“…The ACO algorithm is admired by researchers because of its unique advantages in solving business travel problems. Besides, many excellent nature-inspired swarm intelligent approaches have been validated to be effective in tricky global optimization projects, they include but are not limited to: bat algorithm (BA) ( Yang and Gandomi, 2012 ), krill herd optimization (KHO) ( Gandomi et al, 2012 ), cuckoo search (CS) algorithm ( Gandomi et al, 2013 ), fruit-fly optimization algorithm (FOA) ( Mitić et al, 2015 ), grey wolf optimizer (GWO) ( Mirjalili et al, 2014 ), moth-flame optimization (MFO) ( Mirjalili, 2015 ), grasshopper optimization algorithm (GOA) ( Abualigah and Diabat, 2020 ), whale optimization algorithm (WOA) ( Mirjalili and Lewis, 2016 ), marine predators algorithm (MPA) ( Faramarzi et al, 2020a ), white shark optimizer (WSO) ( Braik et al, 2022 ), starling murmuration optimizer (SMO) ( Zamani et al, 2022 ), harris hawks algorithm ( Heidari et al, 2019 ), squirrel search optimization (SSO) algorithm ( Jain et al, 2019 ), dragonfly algorithm (DA) ( Mirjalili, 2016 ), chimp optimization algorithm (ChOA) ( Khishe and Mosavi, 2020 ), rat swarm algorithm (RSA) ( Dhiman et al, 2021 ), Animal migration optimization (AMO) ( Li et al, 2014 ), butterfly optimization algorithm (BOA) ( Arora and Singh, 2019 ), emperor penguin optimizer (EPO) ( Dhiman and Kumar, 2018 ), tunicate swarm algorithm (TSA) ( Kaur et al, 2020 ), horse herd optimization algorithm (HOA) ( MiarNaeimi et al, 2021 ), monarch butterfly optimization (MBO) ( Wang et al, 2019 ), firefly algorithm ( Fister et al, 2013 ; Wang et al, 2022a ), and seagull optimization algorithm (SOA) ( Dhiman and Kumar, 2019 ).…”