Geography Reference
In-Depth Information
subject to
DT
opp
k
j
DT
_min
DT
_min
0
ˇ
ˇ
ˇ
ˇ
ˇ
ˇ
ˇ
ˇ
ˇ
ˇ
ˇ
ˇ
1
desire
_
DT
opp
k
j
;p
i
@
A
D
.
time
_
of
_
day
/ exp
(7.18)
added
_T
opp
k
j
;p
i
D
alternative_
time
opp
k
j
;p
i
travel
_
time
opp
k
j
;p
i
(7.19)
opp
k
j
2
TVNBP
.O .p
i
/;D.p
i
/;T .p
i
//
(7.20)
where
p
i
is person
i
,
P
is a set of people who would like to participate jointly,
opp
k
j
is the critical activity opportunity
k
j
available to
p
i
,
K
is a critical activity
opportunity set constrained by TVNBP of
p
i
,and
path
_
dist
opp
k
j
;p
i
represents
the travel distance over the space-time path for critical activity opportunity
opp
k
j
.
Similarly,
travel
_
time
opp
k
j
;p
i
indicates the travel time for this corresponding
critical activity opportunity
opp
k
j
,and
desire
_
DT
opp
k
j
;p
i
represents partic-
ipation desirability by time of day. Equation
7.18
defines the desirability for
person
p
i
to participate in critical activity opportunity
opp
k
j
and (
time
_
of
_
day
)
is a parameter indicating the degree of satisfaction of time-of-day requirements.
DT
_ min is the minimum expected participation activity time of this person,
alternative_time
opp
k
j
;p
i
represents the added travel time for an alternative
space-time path over the shortest space-time path for critical activity opportunity
opp
k
j
in this prism, and added_T
opp
k
j
;p
i
is the added travel time for alternative
space-time paths over the shortest space-time path. Equations
7.13
,
7.14
,
7.15
,
7.16
,and
7.17
constitute the objective function of the optimization problem for
scheduling joint activities for multiple persons. They involve: (i) minimizing travel
distance; (ii) minimizing travel time; (iii) maximizing expected participation activity
time; (iv) minimizing the added travel time relative to alternative space-time paths;
and (v) maximizing the utility index of the selected critical activity opportunity.
Unlike the approach proposed by Fang et al. (
2011
), this modified problem is solved
by limiting the search space using critical activity opportunities.
The proposed approach uses the (NSGA-II) nondominated sorting genetic
algorithm (Deb et al.
2002
) to solve this multi-objective optimization problem.
Detailed descriptions of NSGA-II can be found in Deb et al. (
2002
) and Murugan
et al. (
2009
). The pseudocode for the algorithm as implemented is given in Fig.
7.4
.
The selection operation is based on tournament selection (Murugan et al.
2009
).
The crossover operation is based on a single-point crossover scheme (Hájek et al.
2010
). The mutation operator is the same as that of the standard genetic algorithm.
The operation space of selection, recombination, and mutation in this algorithm
is limited within the critical activity opportunities of the dynamic transportation
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