Artificial Monte Carlo interactions for solving some linear problems

A method of artificial interaction for Monte Carlo solution of ordinary differential equations with respect to probability measures is proposed. Under some conditions this method is advantageous over the standard method. A theoretical comparison of the complexity of the corresponding algorithms is provided. Also, results of numerical experiments are discussed.     

Computing strategies for achieving acceptability: A Monte Carlo approach

We consider a trader who wants to direct his or her portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a Monte Carlo algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and whose outputs are the numerical values of initial capital requirement and the functional form of a trading strategy for achieving acceptability. We also prove optimality of the capital obtained. Explicit theoretical evaluations of hedging strategies are extremely difficult, and we avoid the problem by resorting to such computational methods. The main idea is to utilize the finite Vapnik–C?ervonenkis dimension of a class of possible strategies.     

A new iterative Monte Carlo approach for inverse matrix problem

A new approach of iterative Monte Carlo algorithms for the well-known inverse matrix problem is presented and studied. The algorithms are based on a special techniques of iteration parameter choice, which allows to control the convergence of the algorithm for any column (row) of the matrix using different relaxation parameters. The choice of these parameters is controlled by a posteriori criteria for every Monte Carlo iteration. The presented Monte Carlo algorithms are implemented on a SUN Sparkstation. Numerical tests are performed for matrices of moderate in order to show how work the algorithms. The algorithms under consideration are well parallelized.     

M5 model tree and Monte Carlo simulation for efficient structural reliability analysis

Practically, the performance of many engineering problems can be defined using a complex implicit limit state function. Approximation of the accurate failure probability is very time-consuming and inefficient based on Monte Carlo simulation (MCS) for complex performance functions. M5 model tree (M5Tree) model is robust approach for simulation and prediction phenomena, which provides ability to dealing with complex implicit problems by dividing them into smaller problems. By improving the efficiency of reliability method using accurate approximated failure probability, an efficient reliability method using the MCS and M5Tree is proposed to calibrate the performance function and estimate the failure probability, respectively. The superiorities including simplicity and accuracy of M5Tree meta-model are investigated to evaluate the actual performance function through five nonlinear complex mathematical and structural reliability problems. The proposed reliability method-based MCS and M5Tree improved the computational efforts for evaluating the performance function in reliability analysis. The M5Tree significantly increased the efficiency of reliability analysis with accurate failure probability.     

Fuzzy goal programming for inventory management: A bacterial foraging approach

An efficient inventory planning approach in today’s global trading regime is necessary not only for increasing the profit margin, but also to maintain system flexibility for achieving higher customer satisfaction. Such an approach should hence be comprised of a prudent inventory policy and clear satisfaction of stakeholder’s goals. Relative significance given to various objectives in a supply chain network varies with product as well as time. In this paper, a model is proposed to fill this void for a single product inventory control of a supply chain consisting of three echelons. A generic modification proposed to the membership functions of the fuzzy goal-programming approach is used to mathematically map the aspiration levels of the decision maker. The bacterial foraging algorithm has been modified with enhancement of the algorithms’ capability to map integer solution spaces and utilised to solve resulting fuzzy multi-objective function. An illustrative example comprehensively covers various decision scenarios and highlights the underlying managerial insights.     

Using tree search bounds to enhance a genetic algorithm approach to two rectangle packing problems

A popular approach when using a genetic algorithm in the solution of constrained problems is to exploit problem specific information by representing individuals as ordered lists. A construction heuristic is then often used as a decoder to produce a solution from each ordering. In such a situation further information is often available in the form of bounds on the partial solutions. This paper uses two two-dimensional packing problems to illustrate how this information can be incorporated into the genetic operators to improve the overall performance of the search. Our objective is to use the packing problems as a vehicle for investigating a series of modifications of the genetic algorithm approach based on information from bounds on partial solutions.     

On a Monte Carlo method for neutron transport criticality computations

^** Email: maire{at}univ-tln.fr^*** Email: denis.talay{at}sophia.inria.fr We give a stochastic representation of the principal eigenvalueof some homogeneous neutron transport operators. Our constructionis based upon the Feynman–Kac formula for integral transportequations, and uses probabilistic techniques only. We developa Monte Carlo method for criticality computations. We numericallytest this method on various homogeneous and inhomogeneous problems,and compare our results with those obtained by standard methods.     

Maximum a Posteriori Sequence Estimation Using Monte Carlo Particle Filters

We develop methods for performing maximum a posteriori (MAP) sequence estimation in non-linear non-Gaussian dynamic models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. MAP sequence estimation is then performed using a classical dynamic programming technique applied to the discretised version of the state space. In contrast with standard approaches to the problem which essentially compare only the trajectories generated directly during the filtering stage, our method efficiently computes the optimal trajectory over all combinations of the filtered states. A particular strength of the method is that MAP sequence estimation is performed sequentially in one single forwards pass through the data without the requirement of an additional backward sweep. An application to estimation of a non-linear time series model and to spectral estimation for time-varying autoregressions is described.     

The inventory replenishment planning and staggering problem: a bi-objective approach

To the best of our knowledge, this paper is the first one to suggest formulating the inventory replenishment problem as a bi-objective decision problem where, in addition to minimizing the sum of order and inventory holding costs, we should minimize the required storage space. Also, it develops two solution methods, called the exploratory method (EM) and the two-population evolutionary algorithm (TPEA), to solve the problem. The proposed methods generate a near-Pareto front of solutions with respect to the considered objectives. As the inventory replenishment problem have never been formulated as a bi-objective problem and as the literature does not provide any method to solve the considered bi-objective problem, we compared the results of the EM to three versions of the TPEA. The results obtained suggest that although the TPEA produces good near-Pareto solutions, the decision maker can apply a combination of both methods and choose among all the obtained solutions.     

Using extended Monte Carlo simulation method for the improvement of risk management: Consideration of relationships between uncertainties

This paper considers the relationship of the major uncertainties of a project by using proposed approach. This approach by using rotary algorithm intellectualized the classic Monte Carlo simulation. This will help utility function to come closer to reality so that decision making and risk analysis would be done based on the real and possible modes, providing better conditions for decision making. Analyzing and investigating uncertainties are done in the risk management frame work. Because opportunities and threats are not separated, Monte Carlo simulation analysis is implemented as an integrated tool to reach the project goals, analyzing and investigating a variety of uncertainty permutations simultaneously. This method is a powerful tool for investigating the effects of all uncertainties’ occurrence, so it has noticeable benefits such as simultaneous consideration of uncertainties and the capability of representing several dimensions of utility function. In spite of these benefits, not considering the type and level of relationships, some permutations of uncertainties will occur that are not possible in real world. This would divert the utility function from reality. A simple example is used to illustrate the application of the model in practice.     

Monte Carlo method via a numerical algorithm to solve a parabolic problem

This paper is intended to provide a numerical algorithm consisted of the combined use of the finite difference method and Monte Carlo method to solve a one-dimensional parabolic partial differential equation. The numerical algorithm is based on the discretize governing equations by finite difference method. Due to the application of the finite difference method, a large sparse system of linear algebraic equations is obtained. An approach of Monte Carlo method is employed to solve the linear system. Numerical tests are performed in order to show the efficiency and accuracy of the present work.     

An analysis of a Monte Carlo algorithm for estimating the permanent

Karmarkar, Karp, Lipton, Lovász, and Luby proposed a Monte Carlo algorithm for approximating the permanent of a non-negativen×n matrix, which is based on an easily computed, unbiased estimator. It is not difficult to construct 0,1-matrices for which the variance of this estimator is very large, so that an exponential number of trials is necessary to obtain a reliable approximation that is within a constant factor of the correct value. Nevertheless, the same authors conjectured that for a random 0,1-matrix the variance of the estimator is typically small. The conjecture is shown to be true; indeed, for almost every 0,1-matrixA, just O(nw(n)e ^-2) trials suffice to obtain a reliable approximation to the permanent ofA within a factor 1±ɛ of the correct value. Here ω(n) is any function tending to infinity asn→∞. This result extends to random 0,1-matrices with density at leastn ^−1/2ω(n). It is also shown that polynomially many trials suffice to approximate the permanent of any dense 0,1-matrix, i.e., one in which every row- and column-sum is at least (1/2+α)n, for some constant α>0. The degree of the polynomial bounding the number of trials is a function of α, and increases as α→0. Supported by NSF grant CCR-9225008. The work described here was partly carried out while the author was visiting Princeton University as a guest of DIMACS (Center for Discrete Mathematics and Computer Science).     

Computing the variance of a conditional expectation via non-nested Monte Carlo

Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the optimal inner-level sample size is bounded as the computational budget increases. In this letter, we construct unbiased non-nested Monte Carlo estimators based on the so-called pick-freeze scheme due to Sobol’. An extension of our approach to compute higher order moments of a conditional expectation is also discussed.