SG-Portfolio Test Problems for Stochastic Multistage Linear Programming

1996 ◽  
pp. 102-107 ◽  
Author(s):  
K. Frauendorfer ◽  
F. Härtel ◽  
M. F. Reiff ◽  
M. Schürle
Keyword(s):  
Linear Programming ◽  
Test Problems ◽  
Multistage Linear Programming

ANALYSING THE IMPACT OF PENALTY CONSTANT ON PENALTY FUNCTION THROUGH PARTICE SWARM OPTIMIZATION

2018 ◽  
Vol 6 (2) ◽  
pp. 01-06
Author(s):  
Raju Prajapati ◽  
Om Prakash Dubey
Keyword(s):  
Linear Programming ◽  
Penalty Function ◽  
Inequality Constraint ◽  
Test Problems ◽  
Swarm Optimization ◽  
Non Linear Programming ◽  
Linear Programming Problems ◽  
The Impact ◽  
The Given ◽  
Computational Purpose

Non Linear Programming Problems (NLPP) are tedious to solve as compared to Linear Programming Problem (LPP).  The present paper is an attempt to analyze the impact of penalty constant over the penalty function, which is used to solve the NLPP with inequality constraint(s). The improved version of famous meta heuristic Particle Swarm Optimization (PSO) is used for this purpose. The scilab programming language is used for computational purpose. The impact of penalty constant is studied by considering five test problems. Different values of penalty constant are taken to prepare the unconstraint NLPP from the given constraint NLPP with inequality constraint. These different unconstraint NLPP is then solved by improved PSO, and the superior one is noted. It has been shown that, In all the five cases, the superior one is due to the higher penalty constant. The computational results for performance are shown in the respective sections.

Application of a New Penalty Function Method to Design Optimization

1977 ◽  
Vol 99 (1) ◽  
pp. 31-36 ◽  
Author(s):  
S. B. Schuldt ◽  
G. A. Gabriele ◽  
R. R. Root ◽  
E. Sandgren ◽  
K. M. Ragsdell
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Design Optimization ◽  
Penalty Function ◽  
Function Method ◽  
Test Problems ◽  
Penalty Function Method ◽  
Method Of Multipliers ◽  
Non Linear Programming ◽  
Linear Programming Problems

This paper presents Schuldt’s Method of Multipliers for nonlinear programming problems. The basics of this new exterior penalty function method are discussed with emphasis upon the ease of implementation. The merit of the technique for medium to large non-linear programming problems is evaluated, and demonstrated using the Eason and Fenton test problems.

Economic Load Dispatch Using Linear Programming

2016 ◽  
Vol 3 (1) ◽  
pp. 16-36 ◽  
Author(s):  
Ahmad A. Al-Subhi ◽  
Hesham K. Alfares
Keyword(s):  
Linear Programming ◽  
Linearization Method ◽  
Test Problems ◽  
Software Environment ◽  
Piecewise Linearization ◽  
Total Cost ◽  
On Line ◽  
Optimum Solution ◽  
The Impact ◽  
Linear Piecewise

This paper presents an optimum solution of the economic dispatch (ED) problem without considering transmission losses using linear programming (LP). In the ED problem, several on-line units (generators) are available, and it is needed to determine the power to produce by each unit in order to meet the required load at minimum total cost. To apply LP, the nonlinear cost functions of all generators are approximated by linear piecewise functions. To examine the effectiveness of this linearization method, a comprehensive set of benchmark test problems is used consisting of 3, 6, 18, 20, 38, and 40 generators. Using this set, LP solutions of linearized ED problems are compared with several other techniques available in the literature. The LP technique with piecewise linearization shows an overall competitive advantage in terms of total cost, solution time, and load satisfaction accuracy. The impact of varying the width of the linearized pieces (segments) is also discussed. All the computational analysis is performed using MATLAB software environment.

Linear Programming Based on Piece-Wise Linearization for Solving the Economic Load Dispatch Problem

2019 ◽  
pp. 20-50
Author(s):  
Ahmad Al-Subhi ◽  
Hesham K. Alfares
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Linearization Method ◽  
Solution Time ◽  
Test Problems ◽  
Economic Load Dispatch ◽  
Total Cost ◽  
Generation Cost ◽  
Cubic Function ◽  
Lp Solutions

This chapter discusses the application of linear programming (LP) techniques to find the optimal solution of the economic dispatch (ED) problem without considering transmission losses. The ED problem is concerned with optimizing the power generated by several generating units. The objective is to find the optimal power produced by each unit to supply the required load at minimum total cost. The generation cost associated with each unit is usually in the form of a quadratic or cubic function of the power produced. To apply LP, these nonlinear cost functions have to be linearized. The optimal solution is then determined by LP based on the approximate linear model. Piece-wise linearization methodology is adopted in this chapter. To evaluate the performance of the linearization method, a comprehensive set of benchmark test problems is used. LP solutions of linearized ED problems are compared with several other techniques from the literature. The LP technique with piece-wise linearization shows an overall competitive advantage in terms of total cost, solution time, and load satisfaction.

OPTIMIZATION PROBLEMS OF MODERNIZATION OF THE CAPACITY OF ARCS OF FAULT-TOLERANT NETWORKS

2021 ◽  
Vol 5 ◽  
pp. 5-20
Author(s):  
Petro Stetsyuk ◽  
◽  
Oleksii Lykhovyd ◽  
Volodymyr Zhydkov ◽  
Anton Suprun ◽  
...  
Keyword(s):  
Linear Programming ◽  
Mathematical Models ◽  
Optimization Problems ◽  
Fault Tolerant ◽  
Physical Structure ◽  
Decomposition Algorithm ◽  
Programming Models ◽  
Test Problems ◽  
Network Problem ◽  
Network Failures

Mathematical models of two classes of problems of modernization of the capacity of arcs of fault-tolerant oriented networks are considered. A network is considered to be fault-tolerant for which it is possible to satisfy all the demands for the transmission of flows when there will be one, but any failure, from all possible single network failures. For the first class of problems (problem A), all possible paths in the network can be used for the transmission of flows. For the second class of problems (problem P), only paths from a predetermined set of paths are used to transfer flows. Mathematical models are represented by linear, Boolean and nonlinear programming problems with a block structure of the constraint matrix.The material of the article is presented in five sections. The first section describes the concepts of a single failure and the scenario of network failures, the content of optimization problems A and P for modernization of capacity of arcs of a fault-tolerant network, a test network (6 vertices and 19 arcs) to test algorithms for solving the problems of modernization of fault-tolerant networks. In the second section, basic models of linear programming problems for finding the capacities of arcs of the fault-tolerant physical structure of a network (problem A) and the fault-tolerant logical structure of a network (problem P) are described, and their properties are considered. The third section describes problems A and P in the form of mixed Boolean linear programming models. Optimal solutions of problem A for various failure scenarios are given for the example of the test network. The solutions were found using the Gurobi program from the NEOS server, where the mathematical model of problem A is described in the AMPL modeling language.The fourth section describes nonlinear convex programming models for problems A and P, developed to find the optimal capacities of fault-tolerant networks according to the selected criterion, and a decomposition algorithm for their solution. The fifth section describes software in the FORTRAN programming language for the decomposition algorithm based on efficient implementations of Shor’s r-algorithms. The decomposition algorithm is compared with the IPOPT program based on the results of solving test problems.

Sign in / Sign up

Export Citation Format

Share Document