On the effect of localized PBI method in MOEA/D for multi-objective optimization

The idea of localization, e.g., mating restriction, local search, is often employed in the design of evolutionary multi-objective algorithms, and has been demonstrated effective in many studies. This paper proposes a localized penalty boundary intersection (PBI) method which is then used in the seminal decomposition based algorithm, i.e., MOEA/D. The localized PBI (LPBI) method works in a pre-defined hypercone, that is, solutions compete with its neighbors in the same hypercone for survive. The size of the hypercone is determined automatically prior to the search. Experimental results show that i) the LPBI method improves the performance of MOEA/D-PBI for a wide range of penalty parameter values, in particular, for small penalty values; ii) for most of test problems, MOEA/D-LPBI with a small penalty value offers the best performance; and iii) The LPBI tends to be less sensitive than the PBI method on penalty parameter values.