Meta-heuristic and Evolutionary Algorithms for Engineering Optimization

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 ...