Hybrid Genetic Algorithms to Determine 2-Optimality Consensus for a Collective of Ordered Partitions

Abstract

Determining consensus for a set of ordered partitions (or a collective) is used for making decisions. Ordered partitions are a helpful structure for representing the opinions of experts or agents. Algorithms to determine 1-Optimality consensus were introduced in the literature. However, no algorithm has yet to be proposed for determining the 2-Optimality consensus. Determining 2-Optimality consensus for a collective of ordered partitions is an NP-hard problem. In this study, first, we present a mathematical formula for determining such a collective. Then, three hybrid genetic algorithms are proposed to solve this problem. The simulation results show that the HG3 algorithm finds the best quality consensus in an acceptable time.