Abstract: A method and system for optimizing a train rail system. The method comprises creating a model of the rail system in a memory, creating an objective function in the memory, and determining, using a computer, a configuration of the rail system which optimizes the objective function for the process systems model. The model may be a process systems model. The aspect being optimized may be a train schedule for the rail system. The trains may be operated in accordance with the train schedule. The system comprises a computer and a memory. The memory stores a program configured to create in the memory the model, create the objective function, and determine the configuration of the rail system, using the computer, which optimizes the objective function for the model.

Abstract: A system includes a plurality of hierarchical layers configured to solve a decision-making problem. Each hierarchical layer is configured to generate solution data representing a possible solution to a sub-problem associated with the decision-making problem. Each hierarchical layer is also configured to receive orders and to use the orders during generation of the solution data. The orders include orders based on the solution data from a higher hierarchical layer, orders based on feedback from a lower hierarchical layer, and/or orders that are exogenously provided. Each hierarchical layer could be configured to use the orders to simplify a search for the possible solution to the sub-problem being solved by that hierarchical layer, such as by excluding solutions inconsistent with the orders.

Abstract: A system includes a coordinator configured to generate a first offer representing a possible solution to a problem being solved. The coordinator is configured to generate the first offer using a first model. The system also includes multiple cooperators each configured to receive the first offer and to determine if a sub-problem associated with the problem can be solved based on the first offer and using a second model. Each cooperator is also configured to identify an infeasibility and communicate the infeasibility to the coordinator when the sub-problem cannot be solved based on the first offer. The coordinator is further configured to receive the infeasibility, generate a second offer by reducing a deviation between the first offer and a consensus of the cooperators, and provide the second offer to the cooperators. The consensus of the cooperators is based on a level of the first offer that each cooperator can achieve.

Abstract: A system includes a plurality of hierarchical layers configured to solve a decision-making problem. Each hierarchical layer is configured to generate solution data representing a possible solution to a sub-problem associated with the decision-making problem. Each hierarchical layer is also configured to receive orders and to use the orders during generation of the solution data. The orders include orders based on the solution data from a higher hierarchical layer, orders based on feedback from a lower hierarchical layer, and/or orders that are exogenously provided. Each hierarchical layer could be configured to use the orders to simplify a search for the possible solution to the sub-problem being solved by that hierarchical layer, such as by excluding solutions inconsistent with the orders.

Abstract: A system includes a coordinator configured to generate a first offer representing a possible solution to a problem being solved. The coordinator is configured to generate the first offer using a first model. The system also includes multiple cooperators each configured to receive the first offer and to determine if a sub-problem associated with the problem can be solved based on the first offer and using a second model. Each cooperator is also configured to identify an infeasibility and communicate the infeasibility to the coordinator when the sub-problem cannot be solved based on the first offer. The coordinator is further configured to receive the infeasibility, generate a second offer by reducing a deviation between the first offer and a consensus of the cooperators, and provide the second offer to the cooperators. The consensus of the cooperators is based on a level of the first offer that each cooperator can achieve.