Methods and devices for optimizing processes and configurations of apparatuses and systems

A device comprising:

• at least one processor, and
• at least one memory comprising computer program code for one or more programs;
• the at least one processor, the at least one memory, and the computer program code configured to cause the device to at least carry out the following:
• provide an equation with a cost function for minimization related to an optimization problem thereby yielding a cost function equation, the cost function equation including a plurality of discrete variables;
• convert the cost function equation with the plurality of discrete variables into an Unconstrained Optimization, UO, problem;
• provide a Tensor Network, TN, with tensors such that the TN covers all possible configurations of variables of the UO problem;
• provide a set of parameters and modify coefficients of each tensor of the TN at least once for the provided set of parameters and such that, when modifying the coefficients of any tensor, a value of the cost function of the UO problem is reduced, the set of parameters relating to at least one of:
• at least one parameter modifying the TN, and at least one parameter that influences the modification of coefficients;
• repeat the modification of coefficients for the provided set of parameters until first one or more predetermined criteria are met, the first one or more predetermined criteria relating to at least one of:
• the value of the cost function of the UO problem, and a number of times that the modification of coefficients has been conducted for the provided set of parameters;
• store at least the value of the cost function associated with the provided set of parameters every time the first one or more predetermined criteria are met;
• repeat the provision of the set of parameters and modification of coefficients one or more times, each time providing a different set of parameters so as to allow further reduction in the value of the cost function;
• check, when the coefficients of the tensors have been modified for at least two provided sets of parameters and every time the first one or more predetermined criteria are met, whether the value of the cost function last stored meets a second predetermined criterion, the second predetermined criterion relating to a convergence reached in the value of the cost function based on one or more other values of the cost function stored;
• at least one of the following, every time the second predetermined has not been met in the check:
• repeat the provision of the set of parameters and modification of coefficients with a different set of parameters thereby allowing further reduction in the value of the cost function, the different set of parameters relating to at least one of:
• at least one parameter modifying the TN, and at least one parameter that influences the modification of coefficients;
• and
• change the first one or more predetermined criteria and repeating the modifying step for the provided set of parameters;
• solve, when the second predetermined criterion has been met in the check, the UO problem using the TN and provide respective values of the plurality of discrete variables of the cost equation.

A non-transitory computer-readable medium encoded with instructions that, when executed by at least one processor or hardware, make an apparatus to at least perform the following steps:

• providing an equation with a cost function for minimization related to an optimization problem thereby yielding a cost function equation, the cost function equation including a plurality of discrete variables;
• converting the cost function equation with the plurality of discrete variables into an Unconstrained Optimization, UO, problem;
• providing a Tensor Network, TN, with tensors such that the TN covers all possible configurations of variables of the UO problem;
• providing a set of parameters and modifying coefficients of each tensor of the TN at least once for the provided set of parameters and such that, when modifying the coefficients of any tensor, a value of the cost function of the UO problem is reduced, the set of parameters relating to at least one of:
• at least one parameter modifying the TN, and at least one parameter that influences the modification of coefficients;
• repeating the modifying step for the provided set of parameters until first one or more predetermined criteria are met, the first one or more predetermined criteria relating to at least one of:
• the value of the cost function of the UO problem, and a number of times that the modifying step has been conducted for the provided set of parameters;
• storing at least the value of the cost function associated with the provided set of parameters every time the first one or more predetermined criteria are met;
• repeating the providing the set of parameters and modifying steps one or more times, each time providing a different set of parameters so as to allow further reduction in the value of the cost function;
• when the coefficients of the tensors have been modified for at least two provided sets of parameters and every time the first one or more predetermined criteria are met, checking whether the value of the cost function last stored meets a second predetermined criterion, the second predetermined criterion relating to a convergence reached in the value of the cost function based on one or more other values of the cost function stored;
• every time the second predetermined has not been met in the checking step, at least one of:
• repeating the providing the set of parameters and modifying steps with a different set of parameters thereby allowing further reduction in the value of the cost function, the different set of parameters relating to at least one of:
• at least one parameter modifying the TN, and at least one parameter that influences the modification of coefficients;
• and
• changing the first one or more predetermined criteria and repeating the modifying step for the provided set of parameters;
• when the second predetermined criterion has been met in the checking step, solving the UO problem using the TN and providing respective values of the plurality of discrete variables of the cost equation.