Work

A Biased-Randomized Algorithm for the Bi-Objective Capacitated Dispersion Problem with Symmetries

Year: 2026

Type: article

Abstract: Given a network of nodes and a certain demand that needs to be satisfied, the capacitated dispersion problem (CDP) involves selecting a subset of nodes to maximize dispersion between them. In many practical instances, symmetry in the structure of the selected nodes (e.g., using nodes of the same type) can lead to synergies. Hence, this paper studies a bi-objective variant of the CDP to account for these symmetries. The first goal seeks to maximize the minimum distance between opened nodes, while the second goal accounts for symmetry by penalizing the use of nodes of different types (in our case, represented by different colors). We formalize the problem as a bi-objective mathematical program and address it through a classical multiobjective strategy, the ϵ-constraint method. Exact methods are used when the problem size allows, even though the problem is NP-hard. To tackle larger instances, we design a biased-randomized algorithm based on a constructive heuristic. Computational experiments show that our biased-randomized algorithm provides high-quality approximations of the Pareto frontier.

Source: Symmetry

DOI: 10.3390/sym18010110

Authors: Juan F. Gomez, Wenwen Chen, Laura Calvet, Majsa Ammouriova, Angel A. Juan

Institutions: Universitat Politècnica de València, Universitat Autònoma de Barcelona, Universitat Oberta de Catalunya, German Jordanian University

Language: English

Topic: Facility Location and Emergency Management

Subfield: Organizational Behavior and Human Resource Management

Field: Business, Management and Accounting

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: Ministerio de Ciencia, Innovación y Universidades, Generalitat Valenciana, Agencia Estatal de Investigación