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)
Entropy maximization model for the trip distribution problem with fuzzy and random parameters. (English) Zbl 1207.90017
Summary: Many trip distribution problems can be modeled as entropy maximization models with quadratic cost constraints. In this paper, the travel costs per unit flow between different zones are assumed to be given fuzzy variables and the trip productions at origins and trip attractions at destinations are assumed to be given random variables. For this case, an entropy maximization model with chance constraint is proposed, and is proved to be convex. In order to solve this model, fuzzy simulation, stochastic simulation and a genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, a numerical example is presented to demonstrate the application of the model and the algorithm.
MSC:
90B06Transportation, logistics
90C70Fuzzy programming
90C59Approximation methods and heuristics
References:
[1]Erlander, S.; Smith, T.: General representation theorems for efficient population behaviour, Applied mathematics and computation 36, 173-217 (1990) · Zbl 0718.92027 · doi:10.1016/0096-3003(90)90012-R
[2]J. Murchland, Some remarks on the gravity model of traffic distribution and equivalent maximizing formulations, LSE-TNT-38, Transport Network Theory Unit, London Graduate School of Business, London, England, 1966.
[3]Wilson, A. G.: A statistical theory of spatial distribution models, Transportation research 1, 253-269 (1967)
[4]Wilson, A. G.: The use of concept of entropy in system modelling, Operational research quarterly 21, 247-265 (1970) · Zbl 0193.20103 · doi:10.1057/jors.1970.48
[5]Tomlin, J.: A mathematical programming model for the combined distribution-assignment of traffic, Transportation science 5, 123-140 (1971)
[6]Fang, S. C.; Tsao, H.: Linear constrained entropy maximization problem with quadratic cost and its application to transportation planning problems, Transportation science 29, 353-365 (1995) · Zbl 0853.90090 · doi:10.1287/trsc.29.4.353
[7]Hallefjord, A.; Jörnsten, K.: Gravity models with multiple objectives-theory and applications, Transportation research, part B: methodol 20, 19-39 (1984)
[8]Roliver, R. Potts: Flows in transportation networks, (1972)
[9]Willumsen, L. G.: Modelling transport, (1990)
[10]Li, X.; Liu, B.: Chance measure for hybrid events with fuzziness and randomness, Soft computing 13, No. 2, 105-115 (2009) · Zbl 1172.28304 · doi:10.1007/s00500-008-0308-x
[11]Zadeh, L.: Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems 1, 3-28 (1978) · Zbl 0377.04002 · doi:10.1016/0165-0114(78)90029-5
[12]Zadeh, L.: A theory of approximate reasoning, Mathematical frontiers of the social and policy sciences, 69-129 (1979)
[13]Liu, B.; Liu, Y. K.: Expected value of fuzzy variable and fuzzy expected value models, IEEE transactions on fuzzy systems 10, No. 4, 445-450 (2002)
[14]Liu, B.: Uncertainty theory, (2007)
[15]Li, X.; Liu, B.: A sufficient and necessary condition for credibility measures, International journal of uncertainty, fuzziness knowledge-based systems 14, No. 5, 527-535 (2006)
[16]Yang, L.; Li, K.; Gao, Z.: Train timetable problem on a single-line railway with fuzzy passenger demand, IEEE transactions on fuzzy systems 17, No. 3, 617-629 (2009)
[17]Yang, L.; Liu, L.: Fuzzy fixed charge solid transportation problem and algorithm, Applied soft computing 7, No. 3, 879-889 (2007)
[18]Liu, B.: A survey of credibility theory, Fuzzy optimization and decision making 5, No. 4, 387-408 (2006)
[19]Liu, B.; Iwamura, K.: Chance constrained programming with fuzzy parameters, Fuzzy sets and systems 94, No. 2, 227-237 (1998) · Zbl 0923.90141 · doi:10.1016/S0165-0114(96)00236-9
[20]Liu, B.; Iwamura, K.: A note on chance constrained programming with fuzzy coefficients, Fuzzy sets and systems 100, No. 1–3, 229-233 (1998) · Zbl 0948.90156 · doi:10.1016/S0165-0114(97)00291-1