{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:38:52Z","timestamp":1775054332383,"version":"3.50.1"},"reference-count":29,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia, Portugal","award":["PEst-OE\/MAT\/UI0013\/2014"],"award-info":[{"award-number":["PEst-OE\/MAT\/UI0013\/2014"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia, Portugal","award":["PEst-OE\/EEI\/UI0319\/2014"],"award-info":[{"award-number":["PEst-OE\/EEI\/UI0319\/2014"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia, Portugal","award":["PEst-OE\/MAT\/UI0013\/2014"],"award-info":[{"award-number":["PEst-OE\/MAT\/UI0013\/2014"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia, Portugal","award":["PEst-OE\/EEI\/UI0319\/2014"],"award-info":[{"award-number":["PEst-OE\/EEI\/UI0319\/2014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Operations Research"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper, we address the practical testing of a heuristic-based FA (HBFA) for computing optima of discrete nonlinear optimization problems, where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid \u201cerf\u201d function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid \u201cerf\u201d function with \u201cmovements in continuous space\u201d is the best, in terms of both computational requirements and accuracy.<\/jats:p>","DOI":"10.1155\/2014\/215182","type":"journal-article","created":{"date-parts":[[2014,10,8]],"date-time":"2014-10-08T17:05:39Z","timestamp":1412787939000},"page":"1-12","source":"Crossref","is-referenced-by-count":10,"title":["Heuristic-Based Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6235-286X","authenticated-orcid":true,"given":"M. Fernanda P.","family":"Costa","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applications, Centre of Mathematics, University of Minho, 4710-057 Braga, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8679-2886","authenticated-orcid":true,"given":"Ana Maria A. C.","family":"Rocha","sequence":"additional","affiliation":[{"name":"Algoritmi Research Centre, University of Minho, 4710-057 Braga, Portugal"}]},{"given":"Rog\u00e9rio B.","family":"Francisco","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applications, Centre of Mathematics, University of Minho, 4710-057 Braga, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0722-9361","authenticated-orcid":true,"given":"Edite M. G. 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