General Method Of Solution Research Articles

A Dynare toolbox for social learning expectations

Social learning (SL) is a behavioral model in which expectations and the resulting aggregate dynamics stem from the interactions of a large number of heterogeneous agents. Nonetheless, this framework has so far lacked a parsimonious development with a general-solution method. This paper bridges this gap and introduces a Dynare toolbox to solve any linear state-space model with SL expectations, opening up a wide range of potential applications. As an illustration, optimal monetary policy rules are studied in a microfounded New Keynesian (NK) model under SL and rational expectations (RE).

LOGICAL STYLE OF ANALYSIS OF TEXT AND OTHER INFORMATION FOR SOLVING TESTS ON GENERAL COMPETENCES

The article substantiates the effectiveness of using the logical style of analyzing text and other information for solving test tasks in conditions of time shortage. For this, a general classification of tasks was carried out, visual and other methods of their solution were selected, a generalized solution method based on the coding of available information, analysis and comparison of logical structures to identify contradictions, violations of completeness and integrity, etc.

Intelligent calculation of reachable domain under No-fly zone influence based on tangent flight trajectories

Rapid and accurate calculation of reachable domain, especially under the no-fly zone influence, is important in the reentry mission of reentry vehicles. The basic problem is the complex boundary of the reachable domain. Aiming to solve this problem, the intelligent reachable domain calculation approach with unfixed no-fly zone location based on tangent flight trajectory is presented. First, the algorithm of reachable domain calculation under no-fly zone influence is proposed. After finding the tangent flight trajectories, the tangency point states are determined and the subdomains are generated. To obtain a closed domain, the new algorithm for limiting boundary calculation is given. The no-fly zones are classified and the solution ideas of different categories are given separately to ensure that the algorithm can apply to different kinds of no-fly zones. Back Propagation neural networks are introduced and trained for different types of no-fly zones to solve reachable domains rapidly. Finally, the simulations of the proposed algorithm are presented, including each category of a single no-fly zone and different categories of multiple no-fly zones. Comparisons are also made between the general solution method and the method using neural networks. The results illustrate the effectiveness of the proposed method and the calculation time reduced by a factor of 103 through neural networks.

Multi-task collaborative method based on manifold optimization for automated test case generation based on path coverage

Automated test case generation based on path coverage is not only a large-scale black-box optimization problem, but also a key scientific problem in software automatic testing technology. Evolutionary algorithms and other search-based algorithms are representative methods for this problem. However, existing research mainly focuses on the multi-function case, where generating test cases for multiple functions is difficult due to the combinatorial explosion of the path number. In this paper, we propose a multi-task collaborative method based on manifold optimization by considering the topological manifold relationship between the test case space (decision space) and the program path space (target space). This method achieves the goal of collaborative optimization for different function coverage tasks by coordinating the allocation of computing resources and knowledge transfer mechanisms among them. To verify the effectiveness of the proposed method, we compare it with general solution methods for single-function automated test case generation based on path coverage, such as the manifold-inspired search-based algorithm. The experimental results show that the proposed method outperforms the compared single-function optimization algorithms especially on programs with strong coding similarities. This study verifies the feasibility of collaborative optimization methods for solving large-scale black-box optimization problems, such as the automated test case generation based on path coverage, and expands their application scenarios.

β-FGJO: A General Metaheuristic Method for Inverse Kinematics Solution of Multi-DOF Robotic Manipulators

<i>β</i>-FGJO: A General Metaheuristic Method for Inverse Kinematics Solution of Multi-DOF Robotic Manipulators

A FAMILY OF 82Q EXPONENTIAL HYBRID METHODS FOR SOLVING IVPS IN ODES

In a recent paper, a new class of exponential general linear methods of second stage seventh order for the numerical solution of first order initial value problems in ordinary deferential equations was derived. In this paper, we derive the new class of higher order extended exponential general linear methods for the numerical solution of first order initial value problems in ordinary deferential equations. The numerical results obtained by the new method for some problems show its superiority in efficiency and accuracy for solving problems for which the proposed general linear method is appropriate

Manipulating hidden-Markov-model inferences by corrupting batch data

Time-series models typically assume untainted and legitimate streams of data. However, a self-interested adversary may have incentive to corrupt this data, thereby altering a decision maker’s inference. Within the broader field of adversarial machine learning, this research provides a novel, probabilistic perspective toward the manipulation of hidden Markov model inferences via corrupted data. In particular, we provision a suite of corruption problems for filtering, smoothing, and decoding inferences leveraging an adversarial risk analysis approach. Multiple stochastic programming models are set forth that incorporate realistic uncertainties and varied attacker objectives. Three general solution methods are developed by alternatively viewing estimation from frequentist and Bayesian perspectives. The efficacy of each method is illustrated via extensive, empirical testing. The developed methods are characterized by their solution quality and computational effort, resulting in a stratification of techniques across varying problem-instance architectures. This research highlights the weaknesses of hidden Markov models under adversarial activity, thereby motivating the need for robustification techniques to ensure their security.

On Solving Stochastic Optimization Problems

Many optimization mathematical models, associated with the technical-economic processes of real-world problems, have elements of uncertainty in their structure, which places them in stochastic optimization programming. Their diversity and complexity, due to the large uncertainty space, require special methods of solving, because there is no general solution method. Within this context, in this paper we consider the category of optimization models that can contain random variable type coefficients and/or imposed probability levels on the constraints. The purpose of the paper is to propose a methodology dedicated to these studied models. Applying the methodology leads to developing a deterministic linear programming model, associated with the initial stochastic model. In fact, the proposed methodology reduces the stochastic formulation to a deterministic formulation. The methodology is illustrated with a numerical case study based on a manufacturing problem. Solving the obtained deterministic model is carried out in the version assisted by a specialized software product (WinQSB Version 2.0). It allows for the performing of a sensitivity analysis of the optimal solution, and/or a parametric analysis relative to certain model coefficients, both also presented in the paper. The main result of the study in this paper is the proposed methodology, which is applicable on a large scale, for any mathematical model of stochastic optimization of the mentioned type, regardless of complexity, dimensions and the domain of the process to which it is associated. The numerical results obtained when applying this methodology indicate its efficiency and effectiveness in finding the solution for the studied models. The approach to this issue in the present paper is determined by the wide range of stochastic optimization problems in the various studied real-life processes and by the imperative need to adopt the best decisions in conditions of uncertainty.

A general framework for optimal stopping problems with two risk factors and real option applications

AbstractA new explicit solution is obtained for a general class of two‐dimensional optimal stopping problems arising in real option theory. First, the solvable case of homogeneous and quasi‐homogeneous problems is presented in a comprehensive framework. Then the general problem—including the unsolved case of inhomogeneous functions—is considered and an explicit expression for the value function is obtained in terms of a modified Bessel function of second kind. Then we clarify the link between the general solution method and the more elementary one in the specific (quasi‐)homogeneous problem. Finally, this article provides some useful formulas and some insights for the one‐dimensional case as well.

Exact Solution of Interacting Particle Systems Related to Random Matrices

We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model of Brownian motions with one-sided collisions, also known as Brownian TASEP, which is equivalent to Brownian last passage percolation. We obtain a formula for the finite dimensional distributions of these particle systems, starting from arbitrary initial condition, in terms of a Fredholm determinant of an explicit kernel. As far as we can tell, in the space-inhomogeneous setting and for general initial condition this is the first time such a result has been proven. We moreover consider the model of non-colliding diffusions, again with polynomial drift and diffusion coefficients, which includes the ones associated to all the classical ensembles of random matrices. We prove that starting from arbitrary initial condition the induced point process has determinantal correlation functions in space and time with an explicit correlation kernel. A key ingredient in our general method of exact solution for both models is the application of the backward in time diffusion flow on certain families of polynomials constructed from the initial condition.

Robotic Contact Juggling

In this article, we define “robotic contact juggling” to be the purposeful control of the motion of a 3-D smooth object as it rolls freely on a motion-controlled robot manipulator, or “hand.” While specific examples of robotic contact juggling have been studied before, in this article, we provide the first general formulation and solution method for the case of an arbitrary smooth object in a single-point rolling contact on an arbitrary smooth hand. Our formulation splits the problem into four subproblems: deriving the second-order rolling kinematics; deriving the 3-D rolling dynamics; planning rolling motions that satisfy the rolling dynamics and achieve the desired goal; and stabilization of planned rolling trajectories. The theoretical results are demonstrated in 3-D simulations and 2-D experiments using feedback from a high-speed vision system.

A general purpose exact solution method for mixed integer concave minimization problems

In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program, which provides a lower bound to the original problem. The bilevel program is reduced to a single level formulation with the help of Karush–Kuhn–Tucker (KKT) conditions. Incorporating the KKT conditions lead to complementary slackness conditions that are linearized using BigM, for which we identify a tight value for general problems. Multiple bilevel programs, when solved over iterations, guarantee convergence to the exact optimum of the original problem. Though the algorithm is general and can be applied to any optimization problem with concave function(s), in this paper, we solve two common classes of operations and supply chain problems; namely, the concave knapsack problem, and the concave production-transportation problem. The computational experiments indicate that our proposed approach outperforms the customized methods that have been used in the literature to solve the two classes of problems by an order of magnitude in most of the test cases.

A Generalized Solution Method to Undamped Constant-Coefficient Second-Order ODEs Using Laplace Transforms and Fourier Series

A Generalized Solution Method to Undamped Constant-Coefficient Second-Order ODEs Using Laplace Transforms and Fourier Series

NEW RESULTS ON K- STABILITY AND BOUNDEDNESS OF SOLUTIONS OF A CERTAIN DIFFERENTIAL EQUATIONS IN BANACH SPACES INTERACTING WITH WEAKLY SUBSYSTEMS

The article gives new results of K- Stability and Boundedness of solutions of certain differential equations in Banach Spaces interacting with weakly subsystems. Some results from the theory of semigroups, and the description of the general method of solution of the posed problem were also given. The application of the matrix – valued Lyapunov function is discussed and the main theorem of the method is formulated for differential equations in a Banach Space. The vector Lyapunov function was the main tool applied for the analysis of K – Stability and Boundedness of a system in Banach Spaces. All the results of this Article for the ‘equation (2.2)’ are essentially new.

Strategic Execution Trajectories

ABSTRACT We obtain the optimal execution strategy for two sequential trades in the presence of a transient price impact. We first present a novel and general solution method for the case of a single trade (a metaorder) that is executed as a sequence of sub-trades (child orders). We then analyze the case of two sequential metaorders, including the case where the size and direction of the second metaorder are uncertain at the time the first metaorder is initiated. We obtain the optimal execution strategy under two different cost functions. First, we minimize the total cost when each metaorder is benchmarked to the price at its initiation, the total separate costs approach widely used by practitioners. Although simple, we show that optimizing total separate costs can lead to a significant understatement of the real costs of trading whilst also adversely impacting order scheduling. We overcome these issues by introducing a new cost function that splits the second metaorder into two parts, one that is predictable when the first metaorder is initiated and a residual that is not. The predictable and residual parts of the second metaorder are benchmarked using the initiation prices of the first and second metaorders, respectively. We prove existence of an optimal execution trajectory for linear instantaneous price impact and positive definite decay, and derive the explicit form of the minimizer in the special case of exponentially decaying impact, however uniqueness in general remains unproven. Various numerical examples are included for illustration.

Scheduling controllable processing time jobs in seru production system with resource allocation

In this article, four scheduling problems with controllable processing times and resource allocation in seru production system (SPS) are first studied. The objective is to minimize the total processing cost plus scheduling measures, which are the total waiting time, the total absolute differences in completion times, the total absolute differences in waiting times and the total earliness and tardiness, respectively. A general exact solution method is proposed to show that these four problems can be transformed into assignment problems and solved in polynomial time if the number of serus and processing times are given in advance. Computational experiments are made finally, and results indicate that the exact solution method is effective to return optimal schedules for four seru scheduling problems. Further, the schedule flexibility of SPS can be enhanced by considering controllable processing times, and workload balance is also need to be concern in seru production practice.

Quantum Fisher information of two atoms with dipole\u2013dipole interaction under the environment of phase noise lasers

We investigate the parameter estimation problems of two-atom system driven by the phase noise lasers (PNLs) environment. And we give a general method of numeric solution to handle the problems of atom system under the PNLs environment. The calculation results of this method on Quantum Fisher Information (QFI) are consistent with our former results. Moreover, we consider the dipole–dipole (d–d) interaction between the atoms under PNLs environment with the collective decay, and the results show that larger d–d interaction and smaller collective decay rate lead to larger QFI of the two-atom system. So the collective decay will destroy the QFI while the d–d interaction will preserve the QFI, these results can be used to protect the QFI of two-atom system driven by the PNLs environment.

Optimal Stopping of a Random Sequence with Unknown Distribution

The subject of this paper is the problem of optimal stopping of a sequence of independent and identically distributed random variables with unknown distribution. We propose a stopping rule that is based on relative ranks and study its performance as measured by the maximal relative regret over suitable nonparametric classes of distributions. It is shown that the proposed rule is first-order asymptotically optimal and nearly rate optimal in terms of the rate at which the relative regret converges to zero. We also develop a general method for numerical solution of sequential stopping problems with no distributional information and use it in order to implement the proposed stopping rule. Some numerical experiments illustrating performance of the rule are presented as well.

Taylor-Aris dispersion for N-zone and continuous systems with variable sorption strength – extending Aris’s approach

It is shown Aris’ general solution method for the asymptotic axial dispersion in nested two-layer systems with a radial distribution of the axial velocity and with different diffusion and sorption properties in each layer can be generalized to nested and distributed N-zone systems and systems with continuously varying sorption strength by introducing a generalized flux expression J = −D.K.∇(C/K). In this expression, the local diffusion coefficient D and the local sorption constant K can be either piecewise constant (N-zone system) or continuous functions of the radial space coordinates (continuous system). After a mathematically sound derivation of the general solution, it is validated by comparing the resulting expressions for Dax with either existing literature expressions or with the dispersion coefficient found by numerically solving the complete, time-dependent advection–diffusion mass balance for a number of selected examples. Applications can be found in continuous flow membrane separations, chromatography, and flows through extruded mesoporous ceramic beds.

Concurrent topology optimization of cellular structures and anisotropic materials

This paper presents a general formulation and solution method for the problem of two-scale concurrent topology optimization of cellular structure and its anisotropic materials. This formulation seeks simultaneous determination of the macro and micro structural topologies and the orientations of microstructures, such as a unit cell with anisotropic and inhomogeneous material properties. In the present formulation, the microstructure of cellular material is uniform in the entire macrostructure but with spatially-varying orientations. The solution method consists of two new features: (a) a mutual strain energy density-based approach proposed for analytically determining the orientations of fully anisotropic materials in compliant mechanism problems, which can also be modified to address minimum compliance designs and (b) an extended and fully-coupled moving iso-surface threshold (MIST) method and algorithm developed for solving the formulated concurrent optimization problem of cellular structures using two-scale physical response functions. The present formulation and algorithm are validated via studying numerical examples of concurrent optimum design of: (i) macro and micro topologies; (ii) macro topology and orthotropic material orientations; and (iii) macro and micro topologies and material orientations.