{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T00:02:13Z","timestamp":1778803333424,"version":"3.51.4"},"reference-count":61,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T00:00:00Z","timestamp":1663113600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Broderick Crawford","award":["ANID\/FONDECYT\/REGULAR\/1210810"],"award-info":[{"award-number":["ANID\/FONDECYT\/REGULAR\/1210810"]}]},{"name":"Broderick Crawford","award":["ANID\/FONDECYT\/REGULAR\/1211905"],"award-info":[{"award-number":["ANID\/FONDECYT\/REGULAR\/1211905"]}]},{"name":"Broderick Crawford","award":["ANID\/FONDECYT\/INICIACI\u00d3N\/11200113"],"award-info":[{"award-number":["ANID\/FONDECYT\/INICIACI\u00d3N\/11200113"]}]},{"name":"Roberto Mu\u00f1oz","award":["ANID\/FONDECYT\/REGULAR\/1210810"],"award-info":[{"award-number":["ANID\/FONDECYT\/REGULAR\/1210810"]}]},{"name":"Roberto Mu\u00f1oz","award":["ANID\/FONDECYT\/REGULAR\/1211905"],"award-info":[{"award-number":["ANID\/FONDECYT\/REGULAR\/1211905"]}]},{"name":"Roberto Mu\u00f1oz","award":["ANID\/FONDECYT\/INICIACI\u00d3N\/11200113"],"award-info":[{"award-number":["ANID\/FONDECYT\/INICIACI\u00d3N\/11200113"]}]},{"name":"Fabi\u00e1n Riquelme","award":["ANID\/FONDECYT\/REGULAR\/1210810"],"award-info":[{"award-number":["ANID\/FONDECYT\/REGULAR\/1210810"]}]},{"name":"Fabi\u00e1n Riquelme","award":["ANID\/FONDECYT\/REGULAR\/1211905"],"award-info":[{"award-number":["ANID\/FONDECYT\/REGULAR\/1211905"]}]},{"name":"Fabi\u00e1n Riquelme","award":["ANID\/FONDECYT\/INICIACI\u00d3N\/11200113"],"award-info":[{"award-number":["ANID\/FONDECYT\/INICIACI\u00d3N\/11200113"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Nature\u2013inspired computing is a promising field of artificial intelligence. This area is mainly devoted to designing computational models based on natural phenomena to address complex problems. Nature provides a rich source of inspiration for designing smart procedures capable of becoming powerful algorithms. Many of these procedures have been successfully developed to treat optimization problems, with impressive results. Nonetheless, for these algorithms to reach their maximum performance, a proper balance between the intensification and the diversification phases is required. The intensification generates a local solution around the best solution by exploiting a promising region. Diversification is responsible for finding new solutions when the main procedure is trapped in a local region. This procedure is usually carryout by non-deterministic fundamentals that do not necessarily provide the expected results. Here, we encounter the stagnation problem, which describes a scenario where the search for the optimum solution stalls before discovering a globally optimal solution. In this work, we propose an efficient technique for detecting and leaving local optimum regions based on Shannon entropy. This component can measure the uncertainty level of the observations taken from random variables. We employ this principle on three well\u2013known population\u2013based bio\u2013inspired optimization algorithms: particle swarm optimization, bat optimization, and black hole algorithm. The proposal\u2019s performance is evidenced by solving twenty of the most challenging instances of the multidimensional knapsack problem. Computational results show that the proposed exploration approach is a legitimate alternative to manage the diversification of solutions since the improved techniques can generate a better distribution of the optimal values found. The best results are with the bat method, where in all instances, the enhanced solver with the Shannon exploration strategy works better than its native version. For the other two bio-inspired algorithms, the proposal operates significantly better in over 70% of instances.<\/jats:p>","DOI":"10.3390\/e24091293","type":"journal-article","created":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T20:50:45Z","timestamp":1663188645000},"page":"1293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Entropy\u2013Based Diversification Approach for Bio\u2013Computing Methods"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0582-954X","authenticated-orcid":false,"given":"Rodrigo","family":"Olivares","sequence":"first","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Universidad de Valpara\u00edso, Valpara\u00edso 2362905, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5755-6929","authenticated-orcid":false,"given":"Ricardo","family":"Soto","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Valpara\u00edso 2362807, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5500-0188","authenticated-orcid":false,"given":"Broderick","family":"Crawford","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Valpara\u00edso 2362807, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4491-0148","authenticated-orcid":false,"given":"Fabi\u00e1n","family":"Riquelme","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Universidad de Valpara\u00edso, Valpara\u00edso 2362905, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1302-0206","authenticated-orcid":false,"given":"Roberto","family":"Munoz","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Universidad de Valpara\u00edso, Valpara\u00edso 2362905, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5578-272X","authenticated-orcid":false,"given":"V\u00edctor","family":"R\u00edos","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Universidad de Valpara\u00edso, Valpara\u00edso 2362905, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rodrigo","family":"Cabrera","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Valpara\u00edso 2362807, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4149-7730","authenticated-orcid":false,"given":"Carlos","family":"Castro","sequence":"additional","affiliation":[{"name":"Departamento de Inform\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Valpara\u00edso 2390123, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Talbi, E.G. 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