A method for enhancing hybrid-classical algorithms for combinatorial optimization includes executing, on a quantum processor, a variational algorithm, the execution producing a subset of a set of solutions (solution space) of the variational algorithm within a predefined period, the variational algorithm computing a quantum state of a quantum system corresponding to a combinatorial optimization problem, each solution in the subset having a corresponding value; sorting, according to a sorting criterion, the subset of solutions; isolating, based on the sorting, a portion of the subset of solutions wherein a value corresponding to each solution in the portion is within a boundary defined by a threshold value; computing an average value of the solutions from the portion of the subset of solutions; and altering the variational algorithm to produce a second subset of solutions such that the second subset of solutions comprises solutions having values within the boundary.