Abstract: A method is provided for solving a given combinatorial problem includes providing a function that has been established for a family of combinatorial problems including the given combinatorial problem. For each problem in the family, the function relates a secondary measure of the problem to a quality metric of a characteristic solution to the problem. The function may be applied to a value of the secondary measure for the given problem to obtain a value of the quality metric of the characteristic solution to the given problem. The given problem may be solved to obtain a solution to the given problem; and the solution evaluated based on comparison of a value of the quality metric of the solution, and the value of the quality metric of the characteristic solution. And in at least one instance based on the evaluation, the solution may be communicated to guide performance of a task.

Abstract: A method is provided for solving a given combinatorial problem includes providing a function that has been established for a family of combinatorial problems including the given combinatorial problem. For each problem in the family, the function relates a secondary measure of the problem to a quality metric of a characteristic solution to the problem. The function may be applied to a value of the secondary measure for the given problem to obtain a value of the quality metric of the characteristic solution to the given problem. The given problem may be solved to obtain a solution to the given problem; and the solution evaluated based on comparison of a value of the quality metric of the solution, and the value of the quality metric of the characteristic solution. And in at least one instance based on the evaluation, the solution may be communicated to guide performance of a task.

Abstract: A system is provided for benchmarking a progressive combinatorial solver. The system may initialize a parametric model collector, and perform a plurality of parametric trials associated with respective numbers of sub-part iterations of the progressive combinatorial solver. For each of the plurality of parametric trials, the system may initialize a statistical data collector. The system may perform a plurality of randomized executions of the progressive combinatorial solver, and add data including metric values for respective solutions of the executions to the statistical data collector. The system may then determine statistical parameter(s) of data in the statistical data collector, and add data including an indication of the respective number of sub-part iterations, a cost of finding the metric values for the respective solutions, and the statistical parameters of the trial to the parametric data collector. And the system may determine a best-fit model from data in the parametric data collector.

Abstract: A system is provided for benchmarking a progressive combinatorial solver. The system may initialize a parametric model collector, and perform a plurality of parametric trials associated with respective numbers of sub-part iterations of the progressive combinatorial solver. For each of the plurality of parametric trials, the system may initialize a statistical data collector. The system may perform a plurality of randomized executions of the progressive combinatorial solver, and add data including metric values for respective solutions of the executions to the statistical data collector. The system may then determine statistical parameter(s) of data in the statistical data collector, and add data including an indication of the respective number of sub-part iterations, a cost of finding the metric values for the respective solutions, and the statistical parameters of the trial to the parametric data collector. And the system may determine a best-fit model from data in the parametric data collector.

Abstract: A system is provided for benchmarking a progressive combinatorial solver. The system may initialize a parametric model collector, and perform a plurality of parametric trials associated with respective numbers of sub-part iterations of the progressive combinatorial solver. For each of the plurality of parametric trials, the system may initialize a statistical data collector. The system may perform a plurality of randomized executions of the progressive combinatorial solver, and add data including metric values for respective solutions of the executions to the statistical data collector. The system may then determine statistical parameter(s) of data in the statistical data collector, and add data including an indication of the respective number of sub-part iterations, a cost of finding the metric values for the respective solutions, and the statistical parameters of the trial to the parametric data collector. And the system may determine a best-fit model from data in the parametric data collector.

Abstract: A system is provided for benchmarking a progressive combinatorial solver. The system may initialize a parametric model collector, and perform a plurality of parametric trials associated with respective numbers of sub-part iterations of the progressive combinatorial solver. For each of the plurality of parametric trials, the system may initialize a statistical data collector. The system may perform a plurality of randomized executions of the progressive combinatorial solver, and add data including metric values for respective solutions of the executions to the statistical data collector. The system may then determine statistical parameter(s) of data in the statistical data collector, and add data including an indication of the respective number of sub-part iterations, a cost of finding the metric values for the respective solutions, and the statistical parameters of the trial to the parametric data collector. And the system may determine a best-fit model from data in the parametric data collector.

Abstract: A tracking unit includes a register for storing initial sequences and an accumulator for effecting a statistical treatment of the initial sequences, and ensures the statistical treatment relates to no more than a number of best sequences based on an evaluating algorithm. A generating unit employs the statistical treatment to present a new sequence. A measuring unit evaluates the new sequence according to the algorithm and cooperates with the tracking unit to effect providing the new sequence to the tracking unit when the evaluating indicates the new sequence is appropriate for the storing and statistical treatment. The measuring unit provides the new sequence to a regulating unit with an indication of efficacy of the new sequence. The regulating unit employs the indication to store a best-sequence-yet-received and responds to a criterion to order the generating unit to present a new sequence or to present the best-sequence-yet-received at an output locus.

Abstract: A system optimizing a sequence according to an algorithm includes: an initiator; a tracker; a generator; a measurer; a regulator; and an output. The initiator provides initial sequences to the tracker. The tracker stores and effects a statistical treatment of the initial sequences. The generator employs the statistical treatment to present a new sequence. The measurer evaluates the new sequence according to the algorithm. The measurer provides the new sequence to the tracker when the evaluating indicates so, and provides the new sequence and a quality indicator to the regulator. The regulator employs the indicator to store at least a best-sequence-yet-received, and responds to a criterion to order the generator to present a new sequence or to present the best-sequence-yet-received at the output.

Abstract: The invention relates to methods for production rate and capacity planning used to answer key questions necessary for planning efficient production operations, where the goal is to plan the performance of some repetitive body of work subject to a combination of constraints on duration, rate, and resources. In one embodiment, resource quantity, unit duration, production interval, and/or resource utilization may be determined utilizing a method of applying derived equations.