Entropy maximization model for the trip distribution problem with fuzzy and random parameters

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.

[1]  Tony E. Smith,et al.  General representation theorems for efficient population behavior , 1990 .

[2]  Baoding Liu,et al.  Chance constrained programming with fuzzy parameters , 1998, Fuzzy Sets Syst..

[3]  Shu-Cherng Fang,et al.  Linearly-Constrained Entropy Maximization Problem with Quadratic Cost and Its Applications to Transportation Planning Problems , 1995, Transp. Sci..

[4]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[5]  R. M. Oliver,et al.  Flows in transportation networks , 1972 .

[6]  Å. Hallefjord,et al.  GRAVITY MODELS WITH MULTIPLE OBJECTIVES. THEORY AND APPLICATIONS , 1986 .

[7]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[8]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[9]  Ziyou Gao,et al.  Train Timetable Problem on a Single-Line Railway With Fuzzy Passenger Demand , 2009, IEEE Transactions on Fuzzy Systems.

[10]  Baoding Liu,et al.  A note on chance constrained programming with fuzzy coefficients , 1998, Fuzzy Sets Syst..

[11]  J. A. Tomlin,et al.  A Mathematical Programming Model for the Combined Distribution-Assignment of Traffic , 1971 .

[12]  Xiang Li,et al.  A Sufficient and Necessary Condition for Credibility Measures , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[13]  Alan Wilson,et al.  A statistical theory of spatial distribution models , 1967 .

[14]  Xiang Li,et al.  Chance measure for hybrid events with fuzziness and randomness , 2009, Soft Comput..

[15]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[16]  Lixing Yang,et al.  Fuzzy fixed charge solid transportation problem and algorithm , 2007, Appl. Soft Comput..

[17]  Baoding Liu,et al.  A survey of credibility theory , 2006, Fuzzy Optim. Decis. Mak..

[18]  A. G. Wilson,et al.  The Use of the Concept of Entropy in System Modelling , 1970 .