scholarly journals From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Akemi Gálvez ◽  
Andrés Iglesias
Keyword(s):  
Convex Optimization ◽  
Nonlinear Optimization ◽  
Firefly Algorithm ◽  
Optimization Problem ◽  
Continuous Optimization ◽  
Optimization Techniques ◽  
Continuous Variables ◽  
Indirect Approach ◽  
Nonlinear Optimization Problem ◽  
Cad Cam

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

scholarly journals Firefly Algorithm for Polynomial Bézier Surface Parameterization

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Akemi Gálvez ◽  
Andrés Iglesias
Keyword(s):  
Computer Animation ◽  
Computer Aided Design ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Well Being ◽  
Optimization Techniques ◽  
Surface Parameterization ◽  
Cad Cam ◽  
Data Points

A classical issue in many applied fields is to obtain an approximating surface to a given set of data points. This problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very often, the preferred approximating surface is polynomial, usually described in parametric form. This leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very difficult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. This paper solves the parameterization problem for polynomial Bézier surfaces by applying the firefly algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address difficult optimization problems. The method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy.

Schedule-Constrained Demand Management in Two-Region Urban Networks

2021 ◽  
Author(s):  
Sakitha Kumarage ◽  
Mehmet Yildirimoglu ◽  
Mohsen Ramezani ◽  
Zuduo Zheng
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Time Window ◽  
Demand Management ◽  
Urban Traffic ◽  
Fundamental Diagram ◽  
Constrained System ◽  
Nonlinear Optimization Problem ◽  
Management Platform ◽  
User Compliance

Demand management aiming to optimize system cost while ensuring user compliance in an urban traffic network is a challenging task. This paper introduces a cooperative demand redistribution strategy to optimize network performance through the retiming of departure times within a limited time window. The proposed model minimizes the total time spent in a two-region urban network by incurring minimal disruption to travelers’ departure schedules. Two traffic models based on the macroscopic fundamental diagram (MFD) are jointly implemented to redistribute demand and analyze travelers’ reaction. First, we establish equilibrium conditions via a day-to-day assignment process, which allows travelers to find their preferred departure times. The trip-based MFD model that incorporates individual traveler attributes is implemented in the day-to-day assignment, and it is conjugated with a network-level detour ratio model to incorporate the effect of congestion in individual traveler route choice. This allows us to consider travelers with individual preferences on departure times influenced by desired arrival times, trip lengths, and earliness and lateness costs. Second, we develop a nonlinear optimization problem to minimize the total time spent considering both observed and unobserved demand—that is, travelers opting in and out of the demand management platform. The accumulation-based MFD model that builds on aggregated system representation is implemented as part of the constraints in the nonlinear optimization problem. The results confirm the resourcefulness of the model to address complex two-region traffic dynamics and to increase overall performance by reaching a constrained system optimum scenario while ensuring the applicability at both full and partial user compliance conditions.

scholarly journals Design of SkSP-R Variables Sampling Plans

2015 ◽  
Vol 38 (2) ◽  
pp. 413-429 ◽  
Author(s):  
Muhammad Aslam ◽  
Saminathan Balamurali ◽  
Chi-Hyuck Jun ◽  
Batool Hussain
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Sampling Plan ◽  
Producer’S Risk ◽  
Sample Number ◽  
Sampling Plans ◽  
Average Sample Number ◽  
Nonlinear Optimization Problem ◽  
Better Than ◽  
Average Sample

In this paper, we present the designing of the skip-lot sampling plan including the re-inspection  called SkSP-R. The plan parameters of the proposed plan are determined through a  nonlinear optimization problem by minimizing the average sample number satisfying both the producer's risk and the consumer's risks. The proposed plan is shown to perform better than the existing sampling plans in terms of the average sample number. The application of the proposed plan is explained with the help of illustrative examples.

Modeling and Identification of a Class of Servomechanism Systems With Stick-Slip Friction

1988 ◽  
Vol 110 (3) ◽  
pp. 324-328 ◽  
Author(s):  
Ka C. Cheok ◽  
Hongxing Hu ◽  
Nan K. Loh
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Optimization Procedure ◽  
Simplex Algorithm ◽  
Identification Algorithm ◽  
Stick Slip ◽  
Process Identification ◽  
Nonlinear Optimization Problem ◽  
System Parameters ◽  
Input Signals

This paper describes a technique for modeling and identifying a class of nonlinear servomechanism systems with stick-slip friction. The physics of the stick-slip friction is considered in modeling the process. Identification of the system parameters is formulated as a nonlinear optimization problem. A modified simplex algorithm is proposed as the optimization procedure. The difficulties encountered in choosing identification algorithm and input signals for the problem are discussed. A simulation example of a servomotor system is provided.

OO-Based STATCOM Installation for Power System Loading Margin Improvement

2013 ◽  
Vol 284-287 ◽  
pp. 1087-1093 ◽  
Author(s):  
Ya Chin Chang ◽  
Rung Fang Chang
Keyword(s):  
Power Systems ◽  
Power System ◽  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Transmission System ◽  
Exact Method ◽  
Ordinal Optimization ◽  
Static Synchronous Compensator ◽  
Nonlinear Optimization Problem ◽  
Voltage Instability

As electricity demands and power transactions continuously increase, it becomes vulnerable to voltage instability for power systems, generally incurred by over-utilized facilities or any contingency. The transmission system loading margin (LM) enhancement problem with Static Synchronous Compensator (STATCOM) installation can be formulated as a mixed discrete-continuous nonlinear optimization problem (MDCP); due to the complexity of the MDCP, the computing burden might be very heavy. In the paper, the proposed ordinal optimization (OO) based STATCOM installation method is applied to the MDCP to solve for good enough solutions rather than the best solution, so as to largely reduce the computation burden. In the method, the crude method is first used to solve the MDCP and, based on OO theory, the exact method is then used to determine the good enough solutions. Finally, the good enough solution, as uses the fewest STATCOM device units for installation and makes the power system able to provide the required LM, is recommended for network reinforcement.

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