Weighted aggregation of partial rankings using Ant Colony Optimization

Abstract

The aggregation of preferences (expressed in the form of rankings) from multiple experts is a well-studied topic in a number of fields. The Kemeny ranking problem aims at computing an aggregated ranking having minimal distance to the global consensus. However, it assumes that these rankings will be complete, i.e., all elements are explicitly ranked by the expert. This assumption may not simply hold when, for instance, an expert ranks only the top-K items of interest, thus creating a partial ranking. In this paper we formalize the weighted Kemeny ranking problem for partial rankings, an extension of the Kemeny ranking problem that is able to aggregate partial rankings from multiple experts when only a limited number of relevant elements are explicitly ranked (top-K), and this number may vary from one expert to another (top-K i). Moreover, we introduce two strategies to quantify the weight of each partial ranking. We cast this problem within the realm of combinatorial optimization and lean on the successful Ant Colony Optimization (ACO) metaheuristic algorithm to arrive at high-quality solutions. The proposed approach is evaluated through a real-world scenario and 190 synthetic datasets from www.PrefLib.org. The experimental evidence indicates that the proposed ACO-based solution is capable of significantly

Rough Cognitive Networks

“…While this approach is straightforward from the Granular Computing viewpoint, further strategies to construct the network topology and activate the neurons should be investigated. 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48} Negative {49,50,51,52,53,54,55,56,57,…”

Heuristic Search for Rank Aggregation with Application to Label Ranking

“…Rank aggregation for partial rankings: To address RAP in the general setting, Aledo et al [19] proposed an improved Borda method for RAP containing any kind of rankings and outperformed the standard Borda method. In addition, Nápoles et al [20] applied ant colony optimization to solve an extension of KRP, that is, the weighted KRP for partial rankings. D'Ambrosio et al [21] proposed a differential evolution algorithm for consensus-ranking detection within Kemeny's axiomatic framework.…”

Lagrangian Inference for Ranking Problems

“…However, users' explicit scores can be inconsistent and noisy, or even not available in some cases. This motivates researchers to develop methods for ranking aggregations from comparison results or partial rankings provided by users (Saaty 2003, Ailon et al 2008, Ailon 2010, Gleich and Lim 2011, Ammar and Shah 2011, Farnoud et al 2012, Volkovs and Zemel 2012, Ammar and Shah 2012, Swain et al 2017, Nápoles et al 2017, Jang et al 2017, Chen et al 2018b, Zhang 2020.…”