Method and apparatus for generating a control signal to control a device in accordance with a constrained hierarchy

Apparatus to generate a control signal to control a device, the apparatus comprising:

• at least one processor;
• and
• at least one memory storing information representing a weight ratio hierarchy comprising a defined hierarchy of a set of objects with respective weight variables for each object of the objects, the defined hierarchy having at least one level of subsets of objects among the set of objects, where
• the subsets in each level have selected relative weights,
• the weight ratio hierarchy further comprising at least one target weight ratio between the weight variables of the objects at the at least one level of the defined hierarchy,
• the at least one memory further storing instructions to cause the processor to:
• generate a cost function corresponding to the weight ratio hierarchy such that, for an optimal solution of the cost function, a ratio of values for the weight variables of the objects in the at least one level will be equal to the at least one target weight ratio for the at least one level;
• obtain at least one defined constraint related to the weight variables in a formulation in accordance with input requirements of an optimization solver;
• combine the cost function and a constraint, among the at least one constraint, to obtain an optimization problem which, when input into the optimization solver, obtains an optimal, or close to optimal, solution satisfying the at least one defined constraint;
• input the optimization problem into the optimization solver and obtain a solution output by the optimization solver, the solution comprising values for the weight variables;
• and
• generate the control signal to control the device in accordance with the obtained solution.