Result Diversification with Negative Type Distances by Multi-Objective Evolutionary Algorithms

Abstract

The result diversification problem is to select an optimal subset with high “quality” and “diversity” from a given ground set of items, which is popular in various applications such as web-based search, multi-document summarization and ensemble pruning. The diversity relies on the distance between items. Previous works mainly focused on metric distances, and applied a greedy or local search algorithm with theoretical guarantees. As a kind of global search algorithm inspired by Darwin’s theory of evolution, evolutionary algorithms (EAs) can have a better optimization ability than greedy and local search, but often lack theoretical support. Recently, EAs have been introduced to result diversification, achieving good theoretical guarantees besides superior empirical performances. In this paper, we study whether EAs can still achieve good theoretical guarantees for result diversification with negative type distances, which are also a class of important dissimilarity measures, especially in information retrieval and sketching techniques. We propose to reformulate the result diversification problem with negative type distances as a bi-objective maximization problem, and solve it by multi-objective evolutionary algorithms (MOEAs). We prove that a simple MOEA (i.e., GSEMO) can achieve the best-known polynomial-time approximation ratio. Experiments are also performed to examine the performance of different MOEAs on the application of web-based search.