12. Chaos Embedded Metaheuristic Algorithms

In nature complex biological phenomena such as the collective behavior of birds, foraging activity of bees, or cooperative behavior of ants may result from relatively simple rules which however present nonlinear behavior being sensitive to initial conditions. Such systems are generally known as “deterministic nonlinear systems” and the corresponding theory as “chaos theory.” Thus real-world systems that may seem to be stochastic or random may present a nonlinear deterministic and chaotic behavior. Although chaos and random signals share the property of long-term unpredictable irregular behavior and many of random generators in programming softwares as well as the chaotic maps are deterministic; however chaos can help order to arise from disorder. Similarly, many metaheuristic optimization algorithms are inspired from biological systems where order arises from disorder. In these cases disorder often indicates both non-organized patterns and irregular behavior, whereas order is the result of self-organization and evolution and often arises from a disorder condition or from the presence of dissymmetries. Self-organization and evolution are two key factors of many metaheuristic optimization techniques. Due to these common properties between chaos and optimization algorithms, simultaneous use of these concepts can improve the performance of the optimization algorithms [1]. Seemingly the benefits of such combination are generic for other stochastic optimization, and experimental studies confirmed this although this has not mathematically been proven yet [2].