Engineering Design by Geometric Programming

Abstract

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions, where all functions are of signomial form. The importance of GP comes from two relatively recent developments: (i) new methods can solve even large-scale GP extremely efficiently and reliably; (ii) a number of practical problems have recently been found to be equivalent to or approximated by GP. This study proposes an optimization approach for solving GP. Our approach is first to convert all signomial terms in GP into convex and concave terms. Then the concave terms are further treated with the proposed piecewise linearization method where only ⌈log 2 (− 1)⌉ binary variables are used. It has the following features: (i) it offers more convenient and efficient means of expressing a piecewise linear function; (ii) fewer 0-1 variables are used; (iii) the computational results show that the proposed method is much more efficient and faster than the conventional one, especially when the number of break points becomes large. In addition, the engineering design problems are illustrated to evaluate the usefulness of the proposed methods.

Design Optimization of a Speed Reducer Using Deterministic Techniques

“…Tosserams et al [10] and Lu and Kim [11] obtained optimal solutions with higher errors and higher objective values than those of the proposed method. Although Ku et al [6], Lin et al [18], and Huang [20] obtained optimal solutions with lower objective values than those of the proposed method, the errors in constraint in these three methods are higher than those in the proposed method. Compared with the solutions of Akhtar et al [7], Rao and Xiong [8], Cagnina et al [9], Jaberipour and Khorram [2], and Li and Papalambros [5], the proposed method results in a lower objective value under the same feasibility tolerance 10 −6 .…”

“…Lu [19] proposed a convexification transformation method (beta method) based on the concept of 1-convex functions to improve the efficiency of solving generalized geometric programming problems. Huang [20] proposed…”

A Single-valued Pentagonal Neutrosophic Geometric Programming Approach to Optimize Decision Maker’s Satisfaction Level

“…In today's world the significance of mathematical optimization and decision making can be explored in various fields [1][2][3][4][5]. Geometric Programming (GP) is a technique in the field of mathematical optimization and multi-objective decision making that is considered a significant optimization problem consisting of objective functions and constraints composed of monomials or posynomials that are designed to solve realworld engineering problems by generating feasible outcomes [6]. The basics of GP were initially introduced in a book by Duffin, Petersen and Zener [7], and afterward its improved and extended applications can be seen in various fields.…”