Analog integrated neural-like circuits for nonlinear programming

A systematic approach for the design of analog neural nonlinear programming solvers using switched-capacitor (SC) integrated circuit techniques is presented. The method is based on formulating a dynamic gradient system whose state evolves in time towards the solution point of the corresponding programming problem. A neuron cell for the linear and the quadratic problem suitable for monolithic implementation is introduced. The design of this neuron and its corresponding synapses using SC techniques is considered in detail. An SC circuit architecture based on a reduced set of basic building blocks with high modularity is presented. Simulation results using a mixed-mode simulator (DIANA) and experimental results from breadboard prototypes are included, illustrating the validity of the proposed technique

Automatic Construction of Parallel Portfolios via Explicit Instance Grouping

Simultaneously utilizing several complementary solvers is a simple yet effective strategy for solving computationally hard problems. However, manually building such solver portfolios typically requires considerable domain knowledge and plenty of human effort. As an alternative, automatic construction of parallel portfolios (ACPP) aims at automatically building effective parallel portfolios based on a given problem instance set and a given rich design space. One promising way to solve the ACPP problem is to explicitly group the instances into different subsets and promote a component solver to handle each of them.This paper investigates solving ACPP from this perspective, and especially studies how to obtain a good instance grouping.The experimental results showed that the parallel portfolios constructed by the proposed method could achieve consistently superior performances to the ones constructed by the state-of-the-art ACPP methods,and could even rival sophisticated hand-designed parallel solvers

Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization

Many artificial intelligence (AI) problems naturally map to NP-hard optimization problems. This has the interesting consequence that enabling human-level capability in machines often requires systems that can handle formally intractable problems. This issue can sometimes (but possibly not always) be resolved by building special-purpose heuristic algorithms, tailored to the problem in question. Because of the continued difficulties in automating certain tasks that are natural for humans, there remains a strong motivation for AI researchers to investigate and apply new algorithms and techniques to hard AI problems. Recently a novel class of relevant algorithms that require quantum mechanical hardware have been proposed. These algorithms, referred to as quantum adiabatic algorithms, represent a new approach to designing both complete and heuristic solvers for NP-hard optimization problems. In this work we describe how to formulate image recognition, which is a canonical NP-hard AI problem, as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The QUBO format corresponds to the input format required for D-Wave superconducting adiabatic quantum computing (AQC) processors.Comment: 7 pages, 3 figure

Automatic Algorithm Selection for Pseudo-Boolean Optimization with Given Computational Time Limits

Machine learning (ML) techniques have been proposed to automatically select the best solver from a portfolio of solvers, based on predicted performance. These techniques have been applied to various problems, such as Boolean Satisfiability, Traveling Salesperson, Graph Coloring, and others. These methods, known as meta-solvers, take an instance of a problem and a portfolio of solvers as input. They then predict the best-performing solver and execute it to deliver a solution. Typically, the quality of the solution improves with a longer computational time. This has led to the development of anytime selectors, which consider both the instance and a user-prescribed computational time limit. Anytime meta-solvers predict the best-performing solver within the specified time limit. Constructing an anytime meta-solver is considerably more challenging than building a meta-solver without the "anytime" feature. In this study, we focus on the task of designing anytime meta-solvers for the NP-hard optimization problem of Pseudo-Boolean Optimization (PBO), which generalizes Satisfiability and Maximum Satisfiability problems. The effectiveness of our approach is demonstrated via extensive empirical study in which our anytime meta-solver improves dramatically on the performance of Mixed Integer Programming solver Gurobi, which is the best-performing single solver in the portfolio. For example, out of all instances and time limits for which Gurobi failed to find feasible solutions, our meta-solver identified feasible solutions for 47% of these

Optimal Charging of Electric Vehicles in Smart Grid: Characterization and Valley-Filling Algorithms

Electric vehicles (EVs) offer an attractive long-term solution to reduce the dependence on fossil fuel and greenhouse gas emission. However, a fleet of EVs with different EV battery charging rate constraints, that is distributed across a smart power grid network requires a coordinated charging schedule to minimize the power generation and EV charging costs. In this paper, we study a joint optimal power flow (OPF) and EV charging problem that augments the OPF problem with charging EVs over time. While the OPF problem is generally nonconvex and nonsmooth, it is shown recently that the OPF problem can be solved optimally for most practical power networks using its convex dual problem. Building on this zero duality gap result, we study a nested optimization approach to decompose the joint OPF and EV charging problem. We characterize the optimal offline EV charging schedule to be a valley-filling profile, which allows us to develop an optimal offline algorithm with computational complexity that is significantly lower than centralized interior point solvers. Furthermore, we propose a decentralized online algorithm that dynamically tracks the valley-filling profile. Our algorithms are evaluated on the IEEE 14 bus system, and the simulations show that the online algorithm performs almost near optimality ($<1$ relative difference from the offline optimal solution) under different settings.Comment: This paper is temporarily withdrawn in preparation for journal submissio

A Bramble-Pasciak conjugate gradient method for discrete Stokes equations with random viscosity

We study the iterative solution of linear systems of equations arising from stochastic Galerkin finite element discretizations of saddle point problems. We focus on the Stokes model with random data parametrized by uniformly distributed random variables and discuss well-posedness of the variational formulations. We introduce a Bramble-Pasciak conjugate gradient method as a linear solver. It builds on a non-standard inner product associated with a block triangular preconditioner. The block triangular structure enables more sophisticated preconditioners than the block diagonal structure usually applied in MINRES methods. We show how the existence requirements of a conjugate gradient method can be met in our setting. We analyze the performance of the solvers depending on relevant physical and numerical parameters by means of eigenvalue estimates. For this purpose, we derive bounds for the eigenvalues of the relevant preconditioned sub-matrices. We illustrate our findings using the flow in a driven cavity as a numerical test case, where the viscosity is given by a truncated Karhunen-Lo\`eve expansion of a random field. In this example, a Bramble-Pasciak conjugate gradient method with block triangular preconditioner outperforms a MINRES method with block diagonal preconditioner in terms of iteration numbers.Comment: 19 pages, 1 figure, submitted to SIAM JU