scholarly journals Minimization over randomly selected lines

2013 ◽  
Vol 3 (2) ◽  
pp. 111-119 ◽  
Author(s):  
Ismet Sahin
Keyword(s):  
Cost Function ◽  
Optimization Method ◽  
Population Based ◽  
Quadratic Functions ◽  
Stopping Criterion ◽  
Crossover Operator ◽  
Selected Lines ◽  
Swarm Algorithms ◽  
Function Domain ◽  
The Cost

This paper presents a population-based evolutionary optimization method for minimizing a given cost function. The mutation operator of this method selects randomly oriented lines in the cost function domain, constructs quadratic functions interpolating the cost function at three different points over each line, and uses extrema of the quadratics as mutated points. The crossover operator modifies each mutated point based on components of two points in population, instead of one point as is usually performed in other evolutionary algorithms. The stopping criterion of this method depends on the number of almost degenerate quadratics. We demonstrate that the proposed method with these mutation and crossover operations achieves faster and more robust convergence than the well-known Differential Evolution and Particle Swarm algorithms.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

Convergence of Simulated Annealing with Feedback Temperature Schedules

1997 ◽  
Vol 11 (3) ◽  
pp. 279-304 ◽  
Author(s):  
M. Kolonko ◽  
M. T. Tran
Keyword(s):  
Simulated Annealing ◽  
Cost Function ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Optimization Method ◽  
Search Process ◽  
Local Optimum ◽  
Fixed Sequence ◽  
Temperature Parameter ◽  
The Cost

It is well known that the standard simulated annealing optimization method converges in distribution to the minimum of the cost function if the probability a for accepting an increase in costs goes to 0. α is controlled by the “temperature” parameter, which in the standard setup is a fixed sequence of values converging slowly to 0. We study a more general model in which the temperature may depend on the state of the search process. This allows us to adapt the temperature to the landscape of the cost function. The temperature may temporarily rise such that the process can leave a local optimum more easily. We give weak conditions on the temperature schedules such that the process of solutions finally concentrates near the optimal solutions. We also briefly sketch computational results for the job shop scheduling problem.

scholarly journals Optimal Eco-Driving Cycles for Conventional Vehicles Using a Genetic Algorithm

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4362
Author(s):  
Subramaniam Saravana Sankar ◽  
Yiqun Xia ◽  
Julaluk Carmai ◽  
Saiprasit Koetniyom
Keyword(s):  
Genetic Algorithm ◽  
Cost Function ◽  
Fuel Consumption ◽  
Optimization Algorithm ◽  
Internal Combustion Engines ◽  
Optimization Method ◽  
Computational Time ◽  
Weight Factor ◽  
Driving Cycles ◽  
The Cost

The goal of this work is to compute the eco-driving cycles for vehicles equipped with internal combustion engines by using a genetic algorithm (GA) with a focus on reducing energy consumption. The proposed GA-based optimization method uses an optimal control problem (OCP), which is framed considering both fuel consumption and driver comfort in the cost function formulation with the support of a tunable weight factor to enhance the overall performance of the algorithm. The results and functioning of the optimization algorithm are analyzed with several widely used standard driving cycles and a simulated real-world driving cycle. For the selected optimal weight factor, the simulation results show that an average reduction of eight percent in fuel consumption is achieved. The results of parallelization in computing the cost function indicates that the computational time required by the optimization algorithm is reduced based on the hardware used.

scholarly journals An Effective Optimization Method for Machine Learning Based on ADAM

2020 ◽  
Vol 10 (3) ◽  
pp. 1073 ◽  
Author(s):  
Dokkyun Yi ◽  
Jaehyun Ahn ◽  
Sangmin Ji
Keyword(s):  
Machine Learning ◽  
Cost Function ◽  
Gradient Descent ◽  
Local Minimum ◽  
Optimization Method ◽  
Activation Function ◽  
Numerical Comparison ◽  
First Derivative ◽  
Artificial Neural Network Ann ◽  
The Cost

A machine is taught by finding the minimum value of the cost function which is induced by learning data. Unfortunately, as the amount of learning increases, the non-liner activation function in the artificial neural network (ANN), the complexity of the artificial intelligence structures, and the cost function’s non-convex complexity all increase. We know that a non-convex function has local minimums, and that the first derivative of the cost function is zero at a local minimum. Therefore, the methods based on a gradient descent optimization do not undergo further change when they fall to a local minimum because they are based on the first derivative of the cost function. This paper introduces a novel optimization method to make machine learning more efficient. In other words, we construct an effective optimization method for non-convex cost function. The proposed method solves the problem of falling into a local minimum by adding the cost function in the parameter update rule of the ADAM method. We prove the convergence of the sequences generated from the proposed method and the superiority of the proposed method by numerical comparison with gradient descent (GD, ADAM, and AdaMax).

scholarly journals Two-Dimensional Symmetric Box Delivery Motion Prediction and Validation: Subtask-Based Optimization Method

2020 ◽  
Vol 10 (24) ◽  
pp. 8798
Author(s):  
Yujiang Xiang ◽  
Shadman Tahmid ◽  
Paul Owens ◽  
James Yang
Keyword(s):  
Cost Function ◽  
Material Handling ◽  
Optimization Method ◽  
Joint Torque ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Inverse Dynamic ◽  
Manual Material Handling ◽  
Research Outcome ◽  
The Cost

Box delivery is a complicated manual material handling task which needs to consider the box weight, delivering speed, stability, and location. This paper presents a subtask-based inverse dynamic optimization formulation for determining the two-dimensional (2D) symmetric optimal box delivery motion. For the subtask-based formulation, the delivery task is divided into five subtasks: lifting, the first transition step, carrying, the second transition step, and unloading. To render a complete delivering task, each subtask is formulated as a separate optimization problem with appropriate boundary conditions. For carrying and lifting subtasks, the cost function is the sum of joint torque squared. In contrast, for transition subtasks, the cost function is the combination of joint discomfort and joint torque squared. Joint angle profiles are validated through experimental results using Pearson’s correlation coefficient (r) and root-mean-square-error (RMSE). Results show that the subtask-based approach is computationally efficient for complex box delivery motion simulation. This research outcome provides a practical guidance to prevent injury risks in joint torque space for workers who deliver heavy objects in their daily jobs.

A Novel Redundancy Resolution Method via Optimization with Additional Tasks

2013 ◽  
Vol 694-697 ◽  
pp. 1787-1792
Author(s):  
Xue Feng Zhou
Keyword(s):  
Cost Function ◽  
Optimization Method ◽  
Initial Configuration ◽  
Main Task ◽  
Joint Position ◽  
Redundancy Resolution ◽  
Redundant Manipulator ◽  
Resolution Method ◽  
Additional Task ◽  
The Cost

This paper presents an optimization method for redundant manipulator redundancy resolution with additional task. The cost function is a compromise between the requirement of accuracy of the main task, the accuracy of the additional task, and the feasibility of the joint velocities. The joint rates that minimize the cost function can be found, and the joint position trajectories can be integrated with an initial configuration. The effectiveness of this presented method is verified by a planar 3-DoF PRR manipulator.

The Cost-Sorted Distance Method for Identifying Minima Within Firefly Optimization Results: Application to Engineering Design

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Christopher M. Elliott ◽  
Scott M. Ferguson ◽  
Gregory D. Buckner
Keyword(s):  
Optimization Method ◽  
Population Based ◽  
Benchmark Problems ◽  
Distance Method ◽  
Vector Population ◽  
Design Alternatives ◽  
Multiple Minima ◽  
Firefly Optimization ◽  
Euclidean Distances ◽  
The Cost

Abstract This paper provides a detailed description of the cost-sorted distance (CSD) method for visually and computationally identifying objective function minima within clustered population-based optimization results. CSD requires sorting the design vector population by cost and computing Euclidean distances between each pair of designs. It may be applied in conjunction with any population-based optimization method (e.g., particle swarm, genetic algorithm, simulated annealing, ant colony, firefly), but it is naturally compatible with the firefly algorithm (FA) because FA also requires the distances between each pair of design vectors and benefits from cost-sorting the population (the computational work required for CSD is a byproduct of FA). A modified FA is presented that uses CSD to more thoroughly search near potential minima and a systematic method for tuning the algorithm to reliably identify multiple minima is documented. The tuned algorithm's efficacy is demonstrated using a class of benchmark problems and a “real world” electromechanical design problem, where the identification of attractive design alternatives can be challenging.

IMAGE COMPOSITION WITH COLOR HARMONIZATION

2012 ◽  
Vol 26 (03) ◽  
pp. 1254001
Author(s):  
YANLI WAN ◽  
ZHEN TANG ◽  
ZHENJIANG MIAO ◽  
BO LI
Keyword(s):  
Cost Function ◽  
Optimization Method ◽  
Image Composition ◽  
Local Smoothness ◽  
Color Harmony ◽  
Matching Cost ◽  
Computer Generated Imagery ◽  
The Cost ◽  
Previous Image

Image composition is a very important technique in computer generated imagery. Besides some factors such as contrast, texture and noise that affect the quality of the composition, color harmony between fore- and background is also an important factor that would affect the quality of the composition. However, in the previous image composition techniques, color harmony between fore- and background is seldom considered. In this paper, an optimization method is proposed to deal with the color harmonization problem that used in image composition. A cost function is derived from the local smoothness of the hue values, and the image is harmonized by minimizing the cost function. A new matching cost function is proposed to select the best matching harmonic schemes. Our approach overcomes several shortcomings of the existing color harmonization methods. We validate the performance of our method and demonstrate its effectiveness with a variety of experiments.

scholarly journals The association between varying levels of palliative care involvement on costs during terminal hospitalizations in Canada from 2012 to 2015

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Sarina R. Isenberg ◽  
Christopher Meaney ◽  
Peter May ◽  
Peter Tanuseputro ◽  
Kieran Quinn ◽  
...  
Keyword(s):  
Palliative Care ◽  
Metastatic Cancer ◽  
Estimating Equation ◽  
Population Based ◽  
Future Research ◽  
Chronic Obstructive ◽  
Discharge Abstract Database ◽  
High Involvement ◽  
Hospitalization Costs ◽  
The Cost

Abstract Background Inpatient palliative care is associated with lower inpatient costs; however, this has yet to be studied using a more nuanced, multi-tiered measure of inpatient palliative care and a national population-representative dataset. Using a population-based cohort of Canadians who died in hospital, our objectives were to: describe patients’ receipt of palliative care and active interventions in their terminal hospitalization; and examine the relationship between inpatient palliative care and hospitalization costs. Methods Retrospective cohort study using data from the Discharge Abstract Database in Canada between fiscal years 2012 and 2015. The cohort were Canadian adults (age ≥ 18 years) who died in hospital between April 1st, 2012 and March 31st, 2015 (N = 250,640). The exposure was level of palliative care involvement defined as: medium-high, low, or no palliative care. The main measure was acute care costs calculated using resource intensity weights multiplied by the cost of standard hospital stay, represented in 2014 Canadian dollars (CAD). Descriptive statistics were represented as median (IQR), and n(%). We modelled cost as a function of palliative care using a gamma generalized estimating equation (GEE) model, accounting for clustering by hospital. Results There were 250,640 adults who died in hospital. Mean age was 76 (SD 14), 47% were female. The most common comorbidities were: metastatic cancer (21%), heart failure (21%), and chronic obstructive pulmonary disease (16%). Of the decedents, 95,450 (38%) had no palliative care involvement, 98,849 (38%) received low involvement, and 60,341 (24%) received medium to high involvement. Controlling for age, sex, province and predicted hospital mortality risk at admission, the cost per day of a terminal hospitalization was: $1359 (95% CI 1323: 1397) (no involvement), $1175 (95% CI 1146: 1206) (low involvement), and $744 (95% CI 728: 760) (medium-high involvement). Conclusions Increased involvement of palliative care was associated with lower costs. Future research should explore whether this relationship holds for non-terminal hospitalizations, and whether palliative care in other settings impacts inpatient costs.

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