Preference-inspired co-evolutionary algorithms (PICEAs) are a novel class of population-based approaches for multi-objective optimization. PICEA-g is one realization of PICEAs in which goal vectors are taken as preferences and are co-evolved with the candidate solutions during the search. The performance of PICEA-g is affected by the distribution of the co-evolved goal vectors. In PICEA-g, new goal vectors are generated within pre-defined bounds determined by the ideal and anti-ideal points in each generation. Such bounds are often unknown or at least problem knowledge requires. In this paper, firstly, we analyse the influence of different initial bounds to the performance of PICEA-g. Then, we propose a method, called cutting plane, which adaptively sets proper bounds for the generation of goal vectors, adjusting the search effort toward different objective appropriately, and therefore guide the candidate solutions toward the Pareto optimal front efficiently. Experimental results show that this adaptive approach is effective.