“…Moreover, hybridization of genetic operators and local searches with other meta-heuristics such as particle swarm optimization (PSO) helps to prevent premature convergence and increase the performance of proposed algorithms (see Yang et al, 2013;Gao and Qin, 2016). Some recent papers that employed the principals of GA in solving the HLPs are Kratica et al (2011), Bashiri et al (2013, Mohammadi et al (2013), Kratica et al (2007), Bashiri et al (2013), Yang et al (2013), Damgacioglu et al (2015), Ebrahimi-Zade et al (2016), Gao and Qin (2016), Qin and Gao (2017), Hasanzadeh et al (2016), Bashiri et al (2017), andLüer-Villagra et al (2019). In the current paper, we aim to study two improved meta-heuristics by taking the following features into account:…”