Multi-objectivization Relaxes Multi-funnel Structures in Single-objective NK-landscapes

This paper investigated the impacts of multi-objectivization on solving combinatorial single-objective NK-landscape problems with multiple funnel structures. Multi-objectivization re-formulates a single-objective target problem into a multi-objective problem with a helper problem to suppress the difficulty of the target problem. This paper analyzed the connectivity of two funnels involving global optima in the target and the helper NK-landscape problems via the Pareto local optimal solutions in the multi-objectivized problem. Experimental results showed that multi-objectivization connects the two funnels with global optima of the target and the helper problems as a single bridging domain consisting of the Pareto local optimal solutions. Also, this paper proposed an algorithm named the multi-objectivized local search (MOLS) that searched for the global optimum of the target problem from the global optimum of an artificially generated helper problem via the Pareto local optimal solutions. Experimental results showed that the proposed MOLS achieved a higher success rate of the target single-objective optimization than iterative local search algorithms on target NK-landscape problems with multiple funnels.