Z. C. YU ET AL.

Copyright © 2013 SciRes. CN

And v stands for the speed of transfer. Then the trans-

fer time

among attractions can be counted by:

(2)

3.2. Optimization Objective

1) The first goal: traveling days

Traveling days are relatively large unit of time in con-

sideration, which is the most direct measure of the route

arrangement. Not only related to the time of trans-fer

among attractions, but also it is connected to the order of

visiting. Differen t attractions have differ ent visiting time,

thus reasonable arrangement will make the days shorter

and better.

Travel order to set the dwell time for each attraction,

different specified time with the number of days, rea-

sonable attractions with the number of travel days w ill be

optimized.

2) The second goal: time spent on roads

This time stands for the one spent on roads, that is to

say the transfer time among attractions. When the travel-

ing days are the same, the less time spent on roads the

better results it obtains.

3) Model of traveling routes Setting

max

min

s.t. ,

,

.

cp

zT

yt

TT

tab

mm

=

=

≤

+≤

≤

(3)

Suppose the limited time of traveling days is

.

While

stands for the visiting time of attraction,

shows the limited time of traveling every day. The jour-

ney cost is

, and the money expected is

.

4. Design for Improved Ant Colony

Algorithm

4.1. Design for the Max-Min Ant Colony

Algorithm

As the basic Ant Colony Algorithm for the shortest path,

the search often falls into local optimal solution, that is to

say after searching for a long time, the solutions found by

all individuals are exactly the same. Thus the process

will break off, which lead to the consequence that it may

not be able to find the global optimal solution. So we

take the Max-Min Ant Colony Algorithm into considera-

tion. This algorithm owns the maximum and minimum

values of the pheromone concentration in case of the big

gap between the relative concentration resulting in the

early ending of searching. Besides, the Max-Min Ant Co-

lony Algorithm has been proved by Stutzle for the best

effect [6].

Referring to the studies of Dorigo [7-14], the parame-

ter adjustment can be summarized as follows: The phe-

romone concentration

, the number of

ants

is twice as the number of attractions. And the

pheromone residues

are 0.7. Besides, the importance

of pheromone

and the inspired factor

change

within the whole iteration process. The degree of phero-

mone is bigger in the later period, while the inspired fac-

tor in the former period.

4.2. The Adjustment of Inspired Factor

Basic Ant Colony Algorithm inspired factor is set as

. And

stands for the transfer time between the

two attractions

and

. In this way, however, the dis-

tance between the hotel and attractions is not taken into

account. In fact, the distance is too important to ignore.

Besides, regarding the traveling route setting problem as

a TSP simply is unable to find the shortest time arranged

attractions combination. So we consider making the in-

spired factor in the Ant Colony Algorithm adjusted by

the method of dynamic distance. The calculating of in-

spired factor is divided into two conditions:

11

ac

ac ac

ac ac

if Qtb

ddd

else dd

+>

= +

=

(4)

Suppose

is the cumulative time between the hotel

and the attraction

and

stands for the visiting time

of attraction

. The inspired factor of attraction

and

can be counted by the Equation (4).

Summarized by the testing process, the adjustment of

desired factor makes great contribution to the optimiza-

tion. But there are still some problems like unreasonable

routes establish ed. This situation can be explained as fol-

lows.

The dashed line indicates the general algorithm route:

from A to O and then from O to B and C till back to O.

And the solid line shows the improved algorithm route:

from A to C and O, and then from O to B and O. It has

been four hours when reaching point A, which means

that there are only two points left. For sake of the time

limit, the improved algorithm will let C in, but the dis-

tance on roads will increase. Besides, the two choices are

same in total days.

Therefore, in such conditions, it is useless to take the

improved algorithm. Maybe the optimal solution will be

ignored.

4.3. The Adjustment of Searching Ways

According to the defects of inspired factor’s adjustment,

we can classify the searching ants into two parts. One

group searches the solution by general algorithm, and the

other by improved algorithm. Thus, we can compare the