On dominance‐based multiobjective local search: design, implementation and experimental analysis on scheduling and traveling salesman problems

This paper discusses simple local search approaches for approximating the efficient set of multiobjective combinatorial optimization problems. We focus on algorithms defined by a neighborhood structure and a dominance relation that iteratively improve an archive of nondominated solutions. Such methods are referred to as dominance‐based multiobjective local search. We first provide a concise overview of existing algorithms, and we propose a model trying to unify them through a fine‐grained decomposition. The main problem‐independent search components of dominance relation, solution selection, neighborhood exploration and archiving are largely discussed. Then, a number of state‐of‐the‐art and original strategies are experimented on solving a permutation flowshop scheduling problem and a traveling salesman problem, both on a two‐ and a three‐objective formulation. Experimental results and a statistical comparison are reported in the paper, and some directions for future research are highlighted.