System and method for representing and solving numeric and symbolic problems

A machine system for solving an optimization or constraint satisfaction problem, comprising:

• a digital computer for receiving and manipulating information in the form of user-defined targets and/or objectives of the problem, said digital computer comprising:
• one or more memory devices for storing said user-defined targets and/or objectives,
• a pure objective function and constraint functions representative of said user-defined targets and/or objectives, said pure objective function and constraint functions containing decision variables capable of accepting a value;
• first means for performing a test on said pure objective function and constraint functions to determine local linearity;
• and
• second means using linear techniques for manipulating said values of said decision variables to attempt to achieve said targets and/or objectives when the results of said test indicate local linearity, and using non-linear techniques for manipulating said values when the results of said test indicate local non-linearity.

A machine system for solving an optimization or constraint satisfaction problem, comprising:

• a digital computer for receiving and manipulating information in the form of user-defined targets and/or objectives of the problem, said digital computer comprising:
• one or more memory devices for storing said user-defined targets and/or objectives,
• a pure objective function and constraint functions representative of said user-defined targets and/or objectives, said pure objective function and said constraint functions containing functions of decision variables capable of accepting a value;
• first means for determining the proximity of constraint boundaries;
• and
• second means for using a combination of constrained and unconstrained optimization techniques for manipulating said values of said decision variables to attempt to achieve said targets and/or objectives, based on the proximity of constraint boundaries.

A method for operating a digital computer to solve an optimization or constraint satisfaction problem, the digital computer having an electronic memory device for storing said problem, comprising the steps of:

• (1) storing, in the electronic memory device, weak and strong problem solving methods, decision variables having decision variable values, and heuristics;
• (2) utilizing said weak and strong problem solving methods to manipulate the decision variable values to find at least a best balanced solution to the problem;
• and
• (3) using said heuristics for dynamically interleaving alternating between said weak and strong problem solving methods.

A method for operating a digital computer to solve an optimization or constraint satisfaction problem, wherein the problem comprises a set of constraint and/or objective functions, said digital computer having an electronic memory device for storing said problem, comprising the steps of:

• (1) creating a pure objective function and constraint functions representative of user-defined targets and/or objectives of the problem in the electronic memory device, said pure objective function and said constraint functions containing functions of decision variables capable of accepting a value;
• (2) determining the proximity of constraint boundaries;
• and
• (3) using a combination of constrained and unconstrained optimization techniques for manipulating said values of said decision variables to attempt to achieve said targets and/or objectives, based on the proximity of constraint boundaries.

A device for representing and solving problems in the form of objects, attributes and constructs, comprising:

• a computer-readable medium for use with a digital computer;
• a first module for parsing and translating said constructs into a machine evaluable form;
• a second module for automatically defining a tabular representation where said tabular representation contains cells corresponding to object-attribute pairs;
• a third module for automatically defining dependencies from said machine evaluable form;
• a fourth module for automatically attaching said constructs to object-attribute pairs and for attaching said dependencies;
• a fifth module for allowing said object-attribute pairs to inherit said constructs from other object-attribute pairs;
• a sixth module for automatically operating on related object-attribute pairs as a function of said defined constructs and dependencies;
• a seventh module for automatically utilizing weak and strong problem solving methods in conjunction with said dependencies and chosen values of said object-attribute pairs to find at least a best balanced solution to the problem;
• and
• an eighth module for using heuristics for dynamically alternating between said weak and strong methods;
• said computer-readable medium for storing computer program logic representative of said objects, attributes and constructs and of said modules.