If the energy function of an artificial neural network system is expressed in quadratic form based on the objective function and constraints of a combinatorial optimization problem, it is possible to get a solution using the equations of system dynamics; a special algorithm is not required. However, even though the subenergy functions based on the constraints can be expressed in quadratic form, minimizing the subenergy functions does not necessarily give a feasible solution satisfying the constraints of the optimization problem. This shows that neural network systems have a limit in their applicability. In this paper we propose new neurons, with an immunological rejective function, so as to extend the applicability of neural network system. These neurons have the function of rejecting the violation of constraints. We apply these neurons to scheduling problems and discuss their capabilities.