Optimization for Engineering Problems

1Review of some Constrained Optimization Schemes

With rapid breakthroughs in the metaheuristic optimization methods in recent times, applications of conventional optimization solution techniques have been reduced. However, in some cases, where the computational issues are of major concern, these standard schemes are still in use. Modification to these core approaches can be appropriately incorporated to handle them more effectively. This chapter summarizes the existing important constrained optimization schemes. Many engineering problems are usually multi-objective in nature. Even though several solution approaches are available; a unified method is always preferred to solve such problems. This chapter will review some direct solution schemes including complex search, random search and method of feasible directions, and their performance in terms of accuracy, computational requirements and time at par with commonly used modern heuristic algorithms.

1.1. Introduction

In computer-aided design (CAD), optimization plays an important role. Optimization problems arise in many areas of engineering, including product design and operational control. Unit cells of atoms in metals and alloys, honeycomb structures and genetic operations are some examples of optimized systems in real life. Depending on the objective function and constraints, different types of optimization problems often arise. After Cauchy invented the gradient concept of a function in 1847, several other researchers, ...