General Method Of Solution Research Articles

An exact solution method for solving seru scheduling problems with past-sequence-dependent setup time and learning effect

This paper concentrates on three scheduling problems with past-sequence-dependent setup time and DeJong's learning effect in seru production system (SPS), including minimizing the total waiting time, the total absolute differences in waiting time, and the total load. The setup time, which is dependent on the seru and jobs that have been processed, is considered. Also, the actual processing time with DeJong's learning effect is concerned. We propose a general exact solution method to show these three problems can be transformed into assignment problems and can be solved in polynomial time. Finally, the computational experiments are made to validate that the proposed method is promising in solving seru scheduling problems effectively.

DCS-ELM: a novel method for extreme learning machine for regression problems and a new approach for the SFRSCC.

Extreme learning machine (ELM) algorithm is widely used in regression and classification problems due to its advantages such as speed and high-performance rate. Different artificial intelligence-based optimization methods and chaotic systems have been proposed for the development of the ELM. However, a generalized solution method and success rate at the desired level could not be obtained. In this study, a new method is proposed as a result of developing the ELM algorithm used in regression problems with discrete-time chaotic systems. ELM algorithm has been improved by testing five different chaotic maps (Chebyshev, iterative, logistic, piecewise, tent) from chaotic systems. The proposed discrete-time chaotic systems based ELM (DCS-ELM) algorithm has been tested in steel fiber reinforced self-compacting concrete data sets and public four different datasets, and a result of its performance compared with the basic ELM algorithm, linear regression, support vector regression, kernel ELM algorithm and weighted ELM algorithm. It has been observed that it gives a better performance than other algorithms.

A solution framework for linear PDE-constrained mixed-integer problems

We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

Mathematical Model of VOCs Emission in Three-layer Building Materials

A simple mathematical model is proposed to account for emissions of Volatile Organic Compounds (VOCs) from three-layer building materials. The model considers both the diffusion within three layer building materials and the mass transfer resistance through the air boundary layer. A general solution method based on Laplace transform is presented. Compared to other models capable of accounting for emissions of VOCs from multi layer building materials, the present model is fully analytical instead of being numerical. The present model was validated by the experimental data from the specially designed test. The results indicated that there was a good agreement between the model predictions and the experimental data. It can also be seen from calculation that model ignoring the boundary layer resistance cannot fully reflect the real situation.

Strategic Execution Trajectories

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. Various numerical examples are included for illustration, each of which admits a unique optimal solution, however uniqueness in general remains unproven.

Nonlinearizing Two-parameter Eigenvalue Problems

We investigate a technique to transform a linear two-parameter eigenvalue problem, into a nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of the equations in the two-parameter eigenvalue problem, by considering it as a (standard) generalized eigenvalue problem. We characterize the equivalence between the original and the nonlinearized problem theoretically and show how to use the transformation computationally. Special cases of the transformation can be interpreted as a reversed companion linearization for polynomial eigenvalue problems, as well as a reversed (less known) linearization technique for certain algebraic eigenvalue problems with square-root terms. Moreover, by exploiting the structure of the NEP we present algorithm specializations for NEP methods, although the technique also allows general solution methods for NEPs to be directly applied. The nonlinearization is illustrated in examples and simulations, with focus on problems where the eliminated equation is of much smaller size than the other two-parameter eigenvalue equation. This situation arises naturally in domain decomposition techniques. A general error analysis is also carried out under the assumption that a backward stable eigenvalue solver method is used to solve the eliminated problem, leading to the conclusion that the error is benign in this situation.

Undrained cylindrical and spherical cavity expansion in elastic–viscoplastic soils

Various undrained cavity expansion solutions for elastic–plastic soil have been proposed previously. However, no solution has been presented for elastic–viscoplastic (EVP) soil until now. This paper presents a general solution method for solving the classical one-dimensional (1D) boundary value problem (BVP) for undrained cylindrical or spherical cavity expansion in EVP soil with an emphasis on the rate effect of soil. The solution method is summarized as three standard procedures: (i) obtaining the soil displacement and strain under incompressible conditions, (ii) calculating the effective stress of soil through a suitable constitutive law, and (iii) obtaining the pore pressure by numerically solving the stress equilibrium equation through the finite difference method (FDM) or other numerical solution techniques. The numerical algorithms for calculating the effective stress and pore pressure are very simple, without any complex iteration processes, and they require little calculation time but provide high computational accuracy. In addition, some numerical results are given to investigate the influence of the cavity expansion velocity on the cavity expansion response. The proposed solution procedure is general and can be applied not only for the EVP model but also for other plasticity models, and the given EVP solution can be applied to interpret the rate effect of the cone penetration test and pile penetration.

Numerical General Solution for Identifying the Position of Point Heat Source for Steady Inverse Heat Conduction Problems

This paper constructs an explicit formula for numerical general solution with position parameters of heat source as variables based on the heat conduction finite element numerical solution in order to convert inverse heat conduction problem with position identification of heat source to multi-variables limit problem. And it establishes linear equations with variables of position parameters of heat source by derivation, and gets the position parameters of heat source. The paper gives out the detailed procedure and formula for numerical general solution method, which includes describing position of point heat source, calculating numerical solutions for homogeneous solution and particular solution of the governing equation for heat conduction problem, constructing numerical general solution, solving the linear equations and getting the position parameters. The paper gives an example of identifying position parameters of heat source for inverse heat conduction problem.

An Iterative Solution Technique to Minimize the Average Transportation Cost of Capacitated Transportation Problem with Bounds on Rim Conditions

The average transportation cost minimization of capacitated transportation problem with bounds on rim conditions (CTPBRC) is an important optimization problem due to the requirement of low unit cost consumption in production system. In the literature, there is only one approach to solving a special case of this problem, but it is not applicable to the general case. In this paper, this problem is reduced to a series of finding the minimum cost maximum flow in a network with lower and upper arc capacities, and two iterative algorithms are proposed as more generalized solution method for this problem as compared to the existing approach. Computational experiments on randomly generated instances validate that the two iterative algorithms are generally able to find the minimum average transportation cost solution to CTPBRC efficiently for the general case, in which one iterative algorithm has higher efficiency than the other for large size instances.

A General Solution Method for Insider Problems

We establish connections between optimal transport theory and the dynamic version of the Kyle model, including new characterizations of informed trading profits via conjugate duality and Monge-Kantorovich duality. We use these connections to extend the model to multiple assets, general distributions, and risk-averse market makers. With risk-averse market makers, liquidity is lower, assets exhibit short-term reversals, and risk premia depend on market maker inventories, which are mean reverting. We illustrate the model by showing that implied volatilities predict stock returns when there is informed trading in stocks and options and market makers are risk averse.

A local analysis to determine all optimal solutions of [formula omitted] location problems on networks

As a generalization of p-center location problems, p-k-max problems minimize the kth largest weighted distance to the customers. In this way, outlier facilities can be detected automatically and excluded from consideration when locating new facilities. Similar to p-center problems, p-k-max problems often have many alternative optimal solutions. Knowledge of the complete optimal set allows to select a most preferred solution using secondary criteria. In this paper, a general solution method is suggested that guarantees to find all alternative optimal solutions of p-k-max problems on networks. This is realized by performing a local analysis on the edges of the underlying graph and identifying edge segments on which the p-k-max function is linear. It is shown that the complete optimal set can be represented by an extended finite dominating set (FDS) which is of polynomial size for fixed values of p. Numerical tests indicate that computing the set of optimal solutions compared to the computation of a single optimal solution of a p-k-max problem requires on average less than 15% additional computing effort. This computational efficiency allows one to select the most preferred solution among them using secondary objectives, like backup coverage or the Weber function.

Closed-Form Solution of Inverse Kinematics for a Minimally Invasive Surgical Robot Slave Manipulator Similar to Da Vinci Robot System

Abstract Closed-form solution inverse kinematics has a unique advantage in robot control; it is quite difficult to be obtained through traditional methods as no effective analytic method has been identified so far, when the robot's joint configuration does not conform to the “Pieper Criterion.” In this paper, a new modeling method named extended Denavit-Hartenberg (DH) method was presented for solving this problem. And the conditions of robots' configuration that conform to the method have been given for different joints combinations. The precise closed-form solution to a minimally invasive surgical robot slave manipulator was obtained through this new method. The correctness of the new method was verified through simulation analyses; this study enriched robot kinematic modeling and the closed-form solution to inverse kinematics of Da Vinci surgical robot, and will help to obtain a fast, accurate, and general method of closed-form solution for the same kind of robots and provide the precondition for robot control and trajectory planning.

Autonomous Dam Surveillance Robot System Based on Multi-Sensor Fusion.

Dams are important engineering facilities in the water conservancy industry. They have many functions, such as flood control, electric power generation, irrigation, water supply, shipping, etc. Therefore, their long-term safety is crucial to operational stability. Because of the complexity of the dam environment, robots with various kinds of sensors are a good choice to replace humans to perform a surveillance job. In this paper, an autonomous system design is proposed for dam ground surveillance robots, which includes general solution, electromechanical layout, sensors scheme, and navigation method. A strong and agile skid-steered mobile robot body platform is designed and created, which can be controlled accurately based on an MCU and an onboard IMU. A novel low-cost LiDAR is adopted for odometry estimation. To realize more robust localization results, two Kalman filter loops are used with the robot kinematic model to fuse wheel encoder, IMU, LiDAR odometry, and a low-cost GNSS receiver data. Besides, a recognition network based on YOLO v3 is deployed to realize real-time recognition of cracks and people during surveillance. As a system, by connecting the robot, the cloud server and the users with IOT technology, the proposed solution could be more robust and practical.

Two Optimized General Methods for Inverse Kinematics of 6R Robots Based on Machine Learning

For the 6R robot, there is no analytical solution for some configurations, so it is necessary to analyse inverse kinematics (IK) by the general solution method, which cannot achieve high precision and high speed as the analytical solution. With the expansion of application fields and the complexity of application scenarios, some robots with special configuration have become the research hotspot, and more high-speed and high-precision general algorithms are still being explored and studied. The present paper optimized two general solutions. Elimination is a numerical solution, which has high accuracy, but the solution process is complex and time-consuming. The present paper optimized the elimination method, derived the final matrix expression directly through complex coefficient extraction and simplifying operation, and realized one-step solution. The solving speed was reduced to 15% of the original, and the integrity of the method was supplemented. This paper proposed a new optimization method for the Gaussian damped least-squares method, in which the variable step-size coefficient is introduced and the machine learning method is used for the research. It was proved that, on the basis of guaranteeing the stability of motion, the average number of iterations can be effectively reduced and was only 4-5 times, effectively improving the solving speed.

3D PIC-MCC simulation of corona discharge in needle-plate electrode with external circuit

This paper investigates the external circuit effect in corona discharge by means of numerical simulation, while the effect is usually disregarded in previous plasma simulations. A general numerical solution method of serial external circuit, which can compute surface charges on any shape of electrodes adaptively and solve electrode potential and circuit current simultaneously, is developed to support the investigation, due to lack of theoretical solution in irregular electrode systems. Brief description and validation of the scheme are presented in section . In general, the accuracy of numerical solution improves with mesh refinement in orthogonal mesh, due to stair step approximation. Simulations are performed in our self-developed 3D PIC-MCC (particle-in-cell, Monte Carlo collision) code with photoionization and external circuit. The simulation model including recently developed photoionization model is described briefly in section . Then the simulation results in a needle-plate electrode in air, such as spatiotemporal evolution of corona discharge and waveforms of electrode voltage and circuit current, are presented. Physical mechanisms of formation of branched corona discharge and self-consistent adjustment of electrode voltage and circuit current are discussed. The waveforms of voltage and current in this simulation are generally consistent with experimental result. The external circuit has negative feedback effect on the discharge, and can adjusts electrode voltage self-consistently. The application of external circuit improves the applicability of particle simulation method to the simulation of discharge phenomenon in actual devices.

General Euler-Poisson-Darboux Equation and Hyperbolic B-Potentials

In this work, we develop the theory of hyperbolic equations with Bessel operators. We construct and invert hyperbolic potentials generated by multidimensional generalized translation. Chapter 1 contains necessary notation, definitions, auxiliary facts and results. In Chapter 2, we study some generalized weight functions related to a quadratic form. These functions are used below to construct fractional powers of hyperbolic operators and solutions of hyperbolic equations with Bessel operators. Chapter 3 is devoted to hyperbolic potentials generated by multidimensional generalized translation. These potentials express negative real powers of the singular wave operator, i. e. the wave operator where the Bessel operator acts instead of second derivatives. The boundedness of such an operator and its properties are investigated and the inverse operator is constructed. The hyperbolic Riesz B-potential is studied as well in this chapter. In Chapter 4, we consider various methods of solution of the Euler-Poisson-Darboux equation. We obtain solutions of the Cauchy problems for homogeneous and nonhomogeneous equations of this type. In Conclusion, we discuss general methods of solution for problems with arbitrary singular operators.

Deadbeat Direct Torque and Flux Control for Permanent Magnet Synchronous Motor Based on Stator Flux Oriented

Direct torque control (DTC) has become a widely acceptable alternative to field-oriented control in permanent magnet synchronous motor (PMSM) drives. Deadbeat direct torque and flux control (DB-DTFC) is a significant improvement over the classical DTC. However, there are some aspects that can be improved, such as insufficiently small electromagnetic torque ripple, unsmooth dynamic response, heavy computation burden, and relatively weak robustness to motor parameters variation. To improve the operation performance, an advanced DB-DTFC strategy is proposed in this article. First, the algorithm model based on stator flux oriented coordinate system is deduced. On this basis, the basic principle of proposed DB-DTFC is presented. Second, a novel graphical analysis method is proposed to help illustrate the proposed strategy. Third, a general solution method is proposed to solve the reference stator voltage, which is a key variable for the DB-DTFC. Finally, the stability of system is analyzed. Theoretical and experimental comparisons between the proposed DB-DTFC and the conventional DB-DTFC are done. The results show that the performance in the aspects of electromagnetic torque and stator current ripples reduction, dynamic response, computation burden, and robustness to motor parameters variation are all improved in the proposed DB-DTFC.

Electrical characteristics of a class of n-order triangular network

This paper investigates the electrical properties of a class of n-order triangular resistor network model. The authors establish, by constructing equivalent model, the second-order nonlinear difference equation model. We propose, by using equivalent transformation method, the general and specific methods of solution for the nonlinear difference equation and at once obtain an accurate equivalent resistance formula of n-order triangular resistor network, and a series of special conclusions are analyzed and compared. Finally, we study the oscillation and resonance characteristics of the triangular LC network under different conditions, where the method used is variable substitution by using the equivalent resistance results obtained. This study reveals the electrical characteristics of triangular LC network and establishes a new theoretical foundation for related disciplines.

Solving the general employee scheduling problem

In many professions the demand for work requires employees to work in different shifts to cover varying requirements including areas like health care, protection services, transportation, manufacturing or call centers. However, there are many constraints that need to be satisfied in order to create feasible schedules. The demands can be specified in various ways, different legal requirements need to be respected and employee satisfaction has to be taken into account. Therefore, automated solutions are mandatory to stay competitive. However, even then it is often hard to provide good solutions in reasonable time as many of the problems are NP-hard.While not each problem will require the whole set of available restrictions, it is cumbersome to develop a new specification format and corresponding solver for each problem. Often these can not be well applied to similar problems differing in some requirements. On the other hand it is a challenging task to provide a general formulation and solution methods that can solve large integrated problems, as even several sub-problems on their own are known to be NP-hard.Therefore a new framework is proposed for the general employee scheduling problem that allows the implementation of various heuristic algorithms and their application to a wide range of problems. This is realized by proposing a unified handling of constraints and the possibility to implement various moves that can be reused across different algorithms. Further, a new search method is developed and implemented in the framework.In order to show the applicability to a wide range of problems, we take different problems from literature that cover different types of demand and constraints, translate their instances to our formulation and apply our solver to those instances as well as our own instances with good results. For one problem class our framework could obtain better solutions for several benchmark instances.

Quaternionic Quantum Particles

Solutions of quaternionic quantum mechanics (QQM) are difficult to grasp, even in simple physical situations. In this article, we provide simple and understandable free particle quaternionic solutions, that can be easily compared to complex quantum mechanics (CQM). As an application, we study the scattering of quaternionic particles through a scalar step potential. We also provide a general solution method for the quaternionic Schr\"odinger equation, which can be applied to more sophisticated and physically interesting models.