Abstract: There are two major variants of the Simplex
Algorithm: the revised method and the standard, or tableau method.
Today, all serious implementations are based on the revised method
because it is more efficient for sparse linear programming problems.
Moreover, there are a number of applications that lead to dense linear
problems so our aim in this paper is to present some computational
results on parallel implementation of dense Simplex Method. Our
implementation is implemented on a SMP cluster using C
programming language and the Message Passing Interface MPI.
Preliminary computational results on randomly generated dense
linear programs support our results.
Abstract: The present work encounters the solution of the defect identification problem with the use of an evolutionary algorithm combined with a simplex method. In more details, a Matlab implementation of Genetic Algorithms is combined with a Simplex method in order to lead to the successful identification of the defect. The influence of the location and the orientation of the depressed ellipsoidal flaw was investigated as well as the use of different amount of static data in the cost function. The results were evaluated according to the ability of the simplex method to locate the global optimum in each test case. In this way, a clear impression regarding the performance of the novel combination of the optimization algorithms, and the influence of the geometrical parameters of the flaw in defect identification problems was obtained.
Abstract: Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.
Abstract: Overcurrent (OC) relays are the major protection
devices in a distribution system. The operating time of the OC relays
are to be coordinated properly to avoid the mal-operation of the
backup relays. The OC relay time coordination in ring fed
distribution networks is a highly constrained optimization problem
which can be stated as a linear programming problem (LPP). The
purpose is to find an optimum relay setting to minimize the time of
operation of relays and at the same time, to keep the relays properly
coordinated to avoid the mal-operation of relays.
This paper presents two phase simplex method for optimum time
coordination of OC relays. The method is based on the simplex
algorithm which is used to find optimum solution of LPP. The
method introduces artificial variables to get an initial basic feasible
solution (IBFS). Artificial variables are removed using iterative
process of first phase which minimizes the auxiliary objective
function. The second phase minimizes the original objective function
and gives the optimum time coordination of OC relays.
Abstract: The fuzzy set theory has been applied in many fields,
such as operations research, control theory, and management
sciences, etc. In particular, an application of this theory in decision
making problems is linear programming problems with fuzzy
numbers. In this study, we present a new method for solving fuzzy
number linear programming problems, by use of linear ranking
function. In fact, our method is similar to simplex method that was
used for solving linear programming problems in crisp environment
before.