{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T21:16:46Z","timestamp":1776374206953,"version":"3.51.2"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T00:00:00Z","timestamp":1738022400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T00:00:00Z","timestamp":1738022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"The Deanship of Graduate Studies and Scientific Research at Jouf University","award":["DGSSR-2023-02-02125"],"award-info":[{"award-number":["DGSSR-2023-02-02125"]}]},{"name":"NTNU Norwegian University of Science and Technology"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Big Data"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>This paper presents a binary variant of the recently proposed spider wasp optimizer (SWO), namely BSWO, for accurately tackling the multidimensional knapsack problem (MKP), which is classified as an NP-hard optimization problem. The classical methods could not achieve acceptable results for this problem in a reasonable amount of time. Therefore, the researchers have recently turned their focus to metaheuristic algorithms to address this problem more accurately and in an acceptable amount of time. However, the majority of metaheuristic algorithms proposed for MKP suffer from slow convergence speed and low quality of final results, especially as the number of dimensions increases. This motivates us to present BSWO discretized using nine well-known transfer functions belonging to three categories\u2014X-shaped, S-shaped, and V-shaped families\u2014for effectively and efficiently tackling this problem. In addition, it is integrated with the improved repair operator 4 (RO4) to present a hybrid variant, namely BSWO-RO4, which could effectively repair and improve infeasible solutions for achieving better performance. Several small, medium, and large-scale MKP instances are used to assess both BSWO and BSWO-RO4.\u00a0The usefulness and efficiency of the proposed algorithms are also demonstrated by comparing both of them to several metaheuristic optimizers in terms of some performance criteria. The experimental findings demonstrate that BSWO-RO4 can achieve exceptional results for the small and medium-scale instances, while the genetic algorithm integrated with RO4 can be superior for the large-scale instances. Additionally, the results of the experiments demonstrate that BSWO integrated with RO4 is more efficient than BSWO integrated with RO2.<\/jats:p>","DOI":"10.1186\/s40537-024-01055-9","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T13:18:45Z","timestamp":1738070325000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An efficient binary spider wasp optimizer for multi-dimensional knapsack instances: experimental validation and analysis"],"prefix":"10.1186","volume":"12","author":[{"given":"Mohamed","family":"Abdel-Basset","sequence":"first","affiliation":[]},{"given":"Reda","family":"Mohamed","sequence":"additional","affiliation":[]},{"given":"Karam M.","family":"Sallam","sequence":"additional","affiliation":[]},{"given":"Ibrahim","family":"Alrashdi","sequence":"additional","affiliation":[]},{"given":"Ibrahim A.","family":"Hameed","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,28]]},"reference":[{"key":"1055_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2024.111934","volume":"164","author":"J Xu","year":"2024","unstructured":"Xu J, Li H, Yin M. Finding and exploring promising search space for The 0\u20131 Multidimensional Knapsack Problem. Appl Soft Comput. 2024;164: 111934.","journal-title":"Appl Soft Comput"},{"key":"1055_CR2","doi-asserted-by":"publisher","first-page":"45255","DOI":"10.1109\/ACCESS.2023.3264966","volume":"11","author":"A Mkaouar","year":"2023","unstructured":"Mkaouar A, Htiouech S, Chabchoub H. Modified artificial bee colony algorithm for multiple-choice multidimensional knapsack problem. IEEE Access. 2023;11:45255\u201369.","journal-title":"IEEE Access"},{"key":"1055_CR3","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1016\/j.matcom.2023.12.033","volume":"219","author":"Y He","year":"2024","unstructured":"He Y, et al. Modeling and solving of knapsack problem with setup based on evolutionary algorithm. Math Comput Simul. 2024;219:378\u2013403.","journal-title":"Math Comput Simul"},{"key":"1055_CR4","unstructured":"Gavish B. Allocation of databases and processors in a distributed computing system. Management of Distributed Data Processing, 1982: p. 215\u2013231."},{"key":"1055_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2021.102559","volume":"107","author":"M Gajda","year":"2022","unstructured":"Gajda M, et al. An optimization approach for a complex real-life container loading problem. Omega. 2022;107: 102559.","journal-title":"Omega"},{"key":"1055_CR6","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.knosys.2013.04.003","volume":"48","author":"L Wang","year":"2013","unstructured":"Wang L, Zheng X-L, Wang S-Y. A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowl-Based Syst. 2013;48:17\u201323.","journal-title":"Knowl-Based Syst"},{"key":"1055_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.121222","volume":"236","author":"G Jiao","year":"2024","unstructured":"Jiao G, et al. Container loading problem based on robotic loader system: an optimization approach. Expert Syst Appl. 2024;236: 121222.","journal-title":"Expert Syst Appl"},{"issue":"22","key":"1055_CR8","first-page":"11042","volume":"218","author":"JC Bansal","year":"2012","unstructured":"Bansal JC, Deep K. A modified binary particle swarm optimization for knapsack problems. Appl Math Comput. 2012;218(22):11042\u201361.","journal-title":"Appl Math Comput"},{"issue":"1","key":"1055_CR9","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.ejor.2024.06.034","volume":"319","author":"ME Fennich","year":"2024","unstructured":"Fennich ME, Fomeni FD, Coelho LC. A novel dynamic programming heuristic for the quadratic knapsack problem. Eur J Oper Res. 2024;319(1):102\u201320.","journal-title":"Eur J Oper Res"},{"key":"1055_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.esr.2024.101298","volume":"51","author":"A Akter","year":"2024","unstructured":"Akter A, et al. A review on microgrid optimization with meta-heuristic techniques: scopes, trends and recommendation. Energy Strat Rev. 2024;51: 101298.","journal-title":"Energy Strat Rev"},{"issue":"4","key":"1055_CR11","doi-asserted-by":"publisher","first-page":"3123","DOI":"10.1007\/s00500-023-09276-5","volume":"28","author":"P Sharma","year":"2024","unstructured":"Sharma P, Raju S. Metaheuristic optimization algorithms: a comprehensive overview and classification of benchmark test functions. Soft Comput. 2024;28(4):3123\u201386.","journal-title":"Soft Comput"},{"key":"1055_CR12","doi-asserted-by":"crossref","unstructured":"Rautray R, et al. A review on metaheuristic approaches for optimization problems. Computational Intelligence in Healthcare Informatics, 2024: p. 33\u201355.","DOI":"10.1007\/978-981-99-8853-2_3"},{"issue":"7","key":"1055_CR13","doi-asserted-by":"publisher","first-page":"1547","DOI":"10.3390\/en17071547","volume":"17","author":"TL Pillay","year":"2024","unstructured":"Pillay TL, Saha AK. A Review of metaheuristic optimization techniques for effective energy conservation in buildings. Energies. 2024;17(7):1547.","journal-title":"Energies"},{"issue":"1","key":"1055_CR14","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1111\/itor.12001","volume":"22","author":"K S\u00f6rensen","year":"2015","unstructured":"S\u00f6rensen K. Metaheuristics\u2014the metaphor exposed. Int Trans Oper Res. 2015;22(1):3\u201318.","journal-title":"Int Trans Oper Res"},{"key":"1055_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2024.111574","volume":"158","author":"L Deng","year":"2024","unstructured":"Deng L, Liu S. Exposing the chimp optimization algorithm: a misleading metaheuristic technique with structural bias. Appl Soft Comput. 2024;158: 111574.","journal-title":"Appl Soft Comput"},{"key":"1055_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2024.111696","volume":"160","author":"L Deng","year":"2024","unstructured":"Deng L, Liu S. Metaheuristics exposed: unmasking the design pitfalls of arithmetic optimization algorithm in benchmarking. Appl Soft Comput. 2024;160: 111696.","journal-title":"Appl Soft Comput"},{"issue":"6","key":"1055_CR17","doi-asserted-by":"publisher","first-page":"2945","DOI":"10.1111\/itor.13176","volume":"30","author":"CL Camacho-Villal\u00f3n","year":"2023","unstructured":"Camacho-Villal\u00f3n CL, Dorigo M, St\u00fctzle T. Exposing the grey wolf, moth-flame, whale, firefly, bat, and antlion algorithms: six misleading optimization techniques inspired by bestial metaphors. Int Trans Oper Res. 2023;30(6):2945\u201371.","journal-title":"Int Trans Oper Res"},{"key":"1055_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.121544","volume":"237","author":"L Deng","year":"2024","unstructured":"Deng L, Liu S. Deficiencies of the whale optimization algorithm and its validation method. Expert Syst Appl. 2024;237: 121544.","journal-title":"Expert Syst Appl"},{"key":"1055_CR19","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1016\/j.aej.2022.12.025","volume":"67","author":"M Abdel-Basset","year":"2023","unstructured":"Abdel-Basset M, et al. Binary light spectrum optimizer for knapsack problems: an improved model. Alex Eng J. 2023;67:609\u201332.","journal-title":"Alex Eng J"},{"issue":"8","key":"1055_CR20","doi-asserted-by":"publisher","first-page":"1811","DOI":"10.3390\/math11081811","volume":"11","author":"Y Feng","year":"2023","unstructured":"Feng Y, et al. Hybrid learning moth search algorithm for solving multidimensional knapsack problems. Mathematics. 2023;11(8):1811.","journal-title":"Mathematics"},{"key":"1055_CR21","doi-asserted-by":"publisher","first-page":"110583","DOI":"10.1016\/j.asoc.2023.110583","volume":"146","author":"M Banaie-Dezfouli","year":"2023","unstructured":"Banaie-Dezfouli M, Nadimi-Shahraki MH, Beheshti Z. BE-GWO: binary extremum-based grey wolf optimizer for discrete optimization problems. Appl Soft Comput. 2023;146:110583.","journal-title":"Appl Soft Comput"},{"key":"1055_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2022.109682","volume":"130","author":"S Gupta","year":"2022","unstructured":"Gupta S, Su R, Singh S. Diversified sine\u2013cosine algorithm based on differential evolution for multidimensional knapsack problem. Appl Soft Comput. 2022;130: 109682.","journal-title":"Appl Soft Comput"},{"key":"1055_CR23","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.future.2021.07.033","volume":"126","author":"Y Feng","year":"2022","unstructured":"Feng Y, Wang G-G. A binary moth search algorithm based on self-learning for multidimensional knapsack problems. Future Gener Comput Syst. 2022;126:48\u201364.","journal-title":"Future Gener Comput Syst"},{"key":"1055_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2021.107469","volume":"159","author":"M Abdel-Basset","year":"2021","unstructured":"Abdel-Basset M, et al. BSMA: a novel metaheuristic algorithm for multi-dimensional knapsack problems: method and comprehensive analysis. Comput Ind Eng. 2021;159: 107469.","journal-title":"Comput Ind Eng"},{"key":"1055_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-77445-5_35","volume-title":"A binary firefly algorithm applied to knapsack problem","author":"H Pinto","year":"2021","unstructured":"Pinto H, et al. A binary firefly algorithm applied to knapsack problem. Springer; 2021."},{"issue":"11","key":"1055_CR26","doi-asserted-by":"publisher","first-page":"3458","DOI":"10.1016\/j.cor.2006.02.008","volume":"34","author":"MJ Alves","year":"2007","unstructured":"Alves MJ, Almeida M. MOTGA: a multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem. Comput Oper Res. 2007;34(11):3458\u201370.","journal-title":"Comput Oper Res"},{"key":"1055_CR27","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1007\/s00366-019-00853-7","volume":"37","author":"Y He","year":"2021","unstructured":"He Y, et al. An efficient binary differential evolution algorithm for the multidimensional knapsack problem. Eng Comput. 2021;37:745\u201361.","journal-title":"Eng Comput"},{"key":"1055_CR28","doi-asserted-by":"publisher","first-page":"4221","DOI":"10.1007\/s00500-017-2744-y","volume":"22","author":"M Abdel-Basset","year":"2018","unstructured":"Abdel-Basset M, et al. A modified flower pollination algorithm for the multidimensional knapsack problem: human-centric decision making. Soft Comput. 2018;22:4221\u201339.","journal-title":"Soft Comput"},{"key":"1055_CR29","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1016\/j.asoc.2016.02.027","volume":"43","author":"X Zhang","year":"2016","unstructured":"Zhang X, et al. Binary artificial algae algorithm for multidimensional knapsack problems. Appl Soft Comput. 2016;43:583\u201395.","journal-title":"Appl Soft Comput"},{"key":"1055_CR30","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.procs.2017.06.012","volume":"111","author":"E Ulker","year":"2017","unstructured":"Ulker E, Tongur V. Migrating birds optimization (MBO) algorithm to solve knapsack problem. Procedia Comput Sci. 2017;111:71\u20136.","journal-title":"Procedia Comput Sci"},{"key":"1055_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2024.101494","volume":"86","author":"X Li","year":"2024","unstructured":"Li X, et al. An adaptive binary quantum-behaved particle swarm optimization algorithm for the multidimensional knapsack problem. Swarm Evol Comput. 2024;86: 101494.","journal-title":"Swarm Evol Comput"},{"key":"1055_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2024.121170","volume":"680","author":"L Wang","year":"2024","unstructured":"Wang L, et al. A novel discrete differential evolution algorithm combining transfer function with modulo operation for solving the multiple knapsack problem. Inf Sci. 2024;680: 121170.","journal-title":"Inf Sci"},{"issue":"23\u201324","key":"1055_CR33","doi-asserted-by":"publisher","first-page":"9788","DOI":"10.1016\/j.apm.2016.06.002","volume":"40","author":"J Liu","year":"2016","unstructured":"Liu J, et al. A binary differential search algorithm for the 0\u20131 multidimensional knapsack problem. Appl Math Model. 2016;40(23\u201324):9788\u2013805.","journal-title":"Appl Math Model"},{"issue":"2","key":"1055_CR34","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1504\/IJBIC.2014.060598","volume":"6","author":"S Sabba","year":"2014","unstructured":"Sabba S, Chikhi S. A discrete binary version of bat algorithm for multidimensional knapsack problem. Int J Bio-Inspired Comput. 2014;6(2):140\u201352.","journal-title":"Int J Bio-Inspired Comput"},{"issue":"4","key":"1055_CR35","doi-asserted-by":"publisher","first-page":"2284","DOI":"10.1109\/TCYB.2020.3002495","volume":"52","author":"Z Li","year":"2020","unstructured":"Li Z, Tang L, Liu J. A memetic algorithm based on probability learning for solving the multidimensional knapsack problem. IEEE Trans Cybern. 2020;52(4):2284\u201399.","journal-title":"IEEE Trans Cybern"},{"key":"1055_CR36","doi-asserted-by":"crossref","unstructured":"Zhang J, Jiang W, Zhao K. An Improved shuffled frog-leaping algorithm to Solving 0\u20131 Knapsack Problem. IEEE Access, 2024.","DOI":"10.1109\/ACCESS.2024.3424415"},{"key":"1055_CR37","unstructured":"Al-Thanoon NA, Qasim OS, Algamal ZY. A new hybrid pigeon-inspired optimization algorithm for solving multidimensional knapsack problems. IEEE."},{"key":"1055_CR38","doi-asserted-by":"publisher","first-page":"11675","DOI":"10.1007\/s10462-023-10446-y","volume":"56","author":"M Abdel-Basset","year":"2023","unstructured":"Abdel-Basset M, et al. Spider wasp optimizer: a novel meta-heuristic optimization algorithm. Artif Intell Rev. 2023;56:11675.","journal-title":"Artif Intell Rev"},{"key":"1055_CR39","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1023\/A:1009642405419","volume":"4","author":"PC Chu","year":"1998","unstructured":"Chu PC, Beasley JE. A genetic algorithm for the multidimensional knapsack problem. J Heuristics. 1998;4:63\u201386.","journal-title":"J Heuristics"},{"issue":"17","key":"1055_CR40","doi-asserted-by":"publisher","first-page":"11027","DOI":"10.1007\/s00521-020-05560-9","volume":"33","author":"KK Ghosh","year":"2021","unstructured":"Ghosh KK, et al. S-shaped versus V-shaped transfer functions for binary Manta ray foraging optimization in feature selection problem. Neural Comput Appl. 2021;33(17):11027\u201341.","journal-title":"Neural Comput Appl"},{"key":"1055_CR41","first-page":"1","volume":"2021","author":"TK Truong","year":"2021","unstructured":"Truong TK. A new moth-flame optimization algorithm for discounted 0\u20131 knapsack problem. Math Probl Eng. 2021;2021:1\u201315.","journal-title":"Math Probl Eng"},{"issue":"2","key":"1055_CR42","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/j.eswa.2005.09.024","volume":"31","author":"C-L Huang","year":"2006","unstructured":"Huang C-L, Wang C-J. A GA-based feature selection and parameters optimizationfor support vector machines. Expert Syst Appl. 2006;31(2):231\u201340.","journal-title":"Expert Syst Appl"},{"key":"1055_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.110248","volume":"262","author":"M Abdel-Basset","year":"2023","unstructured":"Abdel-Basset M, et al. Nutcracker optimizer: a novel nature-inspired metaheuristic algorithm for global optimization and engineering design problems. Knowl-Based Syst. 2023;262: 110248.","journal-title":"Knowl-Based Syst"},{"key":"1055_CR44","doi-asserted-by":"publisher","first-page":"1","DOI":"10.61185\/SMIJ.2023.44101","volume":"4","author":"S Salem","year":"2023","unstructured":"Salem S. An improved binary quadratic interpolation optimization for 0\u20131 knapsack problems. Sustain Mach Intell J. 2023;4:1\u20131.","journal-title":"Sustain Mach Intell J"},{"key":"1055_CR45","doi-asserted-by":"crossref","unstructured":"Limane A, et al. Binary Electric Eel Foraging Optimization Algorithm for Solving 0\u20131 Knapsack Problems. IEEE.","DOI":"10.1109\/PAIS62114.2024.10541286"},{"key":"1055_CR46","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.107532","volume":"128","author":"R Sowmya","year":"2024","unstructured":"Sowmya R, Premkumar M, Jangir P. Newton-Raphson-based optimizer: a new population-based metaheuristic algorithm for continuous optimization problems. Eng Appl Artif Intell. 2024;128: 107532.","journal-title":"Eng Appl Artif Intell"},{"issue":"5","key":"1055_CR47","doi-asserted-by":"publisher","first-page":"283","DOI":"10.3390\/biomimetics9050283","volume":"9","author":"D Leiva","year":"2024","unstructured":"Leiva D, et al. A Novel approach to combinatorial problems: binary growth optimizer algorithm. Biomimetics. 2024;9(5):283.","journal-title":"Biomimetics"}],"container-title":["Journal of Big Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40537-024-01055-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s40537-024-01055-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40537-024-01055-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T13:47:02Z","timestamp":1738072022000},"score":1,"resource":{"primary":{"URL":"https:\/\/journalofbigdata.springeropen.com\/articles\/10.1186\/s40537-024-01055-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,28]]},"references-count":47,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["1055"],"URL":"https:\/\/doi.org\/10.1186\/s40537-024-01055-9","relation":{},"ISSN":["2196-1115"],"issn-type":[{"value":"2196-1115","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,28]]},"assertion":[{"value":"14 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 December 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 January 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"18"}}