Multicriteria combinatorial linear problems: parametrisation of the optimality principle and the stability of the effective solutions

We suggest a new approach to the investigation of the stability of the effective solutions of an $n$-criteria linear trajectory (on a system of subsets of a finite set) problem, where the optimality principle is determined by an integer parameter $s$ varying from 1 to $n-1$. The extreme values of the parameter correspond to the majority and Pareto optimality principles. For each value of the parameter $s$, the boundary for variation of the parameters of the partial criteria are given under which the effectiveness of trajectories is preserved.