双层规划的两个例子

kuli

The multi-class, multi-criteria traffic network equilibrium and systems optimum problem
It is well known that in the standard traffic network equilibrium model with a single value of time (VOT)
for all users, a so-called marginal-cost toll can drive a user equilibrium flow pattern to a system optimum.
This result holds when either cost (money) or time units are used in expressing the objective function of the
system optimum and the criterion for user equilibrium. This paper examines the multi-criteria or the costversus-
time network equilibrium and system optimum problem in a network with a discrete set of VOTs for
several user classes. Specifically, the following questions are investigated: Are the user-optimal flows dependent
upon the unit (time or money) used in measuring the travel disutility in the presence of road pricing?
Are there any uniform link tolls across all individuals (link tolls that are identical for all user classes) that can
support a multi-class user equilibrium flow pattern as a system optimum when the system objective function
is measured by either money or time units? What are the general properties of the valid toll set?

2003 Elsevier Ltd. All rights reserved.

MODELING PRIVATE HIGHWAY IN NETWORKS WITH ENTRY-EXIT BASED TOLL CHARGES
Previous studies on private highways generally involve network equilibrium models with
link-specific and hence link additive toll charges. In reality, toll charge for private highways
depends on the entry and exit points that is not always link additive. This study formulates
and solves the optimal toll design problem of private highways with entry-exit based toll
charges using a bilevel programming approach. The lower-level traffic equilibrium problem
with entry-exit based toll charge is still formulated as an optimization problem and the Frank-
Wolfe algorithm is adapted for finding its solution, where the descent direction-finding subproblem
(all-or-nothing traffic assignment) is solved via a simple network transformation.
The proposed method circumvents the difficulty of path enumeration or generation
frequently involved in general non-additive traffic assignment problem and hence has the
potential of efficiently solving large network problems. With the exploration of the properties
of the lower-level traffic equilibrium sub-problem, the bilevel optimal toll design problem is
solved by the efficient marginal function approach developed recently.

砳砳858

第二题的看看或许有用

砳砳858

b题的看看或许有用。

二重积分

看看或许有用

zhouxinge

可以的，加油！！！