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.

Abstract: In some examples, a method to interactively repair a software program using one or more automatically generated tests with human-provided test oracles may include identifying a fault location in a software program, generating a potential repair at the fault location based on a repair candidate, automatically generating a first test to test the potential repair, and generating a first query for a first test oracle based on the first test. The method may also include obtaining a response to the first query from a human, generating a first human-provided test oracle based on the first query and the obtained response to the first query, augmenting a test suite to include the first automatically generated test with the first human-provided test oracle, and testing the potential repair using the augmented test suite including the first automatically generated test with the first human-provided test oracle.

Abstract: In some examples, a method to interactively repair a software program using one or more automatically generated tests with human-provided test oracles may include identifying a fault location in a software program, generating a potential repair at the fault location based on a repair candidate, automatically generating a first test to test the potential repair, and generating a first query for a first test oracle based on the first test. The method may also include obtaining a response to the first query from a human, generating a first human-provided test oracle based on the first query and the obtained response to the first query, augmenting a test suite to include the first automatically generated test with the first human-provided test oracle, and testing the potential repair using the augmented test suite including the first automatically generated test with the first human-provided test oracle.

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 determining sequence-execution constraints that constrain execution orders of a plurality of events of an event-driven software application. The method may also include determining sequence-position constraints that constrain positions of the plurality of events in one or more possible event sequences of the plurality of events. Further, the method may include determining event-relation constraints that each indicates a relationship between an event input and an event output of each of the plurality of events. Moreover, the method may include forming a constraint set that enumerates the one or more possible event sequences and that includes the sequence-execution constraints, the sequence-position constraints, and the event-relation constraints. In addition, the method may include encoding control flow information of the one or more possible event sequences into the constraint set.

Abstract: Systems and methods are disclosed to determine “don't care” variables in programming code. The method comprises obtaining an SMT formula having a plurality of SMT variables from programming code; obtaining a simplified SMT formula from the SMT formula, the simplified SMT formula includes a plurality of simplified SMT variables; obtaining an SAT formula from the simplified SMT formula, the SAT formula includes a plurality of SAT variables; determining which of the plurality of the SMT variables are “don't care” variables from the simplified SMT formula; and determining which of the plurality of the SMT variables are “don't care” variables from the simplified SAT formula.