Primer interfaced algorithm for non-linear optimization of engineering systems

Abstract

Majority of engineering system designs are deemed to be optimization problems with unknown multiple variables that are more than the known information and data. Several numerical algorithms have been evolved in the past half a decade in an attempt to improve the accuracy of results. The aim of this paper is to provide a perfect solver for the non-linear, single objective, and multi-variable optimization problems. The algorithm termed primer interfaced algorithm for non-linear optimization (PIANO) is a resolved solution methodology based on Hegde's primer value theorem. The methodology is formulated and developed by computing a primer adapter, which is interfaced with coefficient of the terms of constraints and objective functions to arrive at the decision vector. To demonstrate the procedure, two problems from the mechanics of structure are considered as exercises. The results are compared with the results recently published in the literature. The chosen examples for the optimization are a four bar truss and a simply supported beam with uniformly distributed load. The results of PIANO are compared with the results of fuzzy dynamic programming, and crisp optimal solutions are reported in the literature. The authors are sure of absolute contained perfection in the application of PIANO. To the authors' understanding, PIANO is original, new, and different.