Capacitors placement in distribution systems with nonlinear load by using the variables’ inclusion and interchange algorithm

This work presents a substantial improvement of the variables’ inclusion and interchange algorithm (VIIA) for capacitors placement that considers circuits with harmonic distortion. Several load states are considered, and fixed and switched capacitors are employed in optimization. All the pertinent constraints of voltage magnitude, total harmonic distortion, individual harmonic distortion, and of overstress of capacitors are implemented. The here defined global harmonic-distortion index states the distance to the feasibility or the unfeasibility of a solution with respect the harmonic distortion constraints. The inclusion in the sequential quadratic programming sub-problem of an inequality linear constraint on this global harmonic-distortion index, allows the determining of solutions that comply with the harmonic distortion related constraints. A comparison of the solutions of various examples obtained by the presented method with the best solutions obtained by the Matlab’s genetic algorithm shows the effectiveness of this method.

Automated 3D Fixture Layout Design

This paper presents a new approach to the problem of fixture layout design for 3D workpieces. The approach is based on a concept of optimum experiment design, and the problem is treated as an optimal pursuit to select optimal locators from an initial collection of a large number of fixel locations on the surfaces of the given workpiece and to achieve form-closure for the part. An interchange algorithm is described, in which the fixture locators are generated sequentially first and are further improved. The algorithm uses the D-optimality criterion to minimize the workpiece positioning error. An example of a 3D workpiece is presented to illustrate the effectiveness of the proposed approach.

Analysis and Computational Schemes for p-Median Heuristics

This paper is concerned with solution procedures for the p-median problem: the well-established heuristic of Teitz and Bart, and the GRIA (Global/Regional Interchange Algorithm) technique developed more recently by Densham and Rushton. A computational scheme is presented which facilitates efficient implementations in both cases. The mathematical basis for the computational scheme is explained concisely by means of set-theory notation, and implementation of the Teitz—Bart heuristic is discussed with particular reference to search and storage considerations in large networks and in trees. In addition, it is shown that the two procedures in general do not terminate at solutions of equivalent local optimality.

A Methodology to Handle Inequality Constraints in an Interactve Design Process

The treatment of mechanical design as a constraint management problem has long been related to equality constraints. Work involving inequality constraints has been generally restricted to optimization and symbolic computation. This paper presents a methodology for handling inequality constraints in an interactive mechanical design process. The presented method is similar to the basis interchange algorithm used in the Generalized Reduced Gradient (GRG) method for constrained nonlinear optimization. The main difference is that our method relies on user guidance to select which specification has to be changed in order to satisfy the violated inequality constraint. Also, the specification is only adjusted; unlike the procedure in the GRG method where the basis is changed. An inequality constraint violation is detected whenever the corresponding slack variable becomes negative. An occurrence-matrix formulation is used to represent both the equality and inequality constraints that govern the design. The work is illustrated for the classical weldment design problem.