Method and apparatus for optimizing system operational parameters

Claim 2

Apparatus for optimizing the operating state of a communications network comprising: a plurality of sensors for developing signals representative of present operating state of said network, said signals being related to controllable parameters of said network; first processor, responsive to said sensors, for transforming said signals onto a multi-dimensional space such that said operational state of said communications network is at essentially the center of said multi-dimensional space and said constraints form a polytope in said space; second processor, responsive to said first processor, for computing a path in said space characterized by a power series of order greater than one, along which values of said signals in said space represent a state of said communications network that is monotonically improving with distance from said center; and third processor, reponsive to said second processor, for selecting a point on said curve, developing a modified set of signals corresponding to said selected point and controlling said parameters of said communication network in accordance with said modified set of signals.

Claim 3

Apparatus for optimizing the operational state of a system in accordance with a preselected operational criterion by adjusting values of operational parameters controlling said state of said system, said operational parameters being adjustable within a preselected set of linear constraints, comprising: a first processor portion for developing signal representations of said operational parameters and for developing, a preselected representational form of said operational state of said system, based on said representations, said constraints and said criterion, with said representational form comprising a two dimensional array of values related to said set of constraints and to said state of said system, and a one dimensional array of signals related to said operational criterion; and said two dimensional array defining a polytope in a multidimensional space, with said operational parameters being the variables of said space and said one dimensional array defining a direction in said space; a second processor portion, responsive to said first processor portion, for transforming said operational parameters, said two dimensional array, and said one dimensional array, onto a transformed space where said state of said system is essentially at the center of said space, and computing a power series function in said transformed space, of order greater than one, that approximates a trajectory curve in consonance with said operational criterion; and third processor portion, responsive to said second processor portion, for setting said operational parameters of said system at values corresponding to a point in said transformed space and along said curve.

Claim 4

Apparatus for optimizing the operational state of a system in accordance with a preselected operational criterion by adjusting values of operational parameters controlling said state of said system, said operational parameters being adjustable within a preselected set of linear constraints, comprising: a first processor portion for developing signal representations of said operational parameters and for developing, a preselected representational form of said operational state of said system, based on said representations, said constraints and said criterion, with said representational form comprising a two dimensional array of values related to said set of constraints and to said state of said system, and a one dimensional array of signals related to said operational criterion; and said two dimensional array defining a polytope in a multidimensional space, with said operational parameters being the variables of said space and said one dimensional array defining a direction in said space; a second processor portion, responsive to said first processor portion, for transforming said operational parameters, said two dimensional array, and said one dimensional array, onto a transformed space where said state of said system is essentially at the center of said space, and computing a power series function in said transformed space, of order greater than one, that approximates a trajectory curve in consonance with said operational criterion; and third processor portion, responsive to said second processor portion, for setting said operational parameters of said system at values corresponding to a point in said transformed space and along said curve.

Claim 5

Apparatus for allocating resources of a commercial enterprise in accordance with a preselected operational criterion by adjusting values of operational parameters describing said state of said enterprise, said operational parameters being adjustable within a preselected set of linear constraints, characterized by: sensors for developing said representations of said values of said operational parameters; a first processing portion, responsive to said signal representations, for projecting said signal representations onto a transformed space to place said state of said enterprise at essentially the center of said transformed space; a second processing portion, responsive to said first portion, for computing a power series function in said transformed space, of order greater than one, that approximates a trajectory curve in consonance with said operational criterion; and a controller for setting said operational parameters of said enterprise at values corresponding to a point in said transformed space and along said curve.

Claim 6

Apparatus for allocating resources of a commercial enterprise in accordance with a preselected operational criterion by adjusting values of operational parameters describing said state of said enterprise, said operational parameters being adjustable within a preselected set of linear constraints, characterized by: sensors for developing said representations of said values of said operational parameters; a first processing portion, responsive to said signal representations, for projecting said signal representations onto a transformed space to place said state of said enterprise at essentially the center of said transformed space; a second processing portion, responsive to said first portion, for computing a power series function in said transformed space, of order greater than one, that approximates a trajectory curve in consonance with said operational criterion; and a controller for setting said operational parameters of said enterprise at values corresponding to a point in said transformed space and along said curve.

Claim 7

Apparatus for optimizing operational state of a system described by a set of operational parameters, with said optimizing accomplished by adjusting values of said operational parameters within a preselected set of constraints to minimize a set of preselected operational criterion values, comprising: sensors for developing signal representations of said values of said operational parameters; a first processor portion, responsive to said signal representations of said sensors, to applied values of said constraints and to said operational criterion, for developing a canonical form signal representation of said operational state of said system, such that said minimizing is effected by ##EQU23## where x is a vector related to said operational parameters, c is a vector related to said set of preselected criterion values, n is the number of said operational parameters, A=(a 11 , a 12 , . . . , a ij , . . . , a mn ) is an m by n matrix of coefficients related to said preselected set of constraints, and e is a vector of all 1's; said canonical signal representation forming a multidimensional space, with said operational parameters being the variables of said space, said matrix defining a polytope in said space, and said c vector specifying a direction in said space; a second processor portion, responsive to said first processor portion, for projecting said operational parameters, said matrix, and said c vector unto a transformed space where said state of said system is at essentially a center of said transformed space; a third processor portion, responsive to said second processor portion, for computing a power series function in said transformed space of order greater than one that approximates a trajectory curve in consonance with said operational criterion; and a controller, responsive to said third processor portion, for setting said operational parameters of said system at values corresponding to a point in said transformed space and along said curve.

Claim 8

Apparatus for optimizing operational state of a system described by a set of operational parameters, with said optimizing accomplished by adjusting values of said operational parameters within a preselected set of constraints to minimize a set of preselected operational criterion values, comprising: sensors for developing signal representations of said values of said operational parameters; a first processor portion, responsive to said signal representations of said sensors, to applied values of said constraints and to said operational criterion, for developing a canonical form signal representation of said operational state of said system, such that said minimizing is effected by ##EQU23## where x is a vector related to said operational parameters, c is a vector related to said set of preselected criterion values, n is the number of said operational parameters, A=(a 11 , a 12 , . . . , a ij , . . . , a mn ) is an m by n matrix of coefficients related to said preselected set of constraints, and e is a vector of all 1's; said canonical signal representation forming a multidimensional space, with said operational parameters being the variables of said space, said matrix defining a polytope in said space, and said c vector specifying a direction in said space; a second processor portion, responsive to said first processor portion, for projecting said operational parameters, said matrix, and said c vector unto a transformed space where said state of said system is at essentially a center of said transformed space; a third processor portion, responsive to said second processor portion, for computing a power series function in said transformed space of order greater than one that approximates a trajectory curve in consonance with said operational criterion; and a controller, responsive to said third processor portion, for setting said operational parameters of said system at values corresponding to a point in said transformed space and along said curve.

Claim 9

Apparatus for optimally scheduling resources of a commercial enterprise in accordance with a preselected operational criterion by adjusting values of operational parameters describing said state of said enterprise, said operational parameters being adjustable within a preselected set of constraints, characterized by: first means for developing a tentative state-of-the-system representation based on said values of said operational parameters, and for developing a canonical form representation of the operational state of said enterprise corresponding to said tentative state-of-the-system, said constraints and said criterion; second means, responsive to said first means, for projecting said canonical form representation of said tentative state-of-the-system in response to a "true" activation signal, onto a transformed space to place said state-of-the-system at essentially the center of said space, and computing a power series function in said transformed space, of order greater than one, that approximates a trajectory curve in consonance with said operational criterion; third means responsive to said second means for modifying said tentative state-of-the-system to correspond to a point in said transformed space and along said curve; fourth means responsive to said second means for developing said activation control signal, and setting said control signal to "true" state when said tentative state-of-the-system is not within a preselected stopping region, and set to a "false" state when said tentative state-of-the-system is within said preselected stopping region; and fifth means, responsive to said fourth means, for setting said operational parameters of said enterprise in accordance with said tentative state-of-the-system when said activation control signal is "false".

Claim 10

Apparatus for optimally scheduling resources of a commercial enterprise in accordance with a preselected operational criterion by adjusting values of operational parameters describing said state of said enterprise, said operational parameters being adjustable within a preselected set of constraints, characterized by: first means for developing a tentative state-of-the-system representation based on said values of said operational parameters, and for developing a canonical form representation of the operational state of said enterprise corresponding to said tentative state-of-the-system, said constraints and said criterion; second means, responsive to said first means, for projecting said canonical form representation of said tentative state-of-the-system in response to a "true" activation signal, onto a transformed space to place said state-of-the-system at essentially the center of said space, and computing a power series function in said transformed space, of order greater than one, that approximates a trajectory curve in consonance with said operational criterion; third means responsive to said second means for modifying said tentative state-of-the-system to correspond to a point in said transformed space and along said curve; fourth means responsive to said second means for developing said activation control signal, and setting said control signal to "true" state when said tentative state-of-the-system is not within a preselected stopping region, and set to a "false" state when said tentative state-of-the-system is within said preselected stopping region; and fifth means, responsive to said fourth means, for setting said operational parameters of said enterprise in accordance with said tentative state-of-the-system when said activation control signal is "false".

Claim 11

In an electronic resource allocation optimizing apparatus, a method for assigning values to a plurality of controllable parameters of a system, x, where said parameters are linearly related to each other through inequality and equality constraint relationships, and where said assigning values aims to maximize a benefit specified by a linear objective relationship of said parameters characterized by: a step of transforming said parameters, x, of said system to a domain containing a vector field describing the steepest descent to an optimum allocation, wherein said system parameters are described by a vector signal y; and a step of passing from a first set of values for said transformed parameters, y(1), that satisfy said constraint relationships to a second set of values for said transformed parameters, y(2), that also satisfy said constraint relationships, in correspondence with the equation ##EQU24## where each of said v k vector coefficients is related to said first set of values and to said objective relationship, where m is a preselected integer, and t is a preselected step size.

Claim 12

In an electronic resource allocation optimizing apparatus, a method for assigning values to a plurality of controllable parameters of a system, x, where said parameters are linearly related to each other through inequality and equality constraint relationships, and where said assigning values aims to maximize a benefit specified by a linear objective relationship of said parameters characterized by: a step of transforming said parameters, x, of said system to a domain containing a vector field describing the steepest descent to an optimum allocation, wherein said system parameters are described by a vector signal y; and a step of passing from a first set of values for said transformed parameters, y(1), that satisfy said constraint relationships to a second set of values for said transformed parameters, y(2), that also satisfy said constraint relationships, in correspondence with the equation ##EQU24## where each of said v k vector coefficients is related to said first set of values and to said objective relationship, where m is a preselected integer, and t is a preselected step size.

Claim 13

The method of claim 6 wherein said step of transforming comprises a projective transformation onto a multidimensional space where said transformed parameters, y(1) are essentially at the center of said space.

Claim 16

The method of claim 8 wherein said step of converting comprises a projective transformation.

Claim 17

The method of claim 8, further comprising a step of iterating through said steps of converting, developing coefficients, selecting step size and obtaining a set of values, where at each iteration following the first iteration said step of selecting a starting set comprises assigning the second set of values, y, of the previous iteration to the first set of values of said each iteration; and a step of stopping said iterating based on an elevation of a presented stopping rule.

Claim 20

In a system including resources and users of said resources where allocation of said resources to said users is subject to linear constraints, a method for allocating said resources to said users so as to minimize a given objective function comprising the steps of: treating said resources as variables; iteratively reassigning said resources from a present tentative allocation to a new tentative allocation in accordance with a polynomial approximation of a curve of order greater than one that is related to said present tentative allocation and is a member of a family of curves that describe a generalized steepest descent to an optimum allocation in accordance with said objective function; terminating said step of iteratively reassigning said resources when said given objective function is minimized; and allocating said resources in accordance with the last of said tentative resource reassignments.

Claim 21

In a system including resources and users of said resources where allocation of said resources to said users is subject to linear constraints, a method for allocating said resources to said users so as to minimize a given objective function comprising the steps of: treating said resources as variables; iteratively reassigning said resources from a present tentative allocation to a new tentative allocation in accordance with a polynomial approximation of a curve of order greater than one that is related to said present tentative allocation and is a member of a family of curves that describe a generalized steepest descent to an optimum allocation in accordance with said objective function; terminating said step of iteratively reassigning said resources when said given objective function is minimized; and allocating said resources in accordance with the last of said tentative resource reassignments.