Meta-heuristic and Evolutionary Algorithms for Engineering Optimization

Omid Bozorg-Haddad, Mohammad Solgi, Hugo A. Loáiciga

• Éditeur: Wiley
• Année: 2017
• ISBN:
  9781119387060
• Édition: 1
• Sujet: Mathématiques
• Sous-sujet: Mathématiques discrètes

A detailed review of a wide range of meta-heuristic and evolutionary algorithms in a systematic manner and how they relate to engineering optimization problems

This book introduces the main metaheuristic algorithms and their applications in optimization. It describes 20 leading meta-heuristic and evolutionary algorithms and presents discussions and assessments of their performance in solving optimization problems from several fields of engineering. The book features clear and concise principles and presents detailed descriptions of leading methods such as the pattern search (PS) algorithm, the genetic algorithm (GA), the simulated annealing (SA) algorithm, the Tabu search (TS) algorithm, the ant colony optimization (ACO), and the particle swarm optimization (PSO) technique.

Chapter 1 of Meta-heuristic and Evolutionary Algorithms for Engineering Optimization provides an overview of optimization and defines it by presenting examples of optimization problems in different engineering domains. Chapter 2 presents an introduction to meta-heuristic and evolutionary algorithms and links them to engineering problems. Chapters 3 to 22 are each devoted to a separate algorithm— and they each start with a brief literature review of the development of the algorithm, and its applications to engineering problems. The principles, steps, and execution of the algorithms are described in detail, and a pseudo code of the algorithm is presented, which serves as a guideline for coding the algorithm to solve specific applications. This book:

• Introduces state-of-the-art metaheuristic algorithms and their applications to engineering optimization;
• Fills a gap in the current literature by compiling and explaining the various meta-heuristic and evolutionary algorithms in a clear and systematic manner;
• Provides a step-by-step presentation of each algorithm and guidelines for practical implementation and coding of algorithms;
• Discusses and assesses the performance of metaheuristic algorithms in multiple problems from many fields of engineering;
• Relates optimization algorithms to engineering problems employing a unifying approach.

Meta-heuristic and Evolutionary Algorithms for Engineering Optimization is a reference intended for students, engineers, researchers, and instructors in the fields of industrial engineering, operations research, optimization/mathematics, engineering optimization, and computer science.

OMID BOZORG-HADDAD, PhD, is Professor in the Department of Irrigation and Reclamation Engineering at the University of Tehran, Iran.

MOHAMMAD SOLGI, M.Sc., is Teacher Assistant for M.Sc. courses at the University of Tehran, Iran.

HUGO A. LOÁICIGA, PhD, is Professor in the Department of Geography at the University of California, Santa Barbara, United States of America.

1
Overview of Optimization

Summary

This chapter defines optimization and its basic concepts. It provides examples of various engineering optimization problems.

1.1 Optimization

Engineers are commonly confronted with the tasks of designing and operating systems to meet or surpass specified goals while meeting numerous constraints imposed on the design and operation. Optimization is the organized search for such designs and operating modes. It determines the set of actions or elements that must be implemented to achieve optimized systems. In the simplest case, optimization seeks the maximum or minimum value of an objective function corresponding to variables defined in a feasible range or space. More generally, optimization is the search of the set of variables that produces the best values of one or more objective functions while complying with multiple constraints. A single‐objective optimization model embodies several mathematical expressions including an objective function and constraints as follows:

(1.1)

subject to

(1.2 )

(1.3 )

in which f(X) = the objective function; X = a set of decision variables x_i that constitutes a possible solution to the optimization problem; x_i = ith decision variable; N = the number of decision variables that determines the dimension of the optimization problem; g_j(X) = jth constraint; b_j = constant of the jth constraint; m = the total number of constraints;

= the lower bound of the ith decision variable; and

= the upper bound of the ith decision variable.

1.1.1 Objective Function

The objective function constitutes the goal of an optimization problem. That goal could be maximized or minimized by choosing variables, or decision variables, that satisfy all problem constraints. The desirability of a set of variables as a possible solution to an optimization problem is measured by the value of objective function corresponding to a set of variables.

Some of the algorithms reviewed in this book are explained with optimization problems that involve maximizing the objective function. Others do so with optimization problems that minimize the objective function. It is useful to keep in mind that a maximization (or minimization) problem can be readily converted, if desired, to a minimization (or maximization) problem by multiplying its objective function by −1.

1.1.2 Decision Variables

The decision variables determine the value of the objective function. In each optimization problem we search for the decision variables that yield the best value of the objective function or optimum.

In some optimization pro...