRR abs/1203.6093 (2012)Google Scholar
- 15.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)Google Scholar
- 18.Pedroche, F., Rebollo, M., Carrascosa, C., Palomares, A.: On the convergence of weighted-average consensus. CoRR [math.OC] (2013). arXiv:1203.6093
- 21.Yuan, K., Ling, Q., Yin, W.: On the convergence of decentralized gradient descent. Technical report, 13–61, UCLA CAM (2014)Google Scholar