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This research was funded by MICINN grant numbers MODAS-IN RTI2018-094269-B-I00 and PGC2018-095322-B-C22, URJC grant number AYUDA PUENTE 2019, URJC, 2020/00006/014, and Comunidad de Madrid and Fondos Estructurales of European Union grant number S2018/TCS-4566.

Analysis of institutional authors

Cano, JCorresponding AuthorAlfaro, CAuthorGomez, JAuthorDuarte, AAuthor
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Article

Out of the Niche: Using Direct Search Methods to Find Multiple Global Optima

Publicated to:Mathematics. 10 (9): 1494- - 2022-05-01 10(9), DOI: 10.3390/math10091494

Authors: Cano, Javier; Alfaro, Cesar; Gomez, Javier; Duarte, Abraham

Affiliations

Rey Juan Carlos Univ, Dept Comp Sci & Stat, Madrid 28933, Spain - Author
Univ Auckland, Dept Stat, Auckland 1010, New Zealand - Author

Abstract

Multimodal optimization deals with problems where multiple feasible global solutions coexist. Despite sharing a common objective function value, some global optima may be preferred to others for various reasons. In such cases, it is paramount to devise methods that are able to find as many global optima as possible within an affordable computational budget. Niching strategies have received an overwhelming attention in recent years as the most suitable technique to tackle these kinds of problems. In this paper we explore a different approach, based on a systematic yet versatile use of traditional direct search methods. When tested over reference benchmark functions, our proposal, despite its apparent simplicity, noticeably resists the comparison with state-of-the-art niching methods in most cases, both in the number of global optima found and in the number of function evaluations required. However, rather than trying to outperform niching methods-far more elaborated-our aim is to enrich them with the knowledge gained from exploiting the distinctive features of direct search methods. To that end, we propose two new performance measures that can be used to evaluate, compare and monitor the progress of optimization algorithms of (possibly) very different nature in their effort to find as many global optima of a given multimodal objective function as possible. We believe that adopting these metrics as reference criteria could lead to more sophisticated and computationally-efficient algorithms, which could benefit from the brute force of derivative-free local search methods.

Keywords
AlgorithmsDifferential evolutionDirect search methodsLatin hypercubeMultimodal optimizationNiching methodsOptimizationPerformance measuresSimplex-methodVariables

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2022, it was in position 23/330, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.13. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Field Citation Ratio (FCR) from Dimensions: 2.03 (source consulted: Dimensions May 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-05-10, the following number of citations:

  • WoS: 3
  • Scopus: 3
  • OpenCitations: 3
Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-05-10:

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

    It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

    • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
    Leadership analysis of institutional authors

    This work has been carried out with international collaboration, specifically with researchers from: New Zealand.

    There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Cano Cancela, Javier Fernando) and Last Author (Duarte Muñoz, Abraham).

    the author responsible for correspondence tasks has been Cano Cancela, Javier Fernando.