A multi-objective antlion optimizer for the ring tree problem with secondary sub-depots

Abstract

This article proposes a multi-objective ring tree problem with secondary sub-depots (MORTPSSD), which focusses on the problems of telecommunication and logistics networks. In this problem, we have considered a fixed node as the main depot. Other nodes are divided into primary sub-depots, secondary sub-depots, and left-out nodes referred to type 1, type 2, and type 3 customers. The first objective of the proposed model MORTPSSD is to minimize the circuits’ total routing cost through type 1 and type 2 customers added by the minimal spanning tree cost of type 3 customers. The second objective is to minimize the total number of type 3 customers, which influences the first objective. The model is solved by a discrete multi-objective antlion optimizer (DMOALO) with a ternary encoding. The proposed algorithm is also tested on some instances derived from TSP benchmark problems. Statistical analyses are performed to compare the convergence and the diversity of the proposed DMOALO against NSGAII and MOPSO, which yields a better efficiency of DMOALO for most instances.