New trends in optimization

Approaches used to solve optimization tasks generated in problems of control, planning, designing and management have completely changed during recent years. Cases with unimodal, convex, differentiable scalar goal functions have disappeared from research labs, because a lot of satisfactory efficient methods were developed. On the battle square there have remained hard cases: multimodal, multi-criteria, non-differentiable, NP-hard, discrete, with huge dimensionality. These practical tasks, generated by industry and market, have caused serious troubles in seeking global optimum. Main reasons of these troubles are recognized as: huge cardinality of local extremes frequently with the exponential number of extremes; curse of dimensionality; NP-hardness; lack of differentiability. Unfortunately, known “classical” exact solution methods have considered as rather weak in so hard conditions of the work. From the beginning of eighties have been observed fast development of approximate methods, resistant to local extremes. In fact, practice of these methods antecede development of the suitable theory, which has been formed usually 10–15 years later than the time moment of creating the approach. That´s why we observe now more than 20 different approaches inspired by Nature and more than 30 if we include parallel computing environments. The paper presents critical survey of methods, approaches and trends observed in modern optimization, focusing on nature-inspired techniques recommended for particularly hard problems. Applicability of the methods, depending the class of stated optimization task and classes of goal function, have been discussed. Numerical as well theoretical properties of these algorithms are shown. Newest our own very efficient proposals are also provided.