Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The methods compared are Monte Carlo with pseudo-random numbers, Latin Hypercube Sampling, and Quasi Monte Carlo with sampling based on Sobol’ sequences. Generally results show superior performance of the Quasi Monte Carlo approach based on Sobol’ s...

In this paper we propose a mechanism for enhancing the performance of the Artificial Bee Colony Algorithm (ABCA) by making use low discrepancy Sobol sequence. The performance of the proposed Sobol sequence guided ABC (S-ABC) is analyzed over several benchmark functions and also compared to that of basic ABC. The empirical results show that the presence of low discrepancy sequence like that of S...

We introduce a new method for screening inputs in mathematical or computational models with large numbers of inputs. The method proposed here represents an improvement over the best available practice for this setting when dealing with models having strong interaction effects. When the sample size is sufficiently high the same design can also be used to obtain accurate quantitative estimates of...

The estimation of variance-based importance measures (called Sobol’ indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a large number of input variables (typically more than ten). Recently, Sobol and Kucherenko have proposed the Derivative-based Global Sensitivity Measures (DGSM),...

Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (TT) as a unified framework for surrogate modeling and global sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate of the un...

This paper presents a new mutation operator called the Sobol Mutation (SOM) operator for enhancing the performance of Quantum Particle Swarm Optimization (QPSO) algorithm. The SOM operator unlike most of its contemporary mutation operators do not use the random probability distribution for perturbing the swarm population, but uses a quasi random Sobol sequence to find new solution vectors in th...

Direction numbers for generating Sobol′ sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 (2003), pp. 49–57]. However, these Sobol′ sequences may have poor two-dimensional projections. Here we provide a new set of direction numbers alleviating this problem. These are obtained by treating Sobol′ seque...

High-dimensional integrals are usually solved with Monte Carlo algorithms although theory suggests that low discrepancy algorithms are sometimes superior. We report on numerical testing which compares low discrepancy and Monte Carlo algorithms on the evaluation of nancial derivatives. The testing is performed on a Collateralized Mortgage Obligation (CMO) which is formulated as the computation o...

The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use ...