Abstract: A system for assigning commuter vehicles (CVs) in a multi-modal transportation network having the CVs and fixed schedule vehicles to passengers is disclosed. The system receives itinerary requests from the passengers, wherein the itinerary requests of the passengers include initial locations, target locations, departure times from the initial locations, and arrival time windows including deadlines at the target locations. The system includes a memory to store computer executable programs including a grouping program, a route-search program, an operation route map program of the CVs, and a commuter assigning program, and a processor to perform steps of the programs in connection with the memory, wherein the steps include grouping the passengers into a set of groups, assigning the CVs to the groups by performing the commuter assigning program and generating assignment information of assigned CVs among the available CVs.

Abstract: Methods and systems for servicing of machines by workers within a period of time. Acquiring for each service an available servicing time, a time duration for servicing, a location of the machine, and a number of workers having appropriate qualifications to be concurrently present for a service. Acquiring for each worker a worker availability, qualifications and location. Determining a cost function representing a service schedule for each worker, wherein an optimization of the cost function is subject to constraints. The constraints include a number of workers with qualifications concurrently present for a service, each worker starts and ends the period of time at the same location and travels independently from other workers. The cost function includes maximizing a number of services to be performed; minimizing a number of workers required to perform servicing for each service; or minimizing a total travel time for each worker to the location.

Abstract: Systems and Methods for controlling vehicles in a multi-modal transportation network having fixed schedule vehicles and commuter vehicles, including a receiver to receive a request for transportation from passengers in a set of passengers. Jointly optimize travel times of the passengers to reach their corresponding target locations. The joint optimization is based on identifying groups of passengers from the set of passengers to obtain a set of groups of passengers. Assign an identified group to a commuter vehicle leaving or reaching an intermediate location, according to a schedule from a set of schedules associated with the identified group, by optimizing jointly a function of a total travel time of the set of passengers, according to at least one schedule of the set of schedules associated with each group, to obtain an assigned travel itinerary for each passenger. Transmit to each passenger their assigned travel itinerary in the network.

Abstract: An amount of electricity passing through an electrical grid is controlled by balancing amount of electricity for each energy provider and each energy consumer. In response to transmitting requests for the electricity, a decentralized control system receives an amount of electricity each energy operator agrees to supply or demand to satisfy the requests, as well as a sensitivity of the amount of electricity to a variation of at least one parameter of a corresponding request. The system updates parameters of at least some requests in directions governed by the corresponding sensitivities to produce a balanced amount of electricity for each energy provider and each energy consumer. The system causes the energy providers to supply into the electrical grid their corresponding balanced amounts of electricity and causes the energy consumers to consume from the electrical grid their corresponding balanced amounts of electricity.

Abstract: Methods and systems for servicing of machines by workers within a period of time. Acquiring for each service an available servicing time, a time duration for servicing, a location of the machine, and a number of workers having appropriate qualifications to be concurrently present for a service. Acquiring for each worker a worker availability, qualifications and location. Determining a cost function representing a service schedule for each worker, wherein an optimization of the cost function is subject to constraints. The constraints include a number of workers with qualifications concurrently present for a service, each worker starts and ends the period of time at the same location and travels independently from other workers. The cost function includes maximizing a number of services to be performed; minimizing a number of workers required to perform servicing for each service; or minimizing a total travel time for each worker to the location.

Abstract: An amount of electricity passing through an electrical grid is controlled by balancing amount of electricity for each energy provider and each energy consumer. In response to transmitting requests for the electricity, a decentralized control system receives an amount of electricity each energy operator agrees to supply or demand to satisfy the requests, as well as a sensitivity of the amount of electricity to a variation of at least one parameter of a corresponding request. The system updates parameters of at least some requests in directions governed by the corresponding sensitivities to produce a balanced amount of electricity for each energy provider and each energy consumer. The system causes the energy providers to supply into the electrical grid their corresponding balanced amounts of electricity and causes the energy consumers to consume from the electrical grid their corresponding balanced amounts of electricity.

Abstract: A method solves a stochastic quadratic program (StQP) for a convex set with a set of general linear equalities and inequalities by an alternating direction method of multipliers (ADMM). The method determines an optimal solution, or certifies that no solution exists. The method optimizes a step size ? for the ADMM. The method is accelerated using a conjugate gradient (CG) method. The StMPC problem is decomposed into two blocks. The first block corresponds to an equality constrained QP, and the second block corresponds to a projection onto the StMPC inequalities and anticipativity constraints. The StMPC problem can be decomposed into a set of time step problems, and then iterated between the time step problems to solve the decoupled problems until convergence.

Abstract: A method estimates an optimal power flows (OPF) in a power grid, which is represented as a graph partitioned into virtual sub-graphs, each including at least one bus, and associated with agents that measure local variables and updates consensus variables (CV). The consensus variables of adjacent virtual sub-graphs are exchanged and updated using the agents. An OPF problem is solved for the virtual sub-graphs using the agents based on the CV and the local variables. The exchanging and the solving are iterated until a termination condition is satisfied, when the optimal OPF is outputted for each virtual sub-graph.

Abstract: A method solves a stochastic quadratic program (StQP) for a convex set with a set of general linear equalities and inequalities by an alternating direction method of multipliers (ADMM). The method determines an optimal solution, or certifies that no solution exists. The method optimizes a step size ? for the ADMM. The method is accelerated using a conjugate gradient (CG) method. The StMPC problem is decomposed into two blocks. The first block corresponds to an equality constrained QP, and the second block corresponds to a projection onto the StMPC inequalities and anticipativity constraints. The StMPC problem can be decomposed into a set of time step problems, and then iterated between the time step problems to solve the decoupled problems until convergence.

Abstract: A power flow problem (OPF) in an electric power network is globally optimized using a branch and bound tree of nodes connected by edges. The BB initially includes at least a root node, and each node represents a feasible region of limits on voltages and powers. An upper bound on the OPF problem is solved for selected nodes using nonlinear programming, while a lower bound is solved using a convex relaxation. The lowest upper and lower bounds are updated using the current upper and lower bound. If a difference between the lowest upper and lowest lower bound is less than a threshold, then outputting the voltages and the powers for the electric power network as represented by the feasibility region for the selected node. Otherwise, the feasible region of the node is partitioned to replace the node. The process is repeated until the tree is empty.

Abstract: A power flow problem (OPF) in an electric power network is globally optimized using a branch and bound tree of nodes connected by edges. The BB initially includes at least a root node, and each node represents a feasible region of limits on voltages and powers. An upper bound on the OPF problem is solved for selected nodes using nonlinear programming, while a lower bound is solved using a convex relaxation. The lowest upper and lower bounds are updated using the current upper and lower bound. If a difference between the lowest upper and lowest lower bound is less than a threshold, then outputting the voltages and the powers for the electric power network as represented by the feasibility region for the selected node. Otherwise, the feasible region of the node is partitioned to replace the node. The process is repeated until the tree is empty.