Keywords: genetic algorithms, multi-modal problems, niching strategy, differential evolution, reliability, convergence rate.

At present, genetic algorithms belong to the most modern and most popular optimization methods available. They follow an analogy of processes that occur in living nature within the evolution of live organisms during a period of many millions of years. Because in engineering and scientific problems we usually deal with the real-valued parameters, we focus on real-coded algorithms. A very well known real-coded evolutionary algorithm is the so-called differential evolution (DE) [1]. In [2], Hrstka and Kucerová have proposed an adaptation of the differential evolution called SADE algorithm (Simplified Atavistic Differential Evolution) with the aim of formulating a method which is able to solve optimization problems on real domains with a high number of variables. This algorithm uses the simplified differential operator, but contrary to the differential evolution, the SADE method uses the algorithmic scheme very similar to the standard genetic algorithm. A detailed comparison of these two algorithms with binary genetic algorithms is presented in [3].

During last few years some modifications and simplifications were proposed to the SADE algorithm with two principal motivations: (i) to increase the convergence rate of the algorithm for smooth objective functions with just one optimum and (ii) to reduce the number of control parameters of the algorithm. A new version called the GRADE algorithm has only three control parameters and results for the set of twenty mathematical functions has shown that for smooth objective functions with one or just several local extremes the GRADE algorithm achieved better convergence rate than the SADE algorithm.

Another enhancement to genetic algorithms was required to increase the reliability of these algorithms for multi-modal problems. A niching strategy [4] called CERAF (Abbreviation of the French expression CEntre RAdioactiF - the radioactivity center) method was proposed in [3] to mark previously found local extremes and restart the algorithm. Accordingly, it produces areas of a higher level of "radioactivity" in the neighborhood of all local extremes by increasing the mutation probability in these areas many times. Extensive test computations have shown that this methodology can be considered as a universal technique capable of solving any multi-modal optimization problem.

1

Storn R., Price K., "Differential Evolution : A simple and efficient adaptive scheme for global optimization over continuous spaces", Technical Report TR-95-012, University of Berkeley, 1995.

2

Hrstka O., Kucerová A., "Searching for optimization method on multidimensional real domains", In Contributions to Mechanics of Materials and Structures, CTU Reports, volume 4, pages 87-104, Czech Technical University in Prague, 2000.

3

Hrstka O., Kucerová A., "Improvements of real coded genetic algorithms based on differential operators preventing the premature convergence", Advances in Engineering Software, 35(3-4):237-246, 2004. doi:10.1016/S0965-9978(03)00113-3

4

Mahfoud S.W., "Niching methods for genetic algorithms", PhD thesis, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1995.

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