Abstract
Nearly all work on the optimal design of networks has been confined to single objective optimal design. Less attention has been paid to multi-objective optimal design where one must simultaneously optimize precision, reliability and other quantities. This paper discusses the concept of multi-objective optimal second order design of networks and its properties, which proves very different from that of single objective optimal design. To demonstrate its applications, a levelling network located in an earthquake area in the north east of China is taken as an example. The result shows in this case that multi-objective optimal design is optimal from the point of view of total objectives.
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F. CROSILLA: A criterion matrix for the second order design of control networks. Bulletin Géodésique, No. 3, pp. 226–239, 1983.
F. CROSILLA: A criterion matrix for deforming networks by multifactorial techniques, in Optimization and design of geodetic network edited by Grafarend and Sansò. Springer-Verlag Berlin Heidelberg New York Tokyo, pp. 429–435, 1985.
F. CROSILLA and C. MARCHESINI: Realization of the second order design by modelling the environmental and instrument error sources in distance measurements. Manuscripta geodaetica, Vol. 13, No. 4, pp. 210–217, 1988.
P.A. CROSS: Numerical methods in network design, in Optimization and design of geodetic networks edited by Grafarend and Sansò. Springer-Verlag Berlin Heidelberg New York Tokyo, pp. 132–168, 1985.
P.A. CROSS and K. THAPA: The optimal design of levelling networks. Survey Review, Vol. XXV, No. 192, pp. 68–79, 1979.
E.W. GRAFAREND: Criterion matrices for deforming networks, in Optimization and design of geodetic networks edited by Grafarend ans Sansò. Springer-Verlag Berlin Heidelberg New York Tokyo, pp. 363–428, 1985.
E.W. GRAFAREND and B. SCHAFFRIN: Kriterion Matrizen I–Zweidimensional homogene und isotrope geodätische Netze. ZfV, No. 4, pp. 133–149, 1979.
E.W. GRAFARENO, F. KRUMM and B. SCHAFFRIN: Kriterion Matrizen III–Zweidimensionale homogene und isotrope geodätische Netze. ZfV, No. 5, pp. 197–207, 1986.
E.W. GRAFAREND et al.: Optimierung geodatischer Messoperationen. Herbert Wichmann Verlag Karlsruhe, 1979.
D.M. HIMMELBLAU: Applied nonlinear programming. McGraw-Hill Book Company, New York, 1972.
R. JAGER: Analyse und Optimierung geodätischer Netze nach spektralen Kriterion und mechanische Analogien. Dissertation, AVN, 6/88. 1988.
H. KALTENBACH and G. SCHMITT: A new approach for criterion matrices based on graph theory. Manuscripta geodaetica. Vol. 13, No. 5, pp. 296–305, 1988. K.R. KOCH: Optimization of the configuration of geodetic networks. Int. Syrup. on geodetic networks and computations, DGK, Reihe B, Heft NrInt. Syrup. on geodetic networks and computations, DGK, Reihe B, Heft Nr. 258:111, pp. 82–89. 1982.
H. MULLER: A numerically efficient solution of the second order design problem. Bulletin Géodésique, No. 1, pp. 85–99, 1984.
H. MULLER: Second order design of combined linear angular geodetic networks. Bulletin Géodésique, No. 4, pp. 316–331, 1985.
The People's University of China: Introduction to operations research. The People' University Press of China, 1987.
A. SARHIDAI: Design of fundamental gravity networks based on theapproximation of the given variance-covariance matrix. Bulletin Géodésique, No. 4, pp. 355–376, 1986.
Y. SAWARAGI, H. NAKAYAMA and T. TANINO: Theory of multi-objective optimization. Academic Press, Inc. Orlando San Diego New York London Toronto Montreal Sydney Tokyo, 1985.
B. SCHAFFRIN: Aspects of network design, in optimization and design of geodetic networks edited by Grafarend and Sansò. Springer-Verlag Berlin Heidelberg New York Tokyo, pp. 548–597, 1985.
B. SCHAFFRIN and E.W. GRAFAREND: Kriterion Matrizen II — Zweidimensionale homogene und isotrope geod~tische Netze. ZfV, Tell Ila, No. 5, pp. 183-194 Tell lib, No. 11, pp. 485— 493, 1982.
G. SCHMITT: A review of network designs, criteria, risk, functions and design ordering, in Optimization and design of geodetic networks edited by Grafarend and Sansò. Springer-Verlag Berlin Heidelberg New York Tokyo, pp. 6–10, 1985.
G. SCHMITT: Second order design of a free distance network, considering different types of criterion matrices. Bulletin Géodésique, No. 54, pp. 531–543, 1980.
W.D. SCHUH: Quich computation of geodetic networks using special properties of the eigenvalues, in Optimization and design of geodetic networks edited by Grafarend and Sansò. Springer-Verlag Berlin Heidelberg New York Tokyo, pp. 185–195, 1985.
R.A. SNAY: Network design strategies applicable to GPS surveys using series three or four receivers. Bulletin Géodésique, No. 1, pp. 37–50, 1986.
J. VAN MIERLO: Second order design: precision and reliability aspectsSecond order design: precision and reliability aspects. AVN, pp. 95–101, 1981.
H. WIMMER: Second order design of geodetic networks by an iterative approximation of a given criterion matrix. Int. Syrup. on geodetic networks and computations, DGK, Reihe B, Heft Nr. 258/111, pp. 112–127, 1982.
H. WIMMER: Ein Beitrag zur Gewichtoptimierung geodetischer Netze. DGK, C 269, Munich, 1981.
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Peiliang, X. Multi-objective optimal second order design of networks. Bull. Geodesique 63, 297–308 (1989). https://doi.org/10.1007/BF02520478
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DOI: https://doi.org/10.1007/BF02520478