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A niche hybrid genetic algorithm for global optimization of continuous multimodal functions. (English) Zbl 1062.65065

Summary: A niche hybrid genetic algorithm (NHGA) is proposed to solve continuous multimodal optimization problems more efficiently, accurately and reliably. It provides a new architecture of hybrid algorithms, which organically merges the niche techniques and Nelder-Mead’s simplex method into genetic algorithms (GAs). In the new architecture, the simplex search is first performed in the potential niches, which likely contain a global optimum, to locate the promising zones within search space, quickly and reliably. Then another simplex search is used to quickly discover the global optimum in the located promising zones.

The proposed method not only makes the exploration capabilities of GAs stronger through niche techniques, but also has more powerful exploitation capabilities by using simplex search. So it effectively alleviates premature convergence and improves weak exploitation capacities of GAs. A set of benchmark functions is used to demonstrate the validity of NHGA and the role of every component of NHGA. Numerical experiments show that the NHGA may, efficiently and reliably, obtain a more accurate global optimum for the complex and high-dimension multimodal optimization problems. It also demonstrates that the new hybrid architecture is potential and can be used to generate more potential hybrid algorithms.

65K05Mathematical programming (numerical methods)
90C29Multi-objective programming; goal programming
90C30Nonlinear programming