This chapter presents the Nelder–Mead simplex method and the Broyden– Fletcher–Goldfarb–Shanno (BFGS) method for finite-element-model updating. The methods presented have been tested on a simple beam and an unsymmetrical H-shaped structure. It was noted that, on average, the Nelder–Mead simplex method gives more accurate results than did the BFGS method. This is mainly because the BFGS method r...

A variety of pivot column selection rules based upon the gradient criteria (including the steepest edge) have been explored to improve the efficiency of the primal simplex method. Simplex-like algorithms have been proposed imbedding the gradient direction (GD) which includes all variables whose increase or decrease leads to an improvement in the objective function. Recently a frame work has bee...

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the dual simplex method with the most negative pivoting rule for LP. The bound is comparable with the bound given by Kitahara and Mizuno (2010) for the primal simplex method. We apply the result to the maximum flow problem and get a strong polynomial bound.

One of the main obstacles in applying genetic algorithms (GA's) to complex problems has been the high computational cost due to their slow convergence rate. We encountered such a difficulty in our attempt to use the classical GA for estimating parameters of a metabolic model. To alleviate this difficulty, we developed a hybrid approach that combines a GA with a stochastic variant of the simplex...

We investigate the problem of finding the first basic solution in the simplex algorithm. A modification of two phases simplex method is presented and its implementation in programming language Visual Basic is described. A few Netlib examples are presented.

Transportation problem is a linear programming which considers minimum cost for shipping a product from some origins to other destinations such as from factories to warehouse, or from a warehouse to supermarkets. To solve this problem simplex algorithmis utilized. In real projects costs and the value of supply and demands are fuzzy numbers and it is expected that optimal solutions for determini...

In the mid-1960s, two English statisticians working at the National Vegetable Research Station invented the Nelder–Mead “simplex” direct search method. The method emerged at a propitious time, when there was great and growing interest in computer solution of complex nonlinear real-world optimization problems. Because obtaining first derivatives of the function f to be optimized was frequently i...

-A new feasible direction method for linear programming problems is presented. The method is not boundary following. The method proceeds from a feasible interior point in a direction that improves the objective function until a point on a constraint surface is met. At this point searches are initiated in the hyperplane of constant function value by using projections of the bounding constraints ...

GRADIENT ION CHROMATOGRAPHY WAS USED FOR THE SEPARATION OF EIGHT SUGARS: arabitol, cellobiose, fructose, fucose, lactulose, melibiose, N-acetyl-D-glucosamine, and raffinose. The separation method was optimized using a combination of simplex or genetic algorithm with the isocratic-to-gradient retention modeling. Both the simplex and genetic algorithms provided well separated chromatograms in a s...

The paper presents an approach for avoiding and minimizing the complementary pivots in a simplex based solution method for a quadratic programming problem. The linearization of the problem is slightly changed so that the simplex or interior point methods can solve with full speed. This is a big advantage as a complementary pivot algorithm will take roughly eight times as longer time to solve a ...