Clearing Maximum Height With Constrained Kinetic Energy

1985 ◽  
Vol 52 (1) ◽  
pp. 179-184 ◽  
Author(s):  
M. Hubbard ◽  
J. C. Trinkle
Keyword(s):  
Kinetic Energy ◽  
Ground Plane ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Optimization Techniques ◽  
Initial Kinetic Energy ◽  
Maximum Height ◽  
Nonlinear Constrained Optimization ◽  
Moving Body ◽  
Equality And Inequality Constraints

This paper addresses the question: In order to clear a given height, defined as that which is passed over by all points in the moving body, what is the minimum initial kinetic energy required and what are the other conditions that specify the solution completely? An expression is derived for the height cleared above an original supporting ground plane. This transcendental expression is maximized numerically subject to certain equality and inequality constraints using nonlinear constrained optimization techniques. The optimal solution includes the height cleared and the required control variables. The parameter space of body descriptors in which the optimal solution is presented decomposes into two regions in which the solutions differ qualitatively.

A Comparative Analysis on Economic Load Dispatch Problem Using Soft Computing Techniques

2020 ◽  
Vol 12 (2) ◽  
pp. 50-73 ◽  
Author(s):  
O.V. Singh ◽  
M. Singh
Keyword(s):  
Search Algorithm ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Optimization Techniques ◽  
Flower Pollination Algorithm ◽  
Economic Load Dispatch ◽  
Flower Pollination ◽  
Soft Computing Techniques ◽  
Equality And Inequality Constraints ◽  
Optimization Search

This article aims at solving economic load dispatch (ELD) problem using two algorithms. Here in this article, an implementation of Flower Pollination (FP) and the BAT Algorithm (BA) based optimization search algorithm method is applied. More than one objective is hoped to be achieve in this article. The combined economic emission dispatch (CEED) problem which considers environmental impacts as well as the cost is also solved using the two algorithms. Practical problems in economic dispatch (ED) include both nonsmooth cost functions having equality and inequality constraints which make it difficult to find the global optimal solution using any mathematical optimization. In this article, the ELD problem is expressed as a nonlinear constrained optimization problem which includes equality and inequality constraints. The attainability of the discussed methods is shown for four different systems with emission and without emission and the results achieved with FP and BAT algorithms are matched with other optimization techniques. The experimental results show that conferred Flower Pollination Algorithm (FPA) outlasts other techniques in finding better solutions proficiently in ELD problems.

scholarly journals Linear programming with inequality constraints via entropic perturbation

1996 ◽  
Vol 19 (1) ◽  
pp. 177-184 ◽  
Author(s):  
H.-S. Jacob Tsao ◽  
Shu-Cherng Fang
Keyword(s):  
Linear Inequality ◽  
Optimal Solution ◽  
Path Following ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Optimization Techniques ◽  
Linear Program ◽  
Programming Approach ◽  
Linear Programs ◽  
Dual Program

A dual convex programming approach to solving linear programs with inequality constraints through entropic perturbation is derived. The amount of perturbation required depends on the desired accuracy of the optimum. The dual program contains only non-positivity constraints. Anϵ-optimal solution to the linear program can be obtained effortlessly from the optimal solution of the dual program. Since cross-entropy minimization subject to linear inequality constraints is a special case of the perturbed linear program, the duality result becomes readily applicable. Many standard constrained optimization techniques can be specialized to solve the dual program. Such specializations, made possible by the simplicity of the constraints, significantly reduce the computational effort usually incurred by these methods. Immediate applications of the theory developed include an entropic path-following approach to solving linear semi-infinite programs with an infinite number of inequality constraints and the widely used entropy optimization models with linear inequality and/or equality constraints.

An optimal force distribution scheme for cooperating multiple robot manipulators

Robotica ◽  
1993 ◽  
Vol 11 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Yong Dal Shin ◽  
Myung Jin Chung
Keyword(s):  
Efficient Method ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Force Distribution ◽  
Weak Point ◽  
Contact Points ◽  
Optimal Force ◽  
Distribution Scheme ◽  
Equality And Inequality Constraints ◽  
Optimal Force Distribution

SUMMARYIn this paper, we suggest an optimal force distribution scheme by weak point force minimization and we also present an efficient method to solve the problem. The concept of a weak point is a generalized one which is applicable to any points of interest, as well as joints or contact points between end-effectors and an object. The problem is formulated by a quadratic objective function of the forces exerted at weak points subject to the linear equality and inequality constraints, and its optimal solution is obtained by an efficient method. As regards the solution of the problem, the original problem is reformulated to a reduced order dual problem after the equality constraints are eliminated by force decomposition.

scholarly journals Optimization-based approach to path planning for closed chain robot systems

2011 ◽  
Vol 21 (4) ◽  
pp. 659-670 ◽  
Author(s):  
Wojciech Szynkiewicz ◽  
Jacek Błaszczyk
Keyword(s):  
Path Planning ◽  
Large Scale ◽  
Inequality Constraints ◽  
Optimization Techniques ◽  
Planning Problem ◽  
Closed Chain ◽  
Robot Systems ◽  
Equality And Inequality Constraints ◽  
Primal Dual ◽  
The Given

Optimization-based approach to path planning for closed chain robot systems An application of advanced optimization techniques to solve the path planning problem for closed chain robot systems is proposed. The approach to path planning is formulated as a "quasi-dynamic" NonLinear Programming (NLP) problem with equality and inequality constraints in terms of the joint variables. The essence of the method is to find joint paths which satisfy the given constraints and minimize the proposed performance index. For numerical solution of the NLP problem, the IPOPT solver is used, which implements a nonlinear primal-dual interior-point method, one of the leading techniques for large-scale nonlinear optimization.

scholarly journals Existence of Local Saddle Points for a New Augmented Lagrangian Function

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Wenling Zhao ◽  
Jing Zhang ◽  
Jinchuan Zhou
Keyword(s):  
Augmented Lagrangian ◽  
Saddle Points ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Augmented Lagrangian Function ◽  
Lagrangian Functions ◽  
New Class ◽  
Close Relationship ◽  
Equality And Inequality Constraints ◽  
Local Optimal Solution

We give a new class of augmented Lagrangian functions for nonlinear programming problem with both equality and inequality constraints. The close relationship between local saddle points of this new augmented Lagrangian and local optimal solutions is discussed. In particular, we show that a local saddle point is a local optimal solution and the converse is also true under rather mild conditions.

scholarly journals OPTIMIZATION OF PIECEWISE NON-LINEAR MULTI CONSTRAINED ECONOMIC POWER DISPATCH PROBLEM USING AN IMPROVED GENETIC ALGORITHM

2010 ◽  
pp. 320-326
Author(s):  
B. Padmanabhan ◽  
R. S. SivaKumar ◽  
J. Jasper
Keyword(s):  
Genetic Algorithm ◽  
Power Systems ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Local Optimum ◽  
Improved Genetic Algorithm ◽  
Non Linear ◽  
Equality And Inequality Constraints ◽  
Loading Effects ◽  
Economic Power Dispatch

In this paper, a more realistic formulation of the Economic Dispatch problem is proposed, which considers practical constraints and non linear characteristics. The proposed ED formulation includes ramp rate limits, valve loading effects, equality and inequality constraints, which usually are found simultaneously in realistic power systems. This paper presents a novel Genetic Algorithm to solve the economic load dispatch (ELD) problem of thermal generators of a power system. This method provides an almost global optimal solution, since they don’t get stuck at local optimum. The proposed method and its variants are validated for the two test systems consisting of 3 and 10 thermal units whose incremental fuel cost functions takes into account the valve-point loading effects.

scholarly journals Improved Solutions for the Optimal Coordination of DOCRs Using Firefly Algorithm

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Muhammad Sulaiman ◽  
Waseem ◽  
Shakoor Muhammad ◽  
Asfandyar Khan
Keyword(s):  
Objective Function ◽  
Firefly Algorithm ◽  
Operating Time ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Nonlinear Constrained Optimization ◽  
Design Variables ◽  
Highly Nonlinear ◽  
Overcurrent Relays ◽  
Optimal Coordination

Nature-inspired optimization techniques are useful tools in electrical engineering problems to minimize or maximize an objective function. In this paper, we use the firefly algorithm to improve the optimal solution for the problem of directional overcurrent relays (DOCRs). It is a complex and highly nonlinear constrained optimization problem. In this problem, we have two types of design variables, which are variables for plug settings (PSs) and the time dial settings (TDSs) for each relay in the circuit. The objective function is to minimize the total operating time of all the basic relays to avoid unnecessary delays. We have considered four models in this paper which are IEEE (3-bus, 4-bus, 6-bus, and 8-bus) models. From the numerical results, it is obvious that the firefly algorithm with certain parameter settings performs better than the other state-of-the-art algorithms.

A novel method to solve sustainable economic power loading dispatch problem

2018 ◽  
Vol 118 (4) ◽  
pp. 806-827 ◽  
Author(s):  
Lingling Li ◽  
Yanfang Yang ◽  
Ming-Lang Tseng ◽  
Ching-Hsin Wang ◽  
Ming K. Lim
Keyword(s):  
Optimal Solution ◽  
Inequality Constraints ◽  
Fuel Cost ◽  
Swarm Optimization ◽  
Content Type ◽  
Intelligent Algorithms ◽  
Average Ratio ◽  
Equality And Inequality Constraints ◽  
Chicken Swarm Optimization ◽  
Better Than

Purpose The purpose of this paper is to deal with the economic requirements of power system loading dispatch and reduce the fuel cost of generation units. In order to optimize the scheduling of power load, an improved chicken swarm optimization (ICSO) is proposed to be adopted, for solving economic load dispatch (ELD) problem. Design/methodology/approach The ICSO increased the self-foraging factor to the chicks whose activities were the highest. And the evolutionary operations of chicks capturing the rooster food were increased. Therefore, these helped the ICSO to jump out of the local extreme traps and obtain the global optimal solution. In this study, the generation capacity of the generation unit is regarded as a variable, and the fuel cost is regarded as the objective function. The particle swarm optimization (PSO), chicken swarm optimization (CSO), and ICSO were used to optimize the fuel cost of three different test systems. Findings The result showed that the convergence speed, global search ability, and total fuel cost of the ICSO were better than those of PSO and CSO under different test systems. The non-linearity of the input and output of the generating unit satisfied the equality constraints; the average ratio of the optimal solution obtained by PSO, CSO, and ICSO was 1:0.999994:0.999988. The result also presented the equality and inequality constraints; the average ratio of the optimal solution was 1:0.997200:0.996033. The third test system took the non-linearity of the input and output of the generating unit that satisfied both equality and inequality constraints; the average ratio was 1:0.995968:0.993564. Practical implications This study realizes the whole fuel cost minimization in which various types of intelligent algorithms have been applied to the field of load economic scheduling. With the continuous evolution of intelligent algorithms, they save a lot of fuel cost for the ELD problem. Originality/value The ICSO is applied to solve the ELD problem. The quality of the optimal solution and the convergence speed of ICSO are better than that of CSO and PSO. Compared with PSO and CSO, ICSO can dispatch the generator more reasonably, thus saving the fuel cost. This will help the power sector to achieve greater economic benefits. Hence, the ICSO has good performance and significant effectiveness in solving the ELD problem.

scholarly journals Non-Convex Economic Dispatch with Prohibited Operating Zones through Gravitational Search Algorithm

2015 ◽  
Vol 5 (6) ◽  
pp. 1234
Author(s):  
Prakash Kumar Hota ◽  
Nakul Charan Sahu
Keyword(s):  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
New Approach ◽  
Prohibited Operating Zones ◽  
Optimal Power ◽  
Equality And Inequality Constraints ◽  
Simulation Results ◽  
Gravitational Search

This paper presents a new approach to the solution of optimal power generation for economic load dispatch (ELD) using gravitational search algorithm (GSA) when all the generators include valve point effects and some/all of the generators have prohibited operating zones. In this paper a gravitational search algorithm is suggested that deals with equality and inequality constraints in ELD problems. A constraint treatment mechanism is also discussed to accelerate the optimization process<strong>. </strong>To verify the robustness and superiority of the proposed GSA based approach, a practical sized 40-generators case with valve point effects and prohibited operating zones is considered. The simulation results reveal that the proposed GSA approach ensures convergence within an acceptable execution time and provides highly optimal solution as compared to the results obtained from well established heuristic optimization approaches.

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