A three-dimensional disc model with non-uniform heat generating is built.A series of cooling channels are inserted to cool this disc which is strewn in a hierarchical pattern.To reveal thermal and flow characteristics,a composite objective function comprised of the maximum temperature difference (MTD) and pumping power is constructed.The deployment pattern of cooling channels contains two cases,i.e.,the radial-pattern and dendritic-pattern.By capitalizing on constructal design method together with finite element method,the diameter of radial-pattern cooling channels is optimized in the first place.Next,the diameter,angle coefficient and length coefficient of dendritic-pattern cooling channels are three degrees-of-freedom to be stepwise optimized at different heat generating conditions.Furthermore,NSGA-Ⅱ algorithm is introduced into the multiobjective problem.Upon obtaining its Pareto optimal solution set,Topsis method is invoked to yield the optimal solutions under given weighted coefficients.The heat generation over the entire body and the volume ratio of cooling channels operate as the primary constraints.Based on these premises,constructal design will be stepwise performed by varying three degrees-of-freedom.The obtained results state that more heating components or devices should be installed as close to the cooling water inlet as possible.This can further reduce MTD at the same cost of pumping power,thereby improve thermal and flow performance and prolong the lifespan of devices.As optimized with two degrees-of-freedom,the MTD is reduced by 18.6％ compared with the counterpart obtained from single degree-of-freedom optimization,while the pumping power is increased by 59.8％.As optimized with three degrees-of-freedom,the MTD is decreased by 6.2％ compared with the counterpart from two degrees-of-freedom optimization,while the pumping power is increased by 3.0％.It is manifest that when two sub-objectives form a composite objective,the performance improvement of one sub-objective will inevitably elicit the vitiation of the alternative.