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)
Omni-optimizer: a generic evolutionary algorithm for single and multi-objective optimization. (English) Zbl 1146.90509
Summary: Due to the vagaries of optimization problems encountered in practice, users resort to different algorithms for solving different optimization problems. In this paper, we suggest and evaluate an optimization procedure which specializes in solving a wide variety of optimization problems. The proposed algorithm is designed as a generic multi-objective, multi-optima optimizer. Care has been taken while designing the algorithm such that it automatically degenerates to efficient algorithms for solving other simpler optimization problems, such as single-objective uni-optimal problems, single-objective multi-optima problems and multi-objective uni-optimal problems. The efficacy of the proposed algorithm in solving various problems is demonstrated on a number of test problems chosen from the literature. Because of its efficiency in handling different types of problems with equal ease, this algorithm should find increasing use in real-world optimization problems.

90C29Multi-objective programming; goal programming
90C59Approximation methods and heuristics
Full Text: DOI
[1] Deb, K.; Tiwari, S.: Omni-optimizer: A procedure for single and multi-objective optimization, Lecture notes on computer science 3410, 41-65 (2005)
[2] Deb, K.: Optimization for engineering design: algorithms and examples, (1995)
[3] Ehrgott, M.: Multicriteria optimization, (2000) · Zbl 0956.90039
[4] Miettinen, K.: Nonlinear multiobjective optimization, (1999) · Zbl 0949.90082
[5] Sensor, Y.: Pareto optimality in multi-objective problems, Applied mathematics and optimization 4, No. 1, 41-59 (1977)
[6] D. Whitley. The GENITOR algorithm and selection pressure: Why rank-based allocation of reproductive trials is best, in: Proceedings of the Third International Conference on Genetic Algorithms, 1989, pp. 116 -- 121.
[7] L.J. Eshelman. The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic recombination, in: Proceedings of the Foundations of Genetic Algorithms 1 (FOGA-1), 1991, pp. 265 -- 283.
[8] Deb, K.; Anand, A.; Joshi, D.: A computationally efficient evolutionary algorithm for real-parameter optimization, Evolutionary computation journal 10, No. 4, 371-395 (2002)
[9] T.T. Binh, U. Korn, MOBES: A multiobjective evolution strategy for constrained optimization problems, in: Proceedings of the Third International Conference on Genetic Algorithms (Mendel 97), 1997, pp. 176 -- 182.
[10] Knowles, J. D.; Corne, D. W.: Approximating the non-dominated front using the Pareto archived evolution strategy, Evolutionary computation journal 8, No. 2, 149-172 (2000)
[11] Zitzler, E.; Laumanns, M.; Thiele, L.: SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization, Evolutionary methods for design optimization and control with applications to industrial problems, Athens, Greece, 2001, 95-100 (2001)
[12] Srinivas, N.; Deb, K.: Multi-objective function optimization using non-dominated sorting genetic algorithms, Evolutionary computation journal 2, No. 3, 221-248 (1994)
[13] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA -- II, IEEE transactions on evolutionary computation 6, No. 2, 182-197 (2002)
[14] K. Deb, M. Mohan, S. Mishra, Towards a quick computation of well-spread pareto-optimal solutions, in: Proceedings of the Second Evolutionary Multi-Criterion Optimization (EMO-03) Conference (LNCS 2632), 2003, pp. 222 -- 236. · Zbl 1036.90525 · http://link.springer.de/link/service/series/0558/bibs/2632/26320222.htm
[15] D.E. Goldberg, J. Richardson, Genetic algorithms with sharing for multimodal function optimization, in: Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 1987, pp. 41 -- 49.
[16] A. Pétrowski, A clearing procedure as a niching method for genetic algorithms. in: Proceedings of the IEEE Third International Conference on Evolutionary Computation (ICEC’96), 1996, pp. 798 -- 803.
[17] F. Vavak and T.C. Fogarty. Comparison of steady state and generational genetic algorithms for use in nonstationary environments, in: Proceedings of IEEE Conference on Evolutionary Computation, Nagoya, Japan, 20 -- 22 May 1996, pp. 192 -- 195.
[18] Goldberg, D. E.: Genetic algorithms for search, optimization, and machine learning, (1989) · Zbl 0721.68056
[19] Holland, J. H.: Adaptation in natural and artificial systems, (1975) · Zbl 0317.68006
[20] Deb, K.; Agrawal, R. B.: Simulated binary crossover for continuous search space, Complex systems 9, No. 2, 115-148 (1995) · Zbl 0843.68023
[21] Kita, H.; Ono, I.; Kobayashi, S.: The multi-parent unimodal normal distribution crossover for real-coded genetic algorithms, (1998)
[22] Deb, K.: Multi-objective optimization using evolutionary algorithms, (2001) · Zbl 0970.90091
[23] Cruse, T. R.: Reliability-based mechanical design, (1997)
[24] Deb, K.: An efficient constraint handling method for genetic algorithms, Computer methods in applied mechanics and engineering 186, No. 2-4, 311-338 (2000) · Zbl 1028.90533 · doi:10.1016/S0045-7825(99)00389-8
[25] Deb, K.; Goyal, M.: A combined genetic adaptive search (geneas) for engineering design, Computer science and informatics 26, No. 4, 30-45 (1996)
[26] Deb, K.; Mohan, M.; Mishra, S.: Evaluating the &z.epsi;-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions, Evolutionary computation journal 13, No. 4, 501-525 (2005)
[27] Deb, K.; Agrawal, S.; Pratap, A.; Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE transactions on evolutionary computation 6, No. 2, 182-197 (2002)
[28] Hoffmeister, F.; Sprave, J.: Problem-independent handling of constraints by use of metric penalty functions, Proceedings of the fifth annual conference on evolutionary programming, 289-294 (1996)
[29] Schwefel, H. -P.: Evolution and optimum seeking, (1995)
[30] Ho, S. -Y.; Shu, L. -S.; Chen, J. -H.: Intelligent evolutionary algorithms for large parameter optimization problems, IEEE transactions on evolutionary computation 8, No. 6, 522-541 (2004)
[31] K. Deb, Genetic Algorithms in Multi-modal Function Optimization, Master’s thesis, University of Alabama, Tuscaloosa, AL, 1989.
[32] K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, Scalable multi-objective optimization test problems, in: Proceedings of the Congress on Evolutionary Computation (CEC-2002), 2002, pp. 825 -- 830.
[33] Zitzler, E.; Thiele, L.: Multiobjective optimization using evolutionary algorithms -- a comparative case study, Parallel problem solving from nature V (PPSN-V), 292-301 (1998)
[34] Wolpert, D. H.; Macready, W. G.: No free lunch theorems for optimization, IEEE transactions on evolutionary computation 1, No. 1, 67-82 (1977)