Abstract: In an embodiment, a set of parameters associated with a vehicle routing problem is received. A set of decision variables and a set of constraints associated with an optimization problem are received. An optimization problem is constructed. The optimization problem is divided into a set of sub-problems. Each of the set of sub-problems corresponds to a subset of warehouses of a set of warehouses. An intermediate solution is determined for each of the set of sub-problems to determine a set of routes associated with the corresponding sub-problem of the set of sub-problems. The intermediate solution associated with each of the set of sub-problems is combined to determine a final solution of the optimization problem based on the received set of constraints. The determined final solution is indicative of the set of optimal routes to be assigned to the set of vehicles. The final solution is rendered on a display device.

Abstract: According to an aspect of an embodiment, operations include receiving data associated with a vehicle routing problem, the data comprising first information about a plurality of vehicles in a geographical region and second information about a set of locations that the plurality of vehicles is required to serve. The operations further include determining a formulation of a multi-objective clustering problem based on the data and converting the formulation into a QUBO formulation. The operations further include generating a binary solution by solving the QUBO formulation on an optimization solver machine. The operations further include partitioning the set of locations into location clusters based on the binary solution and generating a set of candidate routes for the plurality of vehicles based on the location clusters. The operations further include controlling a device to render at least one route recommendation for the plurality of vehicles based on the set of candidate routes.

Abstract: In an embodiment, a first graph corresponding to an initial solution of a combinatorial optimization problem is received. A reinforcement learning (RL) model is applied on the received first graph. A predefined number of a set of edges is selected from the received first graph. The selected set of edges is deleted from the received first graph to generate a second graph, based on a disconnection of a set of segments associated with the selected set of edges. The generated second graph corresponds to a partial solution. Thereafter, a partial tour may be determined using an annealer-based solver to generate a third graph, based on a connection of the predefined number of a set of disjoint segments. The generated third graph corresponds to a new solution. The RL model is re-trained to determine an improved solution. The determined improved solution is rendered on a display device.

Abstract: In an embodiment, a set of constraints associated with a vehicle routing problem is received. The vehicle routing problem is an optimization problem whose goal is to determine a set of optimal routes, between a depot and a set of customers, for a delivery of a set of items using a set of vehicles, and a total cost associated with the set of optimal routes corresponds to a minimum cost. The optimization problem is constructed. A random-walk graph. A graph partitioner is applied on the constructed random-walk graph. The set of customers is clustered. The constructed optimization problem is split into a set of sub-problems. An intermediate solution for each of the set of sub-problems is determined. The determined intermediate solution associated with each of the set of sub-problems is combined to determine a final solution. The determined final solution is rendered on a display device.

Abstract: According to an aspect of an embodiment, operations include receiving data associated with a vehicle routing problem, the data comprising first information about a plurality of vehicles in a geographical region and second information about a set of locations that the plurality of vehicles is required to serve. The operations further include determining a formulation of a multi-objective clustering problem based on the data and converting the formulation into a QUBO formulation. The operations further include generating a binary solution by solving the QUBO formulation on an optimization solver machine. The operations further include partitioning the set of locations into location clusters based on the binary solution and generating a set of candidate routes for the plurality of vehicles based on the location clusters. The operations further include controlling a device to render at least one route recommendation for the plurality of vehicles based on the set of candidate routes.

Abstract: According to an aspect of an embodiment, operations include receiving an input comprising a node-based graph associated with a real-world optimization problem and generating a sparse graph by removing a subset of edges from the node-based graph, The operations further include formulating operators of a quantum circuit on a quantum computer based on the sparse graph and formulating a cost function for the real-world optimization problem. The operations further include executing a set of operations which includes operating the quantum circuit on the quantum computer to generate a result, estimating a value of the cost function using the result, and updating parameters of the operators based on the value. The operations further include generating a final solution of the real-world optimization problem by repeating the execution of the set of operations using the updated parameters, until the estimated value of the cost function approaches a predefined threshold value.

Abstract: In an embodiment, a set of parameters associated with a vehicle routing problem is received. A set of decision variables and a set of constraints associated with an optimization problem are received. An optimization problem is constructed. The optimization problem is divided into a set of sub-problems. Each of the set of sub-problems corresponds to a subset of warehouses of a set of warehouses. An intermediate solution is determined for each of the set of sub-problems to determine a set of routes associated with the corresponding sub-problem of the set of sub-problems. The intermediate solution associated with each of the set of sub-problems is combined to determine a final solution of the optimization problem based on the received set of constraints. The determined final solution is indicative of the set of optimal routes to be assigned to the set of vehicles. The final solution is rendered on a display device.

Abstract: A method may include obtaining a set of tags and a set of items in which each item is pre-sorted into a cluster and each item corresponds to one or more tags. The method may include generating a bipartite graph that includes the set of tags as a first set of nodes and the clusters of items as a second set of nodes. Relationships between tags and items may be represented as edges between the first nodes and the second nodes. The bipartite graph may be modeled as a quadratic programming formulation, and cluster descriptor sets that each include one or more of the tags may be determined by solving the quadratic programming formulation of the bipartite graph, each of the cluster descriptor sets providing an explanation of how one or more clusters of items were pre-sorted. The method may include analyzing the items based on the luster descriptor sets.

Abstract: A method may include assigning each node of a network to a single first node cluster and selecting nodes of the network as a first set of nodes. The method may further include solving an optimization problem by reassigning one or more of the nodes of the first set of nodes to a second node cluster while maintaining the nodes that are not part of the first set of nodes in the first node cluster. The method may also include after solving the optimization problem, selecting other nodes of the network as another set of nodes and resolving the optimization problem by reassigning one or more of the nodes of the other set of nodes to a third node cluster while maintaining the node cluster assignment of the nodes that are not part of the other set of nodes.

Abstract: According to an aspect of an embodiment, operations may include receiving a set of inputs associated with a set of orders, a set of production lines, and timelines for the production. The operations may further include initializing each of a set of intervals to be used for scheduling of the production, based on a first interval size. The operations may further include generating a first Quadratic Unconstrained Binary Optimization (QUBO) formulation. The operations may further include generating a first solution of the first QUBO formulation. The operations may further include updating each of the initialized set of intervals based on a second interval size. The operations may further include generating a second QUBO formulation. The operations may further include generating a second solution by solving the second QUBO formulation and determining a schedule to be used for the production of the set of orders, based on the generated second solution.

Abstract: A method may include obtaining a first matrix that represents data in a data set and obtaining a number of clusters into which the data is to be grouped. The method may further include constructing a second matrix using the first matrix and the number of clusters. The second matrix may represent a formulation of a first optimization problem in a framework of a second optimization problem. The method may further include solving the second optimization problem using the second matrix to generate a solution of the second optimization problem and mapping the solution of the second optimization problem into a first solution matrix that represents a solution of the first optimization problem. The method may further include grouping the data into multiple data clusters using the first solution matrix. A number of the multiple data clusters may be equal to the number of clusters.

Abstract: According to an aspect of an embodiment, operations may include predicting, by a pre-trained DNN, a first class for a first datapoint of a first dataset. A first set of feature scores is determined for the first datapoint based on the first class associated with the first datapoint. A set of confusing class pairs associated with the DNN is identified based on the first class and a predetermined class of the first datapoint. The first dataset is clustered into one of a set of semantic classes based on the first set of feature score, the first class, and the set of confusing class pairs for each datapoint in the first dataset. Each semantic class indicates a prediction accuracy of a dataset clustered in the semantic class. A classifier is trained based on the clustered first dataset, the first set of feature scores, and the set of semantic classes.

Abstract: A method may include assigning each node of a network to a single first node cluster and selecting nodes of the network as a first set of nodes. The method may further include solving an optimization problem by reassigning one or more of the nodes of the first set of nodes to a second node cluster while maintaining the nodes that are not part of the first set of nodes in the first node cluster. The method may also include after solving the optimization problem, selecting other nodes of the network as another set of nodes and resolving the optimization problem by reassigning one or more of the nodes of the other set of nodes to a third node cluster while maintaining the node cluster assignment of the nodes that are not part of the other set of nodes.

Abstract: According to an aspect of an embodiment, operations may include receiving a first input associated with a set of orders to be produced at a production facility and receiving a second input associated with a set of production lines. The operations may further include extracting a set of production-related datapoints and receiving a third input associated with a set of constraints. The operations may further include generating a Quadratic Unconstrained Binary Optimization (QUBO) formulation based on the extracted set of datapoints and the third input and submitting the generated QUBO formulation to a first optimization solver machine. The operations may further include receiving a first solution of the submitted QUBO formulation from the first optimization solver machine and determining a schedule to be used for the production of the set of orders on the set of production lines, based on the received first solution.

Abstract: A method may include obtaining a first matrix that represents data in a data set and obtaining a number of clusters into which the data is to be grouped. The method may further include constructing a second matrix using the first matrix and the number of clusters. The second matrix may represent a formulation of a first optimization problem in a framework of a second optimization problem. The method may further include solving the second optimization problem using the second matrix to generate a solution of the second optimization problem and mapping the solution of the second optimization problem into a first solution matrix that represents a solution of the first optimization problem. The method may further include grouping the data into multiple data clusters using the first solution matrix. A number of the multiple data clusters may be equal to the number of clusters.

Abstract: A method may include assigning each node of a network to a different node cluster such that a number of nodes equals a number of node clusters and selecting multiple of the nodes of the network as a set of nodes. The method may further include solving a first optimization problem by reassigning one or more of the nodes of the set of nodes to a different node cluster while maintaining assigned node clusters of the nodes that are not part of the set of nodes and after solving the first optimization problem, selecting multiple of the node clusters as a set of node clusters. The method may also include solving a second optimization problem by merging two or more of the node clusters of the set of node clusters while maintaining the node clusters that are not part of the set of node clusters.

Abstract: An electrical energy storage system that can store both grid-based electrical power when electricity prices are low or renewable power generated on-site. It can release the stored electricity for consumer applications when necessary based on a software program and configuration. The system may be networked. The system comprises a port for receiving a central processing unit (CPU), and facilitates the use of different CPU products for different users and uses.

Abstract: A method may include obtaining a deep neural network model and obtaining a first training data point and a second training data point for the deep neural network model during a first training epoch. The method may include determining a first robustness value of the first training data point and a second robustness value of the second training data point. The method may further include omitting augmenting the first training data point in response to the first robustness value satisfying a robustness threshold and augmenting the second training data point in response to the second robustness value failing to satisfy the robustness threshold. The method may also include training the deep neural network model on the first training data point and the augmented second training data point during the first training epoch.

Abstract: A method may include obtaining multiple lines of programming code of a program, and obtaining multiple test cases for testing the program, where each of the test cases includes an assertion upon which a result of a respective test case is based. The method may also include executing the program for each of the test cases, and identifying affected lines of programming code that influence the assertions. The method may additionally include calculating a risk score for at least one of the lines of programming code based on the affected lines of programming code and the assertion, the risk score indicative of a likelihood that the at least one of the lines of programming code includes a fault.

Abstract: A method may include obtaining multiple lines of programming code of a program, and obtaining multiple test cases for testing the program, where each of the test cases includes an assertion upon which a result of a respective test case is based. The method may also include executing the program for each of the test cases, and identifying affected lines of programming code that influence the assertions. The method may additionally include calculating a risk score for at least one of the lines of programming code based on the affected lines of programming code and the assertion, the risk score indicative of a likelihood that the at least one of the lines of programming code includes a fault.