13 Modern Methods of Optimization

13.1 Introduction

In recent years, some optimization methods that are conceptually different from the traditional mathematical programming techniques have been developed. These methods are labeled as modern or nontraditional methods of optimization. Most of these methods are based on certain characteristics and behavior of biological, molecular, swarm of insects, and neurobiological systems. The following methods are described in this chapter:

  1. Genetic algorithms
  2. Simulated annealing
  3. Particle swarm optimization
  4. Ant colony optimization
  5. Fuzzy optimization
  6. Neural‐network‐based methods

Most of these methods have been developed only in recent years and are emerging as popular methods for the solution of complex engineering problems. Most require only the function values (and not the derivatives). The genetic algorithms are based on the principles of natural genetics and natural selection. Simulated annealing is based on the simulation of thermal annealing of critically heated solids. Both genetic algorithms and simulated annealing are stochastic methods that can find the global minimum with a high probability and are naturally applicable for the solution of discrete optimization problems. The particle swarm optimization is based on the behavior of a colony of living things, such as a swarm of insects, a flock of birds, or a school of fish. Ant colony optimization (ACO) is based on the cooperative behavior of real ant colonies, which are ...

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