Evolutionary Algorithms to Find Consensus for Incomplete Ordered Partitions

Abstract

An incomplete ordered partition (IOP) is a helpful structure for representing people's opinions. For a set of elements representing the opinions of a group of people for one problem, one should determine an element called consensus that best describes these elements. Finding consensus for an IOP collective is crucial in making decisions. However, finding one 2-optimality consensus for IOP collectives is an NP-hard problem that has yet to be widely considered for resolution. This study proposes evolutionary algorithms to solve this problem: one genetic algorithm (GA) and one hybrid algorithm (HA). The GA algorithm is based on the traditional genetic algorithm. The HA algorithm focuses on growing the balance of exploitation and exploration. The simulation shows that the two proposed algorithms find high-quality consensus, and the HA generates a higher-quality consensus.