zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
An application of swarm optimization to nonlinear programming. (English) Zbl 1127.90407
Summary: Particle swarm optimization (PSO) is an optimization technique based on population, which has similarities to other evolutionary algorithms. It is initialized with a population of random solutions and searches for optima by updating generations. Particle swarm optimization has become the hotspot of evolutionary computation because of its excellent performance and simple implementation. After introducing the basic principle of the PSO, a particle swarm optimization algorithm embedded with constraint fitness priority-based ranking method is proposed in this paper to solve nonlinear programming problem. By designing the fitness function and constraints-handling method, the proposed PSO can evolve with a dynamic neighborhood and varied inertia weighted value to find the global optimum. The results from this preliminary investigation are quite promising and show that this algorithm is reliable and applicable to almost all of the problems in multiple-dimensional, nonlinear and complex constrained programming. It is proved to be efficient and robust by testing some example and benchmarks of the constrained nonlinear programming problems.

90C30Nonlinear programming
90C59Approximation methods and heuristics
Full Text: DOI
[1] Bazarra, M. S.; Shetty, L. M.: Nonlinear programming: theory and algorithms. 373-378 (1979)
[2] Fung, R. Y. K.; Tang, J. F.; Wang, D.: Extension of a hybrid genetic algorithm for nonlinear programming problems with equality and inequality constraints. Computers and operations research 29, 261-274 (2002) · Zbl 1091.90085
[3] Li, Y.; Gen, M.: Non-linear mixed integer programming problems using genetic algorithm and penalty function. Proceedings of 1996 IEEE int. Conf. on SMC, 2677-2682 (1996)
[4] Takao, Y.; Gen, M.; Takeaki, T.; Li, Y.: A method for interval 0--1 number non-linear programming problems using genetic algorithm. Computers and industrial engineering 29, 531-535 (1995)
[5] Tang, J. F.; Wang, D.: A hybrid genetic algorithm for a type of nonlinear programming problem. Computers math. Applic. 36, No. 5, 11-21 (1998) · Zbl 0941.90068
[6] Su, J.; Hu, A.; He, Z.: Solving a kind of nonlinear programming problems via analog neural networks. Neurocomputing 18, 1-9 (1998)
[7] Wang, Z. L.; Qiu, L.; Fu, Q.; Liang, C.: Application of chaos optimization algorithm to nonlinear constrained programming (in chinese). Journal of north China institute of water conservancy and hydroelectric power 23, No. 2, 1-3 (2002)
[8] Dorigo, M.; Maniezzo, V.; Colori, A.: Ant system: optimization by a colony of cooperating agents. IEEE trans on system, man, and cybernetics 26, No. 1, 28-41 (1996)
[9] Yan, L. X.; Ma, D.: Global optimization of non-convex nonlinear programs using line-up competition algorithm. Computers and chemical engineering 25, 1601-1610 (2001)
[10] Glover, F.: Genetic algorithm and tabu search: hybrid for optimizations. Computers and operations research 22, 111-134 (1995) · Zbl 0813.90093
[11] Lin, T. C.: Applying the genetic approach to simulated annealing in solving some NP-hard problems. IEEE trans. On SMC 23, 1752-1766 (1993)
[12] Ostermark, R.: Solving a nonlinear non-convex trim loss problem with a genetic hybrid algorithm. Computers and operations research 26, 623-635 (1999) · Zbl 0933.90048
[13] Kennedy, J.; Eberhart, R.: Particle swarm optimization. Proc. IEEE int. Conf. on neural networks (1995)
[14] Eberhart, R.; Kennedy, J.: A new optimizer using particle swarm theory. Proc. 6th int. Symposium on micro machine and human science (1995)
[15] Shi, Y.; Eberhart, R.: A modified particle swarm optimizer. Proc. IEEE int. Conf. on evolutionary computation, 69-73 (1998)
[16] Kennedy, J.; Spears, W. M.: Matching algorithms to problems: an experimental tests of the particle swarm and some genetic algorithms on the multimodal problem generator. Proc IEEE int conf on evolutionary computation, 78-83 (1998)
[17] Xie, X. F.; Zhang, W. J.; Ruan, J.; Yang, Z. L.: Genetic algorithm for constrained nonlinear programming problems (in chinese). Computer engineering and application 21, 64-67 (2002)
[18] Back, T.: Evolutionary algorithms in theory and practice. (1996)
[19] Liu, B. D.; Zhao, R.: Stochastic programming and fuzzy programming (in chinese). 26-33 (2001)
[20] Tang, J. F.; Yung, K. L.; Ip, A. W. H.: Heuristics-based integrated decision for logistic networks systems. Journal of manufacturing systems 23, No. 1, 1-13 (2004)
[21] Millonas, M. M.: Swarms, phase transition, and collective intelligence. Artificial life III (1994)
[22] Suganthan, P. N.: Particle swarm optimizer with neighbourhood operator [A]. Proc of the congress on evolutionary computation [C], 1958-1962 (1999)
[23] Shi, Y. F.; Eberhart, R.: Parameter selection in particle swarm optimization. Proc. of the 7th annual conf. On evolutionary programming, 591-600 (1998)