Probabilistic approach in solving an optimization problem with application to in physical and technical systems

The article considers some optimization models with a nonlinear objective function and constraints in the form of equalities and inequalities. The model is considered in two forms – deterministic and stochastic, which allows it to be used to solve various optimization problems in physical and technical systems. The presented stochastic model is based on the inclusion of stochastic parameters into the well-known Cobb-Douglas function. The influence of stochastic variables on the optimal value of the objective function, depending on their distribution type, is analyzed.

Research on Point Cloud Registering Method of Tunneling Roadway Based on 3D NDT-ICP Algorithm

In order to meet the needs of intelligent perception of the driving environment, a point cloud registering method based on 3D NDT-ICP algorithm is proposed to improve the modeling accuracy of tunneling roadway environments. Firstly, Voxel Grid filtering method is used to preprocess the point cloud of tunneling roadways to maintain the overall structure of the point cloud and reduce the number of point clouds. After that, the 3D NDT algorithm is used to solve the coordinate transformation of the point cloud in the tunneling roadway and the cell resolution of the algorithm is optimized according to the environmental features of the tunneling roadway. Finally, a kd-tree is introduced into the ICP algorithm for point pair search, and the Gauss–Newton method is used to optimize the solution of nonlinear objective function of the algorithm to complete accurate registering of tunneling roadway point clouds. The experimental results show that the 3D NDT algorithm can meet the resolution requirement when the cell resolution is set to 0.5 m under the condition of processing the point cloud with the environmental features of tunneling roadways. At this time, the registering time is the shortest. Compared with the NDT algorithm, ICP algorithm and traditional 3D NDT-ICP algorithm, the registering speed of the 3D NDT-ICP algorithm proposed in this paper is obviously improved and the registering error is smaller.

Iterative Tuning of Feedforward Controller with Precise Time-Delay Compensation for Precision Motion System

The accuracy of feedforward control model including system time-delay significantly affects the position tracking performance in a precision motion system. In this paper, an iterative tuning method for feedforward control with precise time-delay compensation is proposed. First, considering system time-delay from actuator, sensor, calculation, and communication in real platform, a feedforward control model with time-delay compensation is established, and a nonlinear objective function with time-delay is designed based on the measured data of a finite time task, to minimize the position tracking error. Second, in order to deal with both the nonlinear objective function and also unknown disturbances and noise in the real system, an optimization strategy combining the Gauss–Newton iterative (GNI) scheme and instrumental variable (IV) is proposed to realize the unbiased estimation of the feedforward parameters and precise delay time. Finally, with the identified feedforward control parameters, the precise system time-delay which is a nonintegral multiple of the sampling period is compensated accurately for the feedforward control with accurate path planning time-shift in the implementation. The effectiveness of the proposed feedforward parameter tuning and precise time-delay compensation scheme is verified by the simulation and also experimental result on a precision motion platform with obvious position tracking performance improvement.

Introducing a Design Framework for a Multi-Modal Public Transportation System, Focusing on Mixed-Fleet Bike-Sharing Systems

Bike-sharing is increasingly becoming more popular. Electric bikes as an emerging transportation technology have extended range and are less physically demanding, compared with regular bicycles, thus they can be incorporated into regular bike-sharing systems to attract more users. This study aims at capturing the users’ preference, while considering investors’ limitations and societal cost and benefits of each mode. The problem is defined as a mixed-integer non-liner problem, with nonlinear objective function and constraints. Because of the computationally challenging nature of the problem, a metaheuristic algorithm based on simulated annealing algorithm is proposed for its solution. The performance of the algorithm is tested in this study and convergence patterns are observed. The main findings of this study which are derived from the hypothetical numerical example, include but are not limited to: (1) the most popular public modes are bus and pedelec, because these two modes (bus and pedelec) are less expensive and have the ability to traverse longer distances in comparison to similar modes (i.e., e-scooter/car and bike), and (2) for small communities with short travel distances (feasible within the ranges of active modes), users would not choose fuel-consuming modes, and thus their choice is insensitive to fuel cost.

A Penalty-Free Method with Trust Region for Nonlinear Semidefinite Programming

In this paper, we propose a class of new penalty-free method, which does not use any penalty function or a filter, to solve nonlinear semidefinite programming (NSDP). So the choice of the penalty parameter and the storage of filter set are avoided. The new method adopts trust region framework to compute a trial step. The trial step is then either accepted or rejected based on the some acceptable criteria which depends on reductions attained in the nonlinear objective function and in the measure of constraint infeasibility. Under the suitable assumptions, we prove that the algorithm is well defined and globally convergent. Finally, the preliminary numerical results are reported.

Dynamic Economic Dispatch Based on Improved Particle Swarm Optimization

Because wind power can reduce the total generation costs under certain conditions, in order to minimize the system production cost, optimize the power output of thermal unit, a dynamic economic dispatching (DED) model containing wind power based on energy-saving and emission reduction benefits is proposed. Such DED model has a nonlinear objective function and the characteristic of high dimension, and is restricted by many constraints. An improved particle swarm optimization (IPSO) is proposed for solving the problem. Feasible regulation scheme is adopted in equality constrains. On the premise that the speed of iterative convergence is assured, the diversity and the excellence of solution are improved by introducing the differential mutation, which enhances the algorithm in breaking away from the local optimum and speeds up the iterative convergence of the algorithm.

An Efficient Approach for Solving Mesh Optimization Problems Using Newton’s Method

We present an efficient approach for solving various mesh optimization problems. Our approach is based on Newton’s method, which uses both first-order (gradient) and second-order (Hessian) derivatives of the nonlinear objective function. The volume and surface mesh optimization algorithms are developed such that mesh validity and surface constraints are satisfied. We also propose several Hessian modification methods when the Hessian matrix is not positive definite. We demonstrate our approach by comparing our method with nonlinear conjugate gradient and steepest descent methods in terms of both efficiency and mesh quality.