zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Multiobjective differential evolution algorithm with multiple trial vectors. (English) Zbl 1253.90205
Summary: This paper presents a multiobjective differential evolution algorithm with multiple trial vectors. For each individual in the population, three trial individuals are produced by the mutation operator. The offspring is produced by using the crossover operator on the three trial individuals. Good individuals are selected from the parent and the offspring and then are put in the intermediate population. Finally, the intermediate population is sorted according to the Pareto dominance relations and the crowding distance, and then the outstanding individuals are selected as the next evolutionary population. Comparing with the classical multiobjective optimization algorithm NSGA-II, the proposed algorithm has better convergence, and the obtained Pareto optimal solutions have better diversity.

MSC:
90C29Multi-objective programming; goal programming
90C59Approximation methods and heuristics
Software:
SPEA2
WorldCat.org
Full Text: DOI
References:
[1] N. Srinivas and K. Deb, “Multi-objective optimization using non-dominated sorting in genetic algorithms,” Evolutionary Computation, vol. 2, no. 3, pp. 221-248, 1994.
[2] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, 2002. · doi:10.1109/4235.996017
[3] E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257-271, 1999.
[4] E. Zitzler, M. Laumanns, and L. Thiele, “SPEA2: improving the strength Pareto evolutionary algorithm,” Tech. Rep. 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Zurich, Switzerland, 2001.
[5] R. Storn and K. Price, “Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341-359, 1997. · Zbl 0888.90135 · doi:10.1023/A:1008202821328
[6] H. A. Abbass, R. Sarker, and C. Newton, “PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems,” in Proceedings of the Congress on Evolutionary Computation (CEC’01), pp. 971-978, May 2001.
[7] H. A. Abbass, “PDE: the self-adaptive Pareto differential evolution algorithm,” in Proceedings of the Congress on Evolutionary Computation (CEC’02), vol. 1, pp. 831-836, IEEE Service Center, Piscataway, NJ, USA, 2002.
[8] N. K. Madavan, “Multi-objective optimization using a Pareto differential evolution approach,” in Proceedings of the Congress on Evolutionary Computation (CEC’02), vol. 2, pp. 1145-1150, IEEE Service Center, Piscataway, NJ, USA, 2002.
[9] F. Xue, A.C. Sanderson, and R.J. Graves, “Pareto-based multi-objective differential evolution,” in Proceedings of the Congress on Evolutionary Computation (CEC’03), vol. 2, pp. 862-869, IEEE Press, Canberra, Australia, 2003.
[10] T. Robi and B. Filipi, “DEMO: differential evolution for multi- objective optimization,” in Lecture Notes in Computer Science, pp. 520-533, Springe, Berlin, Germany, 2005. · Zbl 1109.68633
[11] W. Qian and A. li, “Adaptive differential evolution algorithm for multiobjective optimization problems,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 431-440, 2008. · Zbl 1148.65042 · doi:10.1016/j.amc.2007.12.052
[12] W. Gong and Z. Cai, “An improved multiobjective differential evolution based on Pareto-adaptive \epsilon -dominance and orthogonal design,” European Journal of Operational Research, vol. 198, no. 2, pp. 576-601, 2009. · Zbl 1163.90732 · doi:10.1016/j.ejor.2008.09.022