{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T12:24:24Z","timestamp":1761740664513,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T00:00:00Z","timestamp":1700092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Swarm intelligence has promising applications for firm search and decision-choice problems and is particularly well suited for examining how other firms influence the focal firm\u2019s search. To evaluate search performance, researchers examining firm search through simulation models typically build a performance landscape. The NK model is the leading tool used for this purpose in the management science literature. We assess the usefulness of the NK landscape for simulated swarm search. We find that the strength of the swarm model for examining firm search and decision-choice problems\u2014the ability to model the influence of other firms on the focal firm\u2014is limited to the NK landscape. Researchers will need alternative ways to create a performance landscape in order to use our full swarm model in simulations. We also identify multiple opportunities\u2014endogenous landscapes, agent-specific landscapes, incomplete information, and costly movements\u2014that future researchers can include in landscape development to gain the maximum insights from swarm-based firm search simulations.<\/jats:p>","DOI":"10.3390\/a16110527","type":"journal-article","created":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T07:11:27Z","timestamp":1700118687000},"page":"527","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Search on an NK Landscape with Swarm Intelligence: Limitations and Future Research Opportunities"],"prefix":"10.3390","volume":"16","author":[{"given":"Ren-Raw","family":"Chen","sequence":"first","affiliation":[{"name":"Gabelli School of Business, Fordham University, 45 Columbus Avenue, New York, NY 10019, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7130-8614","authenticated-orcid":false,"given":"Cameron D.","family":"Miller","sequence":"additional","affiliation":[{"name":"Whitman School of Management, Syracuse University, 721 University Avenue, Suite 500, Syracuse, NY 13244, USA"}]},{"given":"Puay Khoon","family":"Toh","sequence":"additional","affiliation":[{"name":"McCombs School of Business, University of Texas at Austin, 2110 Speedway, B6000, Austin, TX 78705, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,16]]},"reference":[{"key":"ref_1","first-page":"285","article-title":"Effective search in rugged performance landscapes: A review and outlook","volume":"45","author":"Buamann","year":"2019","journal-title":"J. Manag."},{"key":"ref_2","unstructured":"Levinthal, D.A., and Marengo, L. (2018). The Palgrave Encyclopedia of Strategic Management, Palgrave Macmillan."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1108\/S1479-8387(2009)0000005010","article-title":"NK modeling methodology in the strategy literature: Bounded search on a rugged landscape","volume":"Volume 5","author":"Ganco","year":"2009","journal-title":"Research Methodology in Strategy and Management"},{"key":"ref_4","first-page":"15","article-title":"A note on how NK landscapes work","volume":"7","author":"Csaszar","year":"2018","journal-title":"J. Organ. Des."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chen, R.-R., Miller, C.D., and Toh, P.K. (2023). Modeling firm search and innovation trajectory using swarm Intelligence. Algorithms, 16.","DOI":"10.3390\/a16020072"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/S0022-5193(87)80029-2","article-title":"Towards a general theory of adaptive walks on rugged landscapes","volume":"128","author":"Kauffman","year":"1987","journal-title":"J. Theor. Biol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/S0022-5193(89)80019-0","article-title":"The NK Model of rugged fitness landscapes and its application to the maturation of the immune response","volume":"141","author":"Kauffman","year":"1989","journal-title":"J. Theor. Biol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1287\/mnsc.43.7.934","article-title":"Adaptation on Rugged Landscapes","volume":"43","author":"Levinthal","year":"1997","journal-title":"Manag. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s10107-005-0609-0","article-title":"Global optima results for the Kauffman NK model","volume":"106","author":"Kaul","year":"2005","journal-title":"Math. Program."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1287\/mnsc.1060.0626","article-title":"Patterned interactions in complex systems: Implications for exploration","volume":"53","author":"Rivkin","year":"2007","journal-title":"Manag. Sci."},{"key":"ref_11","unstructured":"Bahceci, E. (2014). Competitive Multi-Agent Search. [Ph.D. Dissertation, University of Texas at Austin]."},{"key":"ref_12","unstructured":"Beni, G., Wang, J., and Iglesias, A. (1989, January 26\u201330). Swarm Intelligence in Cellular Robotic Systems. Proceedings of the NATO Advanced Workshop on Robots and Biological Systems, Tuscany, Italy."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bonabeau, E., Dorigo, M., and Theraulaz, G. (1999). Swarm Intelligence: From Natural to Artificial Systems, OUP.","DOI":"10.1093\/oso\/9780195131581.001.0001"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Meyers, R.A. (2009). Encyclopedia of Complexity and Systems Science, Springer.","DOI":"10.1007\/978-0-387-30440-3"},{"key":"ref_15","unstructured":"Reynolds, C. (1987). SIGGRAPH \u201987, Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, Anaheim, CA, USA, 27\u201331 July 1987, Association for Computing Machinery."},{"key":"ref_16","unstructured":"Eberhart, R., and Kennedy, J. (December, January 27). Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_17","unstructured":"Shi, Y., and Eberhart, R.C. (1998, January 4\u20139). A modified particle swarm optimizer. Proceedings of the IEEE International Conference on Evolutionary Computation, Anchorage, AK, USA."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1016\/j.ejor.2011.03.030","article-title":"Heuristic algorithms for the cardinality constrained efficient frontier","volume":"213","author":"Lucas","year":"2011","journal-title":"Eur. J. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10161","DOI":"10.1016\/j.eswa.2011.02.075","article-title":"Particle swarm optimization (PSO) for the constrained portfolio optimization problem expert systems with applications","volume":"38","author":"Zhu","year":"2011","journal-title":"Exp. Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2396","DOI":"10.1016\/j.nonrwa.2008.04.023","article-title":"Particle swarm optimization approach to portfolio optimization","volume":"10","author":"Cura","year":"2009","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_21","first-page":"1","article-title":"Portfolio optimization using particle swarm optimization method","volume":"12","author":"Raei","year":"2010","journal-title":"Financ. Res. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1007\/s11831-020-09448-8","article-title":"A comprehensive survey on portfolio optimization, stock price and trend prediction using particle swarm optimization","volume":"28","author":"Thakkar","year":"2021","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Erwin, K., and Engelbrecht, A. (2023). Multi-guide set-based particle swarm optimization for multi-objective portfolio optimization. Algorithms, 16.","DOI":"10.3390\/a16020062"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Erwin, K., and Engelbrecht, A.P. (2020, January 26\u201328). Set-Based particle swarm optimization for portfolio optimization. Proceedings of the International Conference on Swarm Intelligence, ANTS Conference, Barcelona, Spain.","DOI":"10.1109\/SSCI47803.2020.9308579"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.physa.2015.09.061","article-title":"Interest rate next-day variation prediction based on hybrid feedforward neural network, particle swarm optimization, and multiresolution techniques","volume":"444","author":"Lahmiri","year":"2016","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"112724","DOI":"10.1016\/j.cam.2020.112724","article-title":"Analysis of earnings forecast of blockchain financial products based on particle swarm optimization","volume":"372","author":"Gao","year":"2020","journal-title":"J. Comput. Appl. Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"101462","DOI":"10.1016\/j.seps.2022.101462","article-title":"Sustainable inventory management in blood banks considering health equity using a combined metaheuristic-based robust fuzzy stochastic programming","volume":"86","author":"Sohrabi","year":"2023","journal-title":"Socio-Econ. Plan. Sci."},{"key":"ref_28","unstructured":"Eberhart, R.C. (1997, January 12\u201315). A discrete binary version of the particle swarm algorithm. Proceedings of the 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, Orlando, FL, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1016\/j.pnsc.2008.03.018","article-title":"Modified binary particle swarm optimization","volume":"19","author":"Lee","year":"2008","journal-title":"Prog. Nat. Sci."},{"key":"ref_30","unstructured":"Di Caro, G. (2019). Lecture Notes (Chapter 16 of Collective Intelligence: From Multi-Agent Systems to Swarms), Carnegie Mellon University."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1720","DOI":"10.1007\/s42452-020-03511-6","article-title":"Momentum search algorithm: A new meta-heuristic optimization algorithm inspired by momentum conservation law","volume":"2","author":"Dehghani","year":"2020","journal-title":"SN Appl. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/TCYB.2019.2944141","article-title":"A new binary particle swarm optimization approach: Momentum and dynamic balance between exploration and exploitation","volume":"51","author":"Nguyen","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Shokouhifar, A., Shokouhifar, M., Sabbaghian, M., and Soltanian-Zadheh, H. (2023). Swarm intelligence empowered three-stage ensemble deep learning for arm volume measurement in patients with lymphedema. Biomed. Signal Process. Control, 85.","DOI":"10.1016\/j.bspc.2023.105027"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Kumar, A., Kumar, S.A., Dutt, V., Dubey, A.K., and Garcia-Diaz, V. (2022). IoT-based ECG monitoring for arrhythmia classification using Coyote Grey Wolf optimization-based deep learning CNN classifier. Biomed. Signal Process. Control, 76.","DOI":"10.1016\/j.bspc.2022.103638"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"118303","DOI":"10.1016\/j.eswa.2022.118303","article-title":"Forecasting tunnel boring machine penetration rate using LSTM deep neural network optimized by grey wolf optimization algorithm","volume":"209","author":"Mahmoodzadeh","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Yang, X., Zhao, D., Yu, F., Heidari, A.A., Bano, Y., Ibrohimov, A., Liu, Y., Cai, Z., Chen, H., and Chen, X. (2022). An optimized machine learning framework for predicting intradialytic hypotension using indexes of chronic kidney disease-mineral and bone disorders. Comput. Biol. Med., 145.","DOI":"10.1016\/j.compbiomed.2022.105510"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Guerra, J.F., Garcia-Hernandex, R., Llama, M.A., and Santibanez, V. (2023). A comparative study of swarm intelligence metaheuristics in ukf-based neural training applied to the identification and control of robotic manipulator. Algorithms, 16.","DOI":"10.3390\/a16080393"},{"key":"ref_38","first-page":"435104","article-title":"Particle swarm algorithms to solve engineering problems: A comparison of performance","volume":"2013","author":"Tomassetti","year":"2013","journal-title":"J. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Papazoglu, G., and Biskas, P. (2023). Review and comparison of genetic algorithm and particle swarm optimization in the optimal power flow problem. Energies, 16.","DOI":"10.3390\/en16031152"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Kicska, G., and Kiss, A. (2021). Comparing swarm intelligence algorithms for dimension reduction in machine learning. Big Data Cogn. Comput., 5.","DOI":"10.3390\/bdcc5030036"},{"key":"ref_41","unstructured":"Selvaraj, S., and Choi, E. (2020). ICSIM \u201920, Proceedings of the 3rd International Conference on Software Engineering and Information Management, Sydney, NSW, Australia, 12\u201315 January 2020, ACM."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/s10115-012-0512-y","article-title":"Analyzing collective behavior from blogs using swarm intelligence","volume":"33","author":"Banerjee","year":"2012","journal-title":"Knowl. Inf. Syst."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"O\u2019Bryan, L., Beier, M., and Salas, E. (2020). How approaches to animal swarm intelligence can improve the study of collective intelligence in human teams. J. Intell., 8.","DOI":"10.3390\/jintelligence8010009"},{"key":"ref_44","unstructured":"Minar, N., Burkahrt, R., Langston, C., and Askenzi, M. (2023, October 13). The Swarm Simulation System: A Toolkit for Building Multi-Agent Simulations. Available online: https:\/\/EconPapers.repec.org\/RePEc:wop:safiwp:96-06-042."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1287\/orsc.1090.0524","article-title":"Investing in Capabilities: The Dynamics of Resource Allocation","volume":"22","author":"Coen","year":"2011","journal-title":"Organ. Sci."},{"key":"ref_46","first-page":"1","article-title":"Sendero: An extended, agent-based implementation of Kauffman\u2019s NKCS model","volume":"12","author":"Padget","year":"2009","journal-title":"J. Artif. Soc. Soc. Simul."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1186\/s13731-022-00212-9","article-title":"Balancing the Perceptions of NK Modeling with Critical Insights","volume":"11","author":"Arend","year":"2022","journal-title":"J. Innov. Entrep."},{"key":"ref_48","unstructured":"Wu, J. (2022). Withholding Knowledge, Department of Logic and Philosophy of Science, University of California at Irvine."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1006\/jtbi.1995.0074","article-title":"Search strategies for applied molecular evolution","volume":"173","author":"Kauffman","year":"1995","journal-title":"J. Theor. Biol."},{"key":"ref_50","unstructured":"Merz, P. (2006). Memetic Algorithms for Combinatorial Optimization Problems: Fitness Landscapes and Effective Search Strategies. [Ph.D. Dissertation, Fachbereich 12, Elektrotechnik und Informatik]."},{"key":"ref_51","unstructured":"Krasnogor, N., and Smith, J. (2001). GECCO\u201901, Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, San Francisco, CA, USA, 7\u201311 July 2001, ACM."},{"key":"ref_52","first-page":"28","article-title":"On the attainability of NK landscapes global optima","volume":"Volume 5","author":"Bausseur","year":"2021","journal-title":"Proceedings of the Seventh Annual Symposium on Combinatorial Search (SoCS 2014)"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s10614-009-9192-4","article-title":"Searching NK fitness landscapes: On the trade off between speed and quality in complex problem solving","volume":"35","author":"Geisendorf","year":"2010","journal-title":"Comput. Econ."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.neucom.2019.12.141","article-title":"Fitness distance correlation and mixed search strategy for differential evolution","volume":"458","author":"Li","year":"2021","journal-title":"Neurocomputing"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Harrison, J.R., Kemp, A., and Saetre, A.S. (2017, January 9\u201313). Attraction-based fitness landscapes for computational decision search. Proceedings of the PICMET \u201817: Technology Management for Interconnected World, PICMET, Portland, OR, USA.","DOI":"10.23919\/PICMET.2017.8125307"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/11\/527\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:23:57Z","timestamp":1760131437000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/11\/527"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,16]]},"references-count":55,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["a16110527"],"URL":"https:\/\/doi.org\/10.3390\/a16110527","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2023,11,16]]}}}