Time complexity analysis of evolutionary algorithms for 2-hop (1,2)-minimum spanning tree problem

The Minimum Spanning Tree problem (abbr. MSTP) is a well-known combinatorial optimization that has been extensively studied by the researchers in field of evolutionary computing to theoretically analyze performance algorithms. Within paper, we consider constrained version named 2-Hop (1,2)-Minimum 2H-(1,2)-MSTP) context algorithms, which shown be NP-hard. Following how algorithms are applied solve MSTP, first with search points edge-based representation adapted 2H-(1,2)-MSTP (including (1+1) EA, Global Simple Evolutionary Multi-Objective Optimizer and its two variants). More specifically, separately investigate upper bounds on their expected time (i.e., number fitness evaluations) obtain 32-approximate solution respect different functions. Inspired special structure 2-hop spanning trees, also EA vertex-based seems not so natural for give an bound solution, better than above mentioned ones.