Deflection and Stretching Techniques for Detection of Multiple Minimizers in Multimodal Optimization Problems

Multimodal optimization refers to problems where the detection of many local or global minimizers is desirable. A number of methodologies have been developed in the past decades for this purpose. Deflection and stretching are two techniques that can be integrated with any optimization algorithm in order to detect multiple minimizers by properly transforming the objective function. Requiring only a minimal number of control parameters, both techniques have been used with metaheuristics as well as gradient-based optimization algorithms, enhancing their performance while demanding only minor implementation effort. Up until now their applications span various scientific fields, ranging from game theory and numerical optimization to astrophysics, computational intelligence, and medical informatics. The present chapter offers a comprehensive presentation of the two techniques and demonstrates their use through simple examples. Also, their latest developments and applications of the past two decades are concisely reviewed.