This paper considers structural optimization problems featuring discrete variables, as well as nonlinear implicit constraints which can only be evaluated through time-expensive computations. A prominent application consists in the preliminary structural design of large ships, where many of the variables take their values in discrete sets which model standard element dimensions to be selected fr...

Design optimization of structures with discrete and continuous search spaces is a complex optimization problem with lots of local optima. Metaheuristic optimization algorithms, due to not requiring gradient information of the objective function, are efficient tools for solving these problems at a reasonable computational time. In this paper, the Doppler Effect-Mean Euclidian Distance Threshold ...

This paper presents a new approach to deal with the optimal reactive power flow (ORPF) problem with the discrete control variables. First, a quadratic ORPF model based on augmented rectangular coordinates is established by treatment with the TLC branch; and then quadratic penalty functions are incorporated into the proposed model to handle the discrete control variables; at last, the predictor ...

The probability generating function is a powerful technique for studying the law of finite sums of independent discrete random variables taking integer positive values. For real valued discrete random variables, the well known elementary theory of Dirichlet series and the symbolic computation packages available nowadays, such as Mathematica 5 TM, allows us to extend to general discrete random v...

A new non-perturbative approach to quantum field theory — D-theory — is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model emerges from the (2 + 1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicitly by simulating correlation le...

Prediction interval is awidely used tool in industrial applications to predict the distribution of future observations. The exact minimum coverage probability and the average coverage probability of the conventional prediction interval for a discrete random variable have not been accurately derived in the literature. In this paper, procedures to compute the exact minimumconfidence levels and th...

The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propagated by the chain rule through the graph are low variance unbiased estimators...

FGESd is an algorithm that takes as input a dataset of discrete variables, greedily searches over selected causal Bayesian network (CBN) structures (models), and outputs the highest scoring model it finds. The model that FGESd returns serves as a data-supported hypothesis about causal relationships that exist among the variables in the dataset. Such models are intended to help scientists form h...