k-Pareto Optimality-Based Sorting with Maximization of Choice

TL;DR

This paper introduces a generalized topological sorting problem focused on maximizing the number of equally preferable options within a subset, formulates it abstractly, and demonstrates its practical effectiveness in genetic optimization.

Contribution

It formulates a new generalized topological sorting problem based on k-Pareto optimality and shows its practical utility in improving genetic optimization algorithms.

Findings

The k-Pareto optimality-based sorting outperforms NSGA-II and NSGA-III.

The theory applies to various practical applications.

The approach effectively maximizes choice in subset selection.

Abstract

Topological sorting is an important technique in numerous practical applications, such as information retrieval, recommender systems, optimization, etc. In this paper, we introduce a problem of generalized topological sorting with maximization of choice, that is, of choosing a subset of items of a predefined size that contains the maximum number of equally preferable options (items) with respect to a dominance relation. We formulate this problem in a very abstract form and prove that sorting by k-Pareto optimality yields a valid solution. Next, we show that the proposed theory can be useful in practice. We apply it during the selection step of genetic optimization and demonstrate that the resulting algorithm outperforms existing state-of-the-art approaches such as NSGA-II and NSGA-III. We also demonstrate that the provided general formulation allows discovering interesting relationships and applying the developed theory to different applications.