Numerical Methods for Global Optimization

Evtushenko, Yu. G.; Потапов, М. А.; Korotkich, Victor

doi:10.1515/9781400862528.274

Cited by 8 publications

(3 citation statements)

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“…One mentions here some GOMs [26][27][28][29][30][31][32][33], namely, the clustering method which is a modification of the multistart method (here a careful selection of points of the local finding is made); the topographical method; the bisection (covering) and interval (branchand-bound) methods; the branch-and-bound strategy which divides the region of finding to a set of manydimensional cubes; the tunneling method (a principal deficiency of the method is a necessity to solve difficult nonlinear differential equations); the principal idea of the method of simulated annealing comes from the physics of the liquid freezing; the main idea of the evolutionary algorithms is taken from the biological evolution processes; the controlled random search algorithm which is a method of the direct search; trajectory methods, in particular, the continuation method.…”

Section: Existent Approaches To Solve the Global Optimization Problemsmentioning

confidence: 99%

Transient in a two-DOF nonlinear system

2007

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Dynamics of a system containing a linear oscillator, linearly coupled to an essentially nonlinear attachment, is considered. A damping is taken into account. It is assumed that some initial excitation implies vibrations of the linear oscillator. Envelops of the subsystem's kinetic energies are selected to use the numerical investigation of transient in the system. The parametrical optimization approach is used to obtain regions of effective energy transfer in the system parameter space. It is demonstrated that this efficient energy transfer may be obtained for a rather small value of the attachment mass.

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Section: Existent Approaches To Solve the Global Optimization Problemsmentioning

confidence: 99%

Transient in a two-DOF nonlinear system

2007

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“…Covering methods (Evtushenko et al 1992, Baritompa and Cutler 1994) are reliable since, to the extent they work, they have built-in guarantees of solution quality.…”

Section: Global Optimization Methodsmentioning

confidence: 99%

“…Covering methods detect sub regions not containing the global maximum, and exclude them from further consideration. Covering methods provide guarantee of solution quality, and approximate the global solution by iteratively using tighter bounds (Evtushenko et al 1992, Hansen 1992, Moore et al 1992, Horst and Tuy 2003. Obtaining a solution with guaranteed accuracy implies an exhaustive search of the solution space for the global maximum.…”

Section: A Covering Methodsmentioning

confidence: 99%