A Review of Deterministic Optimization Methods in Engineering and Management

Ming-Hua Lin,Jung-Fa Tsai,Chian-Son Yu

doi:10.1155/2012/756023

Abstract

With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed. The approaches developed for treating optimization problems can be classified into deterministic and heuristic. This paper aims to introduce recent advances in deterministic methods for solving signomial programming problems and mixed‐integer nonlinear programming problems. A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods.

Highlights

The field of optimization has grown rapidly during the past few decades
We investigate the advances in deterministic global optimization of nonconvex nonlinear programming NLP problems and nonconvex mixed-integer nonlinear programming MINLP problems
Deterministic approaches take advantage of analytical properties of the problem to generate a sequence of points that converge to a global solution, heuristic approaches have been found to be more flexible and efficient than deterministic approaches

Summary

Introduction

The field of optimization has grown rapidly during the past few decades. Many new theoretical, algorithmic, and computational contributions of optimization have been proposed to solve various problems in engineering and management. Pardalos and Romeijn provided a more complete and broad spectrum of approaches including deterministic and heuristic techniques for dealing with global optimization problems. Floudas et al presented an overview of the research progress in optimization during 1998–2003, including the deterministic global optimization advances in mixed-integer nonlinear programming and related applications. Pinter illustrated the applicability of global optimization modeling techniques and solution strategies to real-world problems such as agroecosystem management, assembly line design, bioinformatics, biophysics, cellular mobile network design, chemical product design, composite structure design, controller design for induction motors, electrical engineering design, feeding strategies in animal husbandry, the inverse position problem in kinematics, laser design, radiotherapy planning, robot design, and satellite data analysis. We investigate the advances in deterministic global optimization of nonconvex nonlinear programming NLP problems and nonconvex mixed-integer nonlinear programming MINLP problems.

Signomial Programming

Mixed-Integer Nonlinear Programming

Conclusions