Abstract
One of the most commonly encountered approaches for the solution of unconstrained global optimization problems is the application of multi-start algorithms. These algorithms usually combine already computed minimizers and previously selected initial points, to generate new starting points, at which, local search methods are applied to detect new minimizers. Multi-start algorithms are usually terminated once a stochastic criterion is satisfied. In this paper, the operators of the Differential Evolution algorithm are employed to generate the starting points of a global optimization method with dynamic search trajectories. Results for various well-known and widely used test functions are reported, supporting the claim that the proposed approach improves drastically the performance of the algorithm, in terms of the total number of function evaluations required to reach a global minimizer.
Similar content being viewed by others
References
L.C.W. Dixon, J. Gomulka and G.P. Szegö, Reflections on the global pptimization problem, in: Optimization in Action, ed. L.C.W. Dixon, 1975, pp. 29–54.
A.O. Griewank, Generalized descent for global optimization, J. Optim. Theory Appl. 34 (1981) 11–39.
R. Horst, P.M. Pardalos and N.V. Thoai, Introduction to Global Optimization (Kluwer Academic, Dordrecht, 1995).
A. Levy, A. Montalvo and S. Gomez, Topics in Global Optimization (Springer, Berlin, 1981).
Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer, Berlin, 1999).
J.J. More, B.S. Garbow and K.E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software 7(1) (1981) 17–41.
K.E. Parsopoulos, V.P. Plagianakos, G.D. Magoulas and M.N. Vrahatis, Objective function “stretching” to alleviate convergence to local minima, Nonlinear Anal. TMA 47(5) (2001) 3419–3424.
K.E. Parsopoulos and M.N. Vrahatis, Modification of the particle swarm optimizer for locating all the global minima, in: Artificial Neural Networks and Genetic Algorithms, eds. V. Kurkova et al. (Springer, Berlin, 2001) pp. 324–327.
K.E. Parsopoulos and M.N. Vrahatis, Recent approaches to global optimization problems through particle swarm optimization, Natural Computing 1(2/3) (2002) 235–306.
V.P. Plagianakos and M.N. Vrahatis, Parallel evolutionary training algorithms for “hardware-friendly” neural networks, Natural Computing 1(2/3) (2001) 307–322.
H.-P. Schwefel, Evolution and Optimum Seeking (Wiley, New York, 1995).
J.A. Snyman, A new and dynamic method for unconstrained minimization, Appl. Math. Modelling 6 (1982) 449–462.
J.A. Snyman and L.P. Fatti, A multi-start global minimization algorithm with dynamic search trajectories, J. Optim. Theory Appl. 54(1) (1987) 121–141.
R. Storn, Sytem design by constraint adaptation and differential evolution, IEEE Trans. Evolutionary Comput. 3(1) (1999) 22–34.
R. Storn and K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces, J. Global Optimization 11 (1997) 341–359.
A. Törn and A. Žilinskas, Global Optimization (Springer, Berlin, 1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Laskari, E., Parsopoulos, K. & Vrahatis, M. Evolutionary Operators in Global Optimization with Dynamic Search Trajectories. Numerical Algorithms 34, 393–403 (2003). https://doi.org/10.1023/B:NUMA.0000005405.78681.a1
Issue Date:
DOI: https://doi.org/10.1023/B:NUMA.0000005405.78681.a1