Abstract: Methods and systems for finding optimal or near optimal solutions for generic optimization problems by an approach to minimizing functions over high-dimensional domains that mathematically model the optimization problems. Embodiments of the disclosed invention receive a mathematical description of a system, in symbolic form, that includes decision variables of various types, including real-number-valued, integer-valued, and Boolean-valued decision variables, and that may also include a variety of constraints on the values of the decision variables, including inequality and equality constraints. The objective function and constraints are incorporated into a global objective function. The global objective function is transformed into a system of differential equations in terms of continuous variables and parameters, so that polynomial-time methods for solving differential equations can be applied to calculate near-optimal solutions for the global objective function.

Abstract: Method and system for determining a near optimal schedule of resources in linear time by providing an optimal resource ordering scheme that increases customer satisfaction and resource satisfaction and lowers operating costs. The present invention is embodied in a scheduling computer program. The method receives a set of resources and associated resource data. The method determines a resource-rank-function value for each resource, based on the associated resource data. Based on the resource-rank-function value associated with each resource, each resource is rank ordered. For each resource, the method determines a set of candidate shifts, based on the associated resource data. The method determines a weight value for the candidate shifts associated with each resource. Based on the weight values associated with each candidate shift, the method determines a schedule of shifts, for each resource in rank order.