Route Optimization Algorithm and Solution for Web ... - Science Direct

Available online at www.sciencedirect.com

Systems Engineering Procedia 5 (2012) 427 – 436

Route Optimization Algorithm and Solution for Web Service Engineering Luo youlong*,Nie guihua Wuhan University of Technology,Luo Shi Road,Wuhan ,430070

Abstract Many modern service systems rely on a network of hub facilities to help concentrate flows of freight or passengers to exploit the economies of scale in transportation. Whereas ,the possible defect that bypass cost caused by hub or intermedia seem unvoided. This paper employs a novel optimal hub-and-spoke network based decision approach which unite “bypass cost “ and “congestion effect” effectively,presents a algorithm in time effect compared with tradional algorithm, sets up a computational work which performed on a personal computer with data for postal operations in Sydney,Australia and draw a conclusion that the approach presented in this paper are much better in time than traditional way. Keywords:extended , route optimization,bypass cost, engineering

1.

introduction

The Service-Oriented Computing(SOC)paradigm foresees the creation of business applications from independently developed services.In this vision,Service Providers(SPs)offer similar competing services corresponding to a functional description and the best set of Web Services(WSs)can be selected at run-time in order to maximize the Quality of Service(QoS) and minimize the price for end users. Furthermore,Internet application workloads can vary by orders of magnitude even within the same business day(Chase et al.,2001)[1].Hence optimization has to be performed when the BPEL process execution starts and has to be iterated at run-time in order to take into account workload fluctuations.In real world ,the price and Qos in users’ vision are close to volume of flow, especially the extended Web service such as physical flow ,human flow etc. In this paper we exploit and refine the ideas first presented by Rosario,Luo [2,3], and we propose a hub-arc based framework which allows the optimal service composition optimazing a set of QoS and cost objective. Hub arc models presented by Compell relax the restriction that the flow cost between every pair of hubs is discounted.The hub arc location problem seeks to locate hub arcs,the end points of which are hubs,whereas it can not solve the confict of “scale economy” and “bypass cost”,even the “congestion effect” for it is excessively depended on “scale economy”. This paper presents a Route Optimize Algorithm and Solution for Web Service Network,ROASWSN problem,which addresses a major deficiency of the p-hub arc location model and try to unite “scale economy” and “bypass cost”. There are the three differences between ROASWSN and p-hub-arc problem. ˄1˅in p-hub arcs problem , The number of hub arcs is limited explicitly,rather than being determined by flow volume on hub arcs. While the ROASWSN design decision is to select hub arcs only if the flow consolided in some path exceed thredhold and,as a consequence,the total number of hub arcs is not limited explicitly. (2)in p-hub arc location problem ,each origin-destination paths include at least one hub node,but in * Luo youlong. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . E-mail address:[email protected].

2211-3819 © 2012 Published by Elsevier Ltd. Selection and peer-review under responsibility of Desheng Dash Wu. Open access under CC BY-NC-ND license. doi:10.1016/j.sepro.2012.04.065

428

Luo youlong and Nie guihua / Systems Engineering Procedia 5 (2012) 427 – 436

ROASWSN,the direct paths connected with od nodes is permitted even the od nodes are not hub nodes. Above all, the hub arc location problem may include three types of arcs:(1)hub arcs joining two hubs(with reduced unit flow cost),(2)access arcs joining a nonhub origin/destination and a hub,and (3)bridge arcs joining two hubs,but without the reduced unit flow costs. Compared with hub arcs location problem, ROASWSN include incompletely different types of arcs: (1)hub arcs joining two hubs(with reduced unit flow cost),(2) direct arc ;(3) not hub arc but a transfer arc,on which include at least one od flow, but it is not a hub arc because that the agglomeration of flow on it cannot reach a given value. Therefore , ROASWSN does not belong to a hub station location problem, is also different from the hub arc location problem presented by Compell.The primary decision-making of ROASWSN is to determine the optimal route, strictly speaking, it belongs to route optimization problem. The remainder of this paper is organized as follows.In Section 2,we provide some background and a formulation of the model.Section 3 describes the solution algorithm and Section 4 includes computational results using real airlines’data.In Section 5,we give concluding remarks and mention some future work. 2.

Model description This section presents MILP formulations for ROASWSN. ROASWSN can be formulated in a

variety of ways,depending on the selection of the decision variables.Different integer programming formulations have different properties and lead to different solution approaches.

Li and

Krishnamoorthy(1996,1998a)[4,5,6] introduced an approach that tracks the flow from each origin(but not for each origin-destination pair).In this approach, Z ik is the flow on an access arc from origin i to hub k.The four subscript formulation introduced by Campbell(1994)[7]is perhaps the clearest,where

X ijkm is the flow from origin i to destination j via hubs k and l,in order iėkėlėj.This approach easily incorporates multiple allocation,because each origin-destination flow is tracked separately.In this paper ,we use the latter approach introduced by Campbell.

1RWDWLRQ This section presents MILP formulations for hub arc location problems.These are designed to allow efficient solution using a mixed-integer LP solver. We formulate the ROASWSN which tracks flows on arcs for each origin.Consider a complete graph G(V,E) with a node set V={1… n},where nodes correspond to origins/destinations and potential hub locations.The

flow from node i and node j is

rij and the distance from node i to node j is d ij

,where these distances satisfy the triangle inequality. km

The parameter cij

is unit cost of od flow

i-j along i-k-m-j. let the binary

varible

y km =1,which denote that the arc k-m is difined as hub arcs related with economy of scale;otherwise, y km =0. Furthermore ,

y km =1 is based on the assumption that the flow exceed D rkm ,e.c.the arc k-m will

be seleced as hub arc of which the aggregated coefficient exceed unit cost presented by a given factor a(00 is impossible.

430


U km

¦r X

i , j

ij

km ij

¦ rki X kimj i , j

of object function U km =0 So Rkm

¦r X

i , j

ij

km ij

is

M

X imjt

k , m

undoubtly.

¦ rki X kimj i , j

Constraint(3) ensures ykm the

ki

im

1 ,then Rkm >0 is possible . Morever , to the minimize the value

ykm

On the contrary, If

¦r

¦r

im

ki

X imjt

k , m

(8)

1 ,and there is no capacity restriction of arc k-m.In the constraint(3),

is a large constant.

Constraint(4)require the flow aggregated on the hub arc is not less than original direct route.

D times of flow on

Constraint(5)ensures all o-d flow be proceeded.

3.

Algorithm of smart enumeration As presented above,the MILP formulation for the general hub arc location problem is very large

and not very tight.There are a number of ways that this formulation can be improved.In the remainder of this section,we will consider an optimal

algorithm,which have equal collection and distribution

cost. Lemma 1: In ROASWSN,if

an od flow along route i-k-m-j

has

the minimal unit cost ,then

the route is called shortest transport route. In general, in spite of

aggregating each od flow to its shortest transport route,we

flow to a route whose flow concequently exceed threshold of

hub arc

transfer part of

. Therefore

,the arc is

selected as hub arc,which bring the whole optimal cost . Lemma 2: If an o-d flow i-j is i-i-i-j or i-i-j-j or i-j-j-j,then the flow i-j is called direct route. Lemma 3:The former route of od flow i-j is S,if we transfer part flow of S called f to route D,then D is load route ,f is load flow. Because ROASWSN Model is too large,it is not approprate to use branch and bound algorithm and enumeric algorithm . To ROASWSN,we are hardly node set V={1…n}, there are Known of

constrant (5)

find its neighbourhood. In

a complete graph G=(V, E) with a

n 2 transport routes for a od pares.

¦¦ X k

km ij

1

km

,the variable X ij

is corelated with each other.

m

Different od flow which go across a same arc are corelated with each other too. km

Therefore, we are hardly give out the difinition of the neighborhood of a given solution X ij

because the range of its neighborhood is too large . Different from MAHMP ,MAHMCP and

arc combination . To

km

variable is transport route X ij

,which comprise

a very complicated

a complete graph with n nodes, we need consider

n 4 type of X ijkm

MAHSCP, the key decision

431

Luo youlong and Nie guihua / Systems Engineering Procedia 5 (2012) 427 – 436 km

the transport route X ij

combination .Whereas , known of

of an od flow(such as a given initial

solution),we can caculate the aggregated volume of each arc. Let FLOWkm denote the aggregated volume of arc k-m ,then

¦r X

FLOWkm

i , j

ij

km ij

¦ rki X kimj i , j

¦

ki m z j

rim X imjt

k , m

(9) Known of the flow of each arc, we can caculate the unit cost of in hub-and-spoke network. Make it for the arckm . If known of other od route flow

, according ifarcC and Fkm ,we can caculate a new transport route and km

by transfering part of X ij

X ijkm

or whole

to new transport route

which bring the

minimal cost. We call the caculation process above as arc-flow optimize algorithm. Known of each route km

( X ij >0)

in given initial solution, we can caculate new optimal route and load flow till the whole

cost can not be reduced. The basic idea of

ROASWSN is that we caculate the optimal new route and

load flow for each transport route without considering the affect to sequent decision. So the algorithm is actually a greed algorithm .

D rkm is

We assume arc (k , m)

km

the threshold of hub arc k-m, Yij is flow of od i-j along route

i-k-m-j.

TC

¦¦¦¦ Y

km ij

i

j

k

(arcik arckm arcmj )

(10)

m

is whole transport

cost of

this od flow. Therefore,the algorithm is as follows:

Table 3-1 Cost Optimize Algorithm

Step 1

Content Initialize solution and threshold of hub arc.Od flow i-j is along route i-i-i-j

and the

aggregated flow of arc k-m is rkm .

Yijkm

rij if (k , m) (i, i) ® ¯0 otherwise

(11)

arc(k , m) D rkm 2

Caculate TC

¦¦¦¦ Y

km ij

i

j

k

(arcik arckm arcmj ) Arrange all transport. route

m

km

od i-j ( Yij >0) by its cost in descend order and update

Yijkm with route-flow optimize

algorithm(Table 3-2) . 3

Evaluate whole transport cost TC

*

¦¦¦¦ Y

km ij

i

j

k

m

(arcik arckm arcmj )

432


4

If

TC* TC ,then return step 2; otherwise end the algorithm. If final solution, the

transport route

Yijkm is finally updated ,thus TC is whole transport cost .

Variable Scost denote transport cost of cost of

flow f in route i-k-m-j. Variable Ecost denote transport

flow f in route i-w-v-j. km

According to difinition above ,route flow optimize algorithm of Yij

can be expressed as blow:

Table 3-2 Route Flow Optimize Algorithm

Step

Content

step 1.Find an initial load flow.

Let

f

Yijkm /100 , t 1 . Regard

Ftempkm as a temp

variable for aggregated flow,ec. Let Ftempkm

step2. Reduce flow of arc i-k,k-m and m-j

Ftempik

Ftempik f ,

Ftempkm

Ftempkm f ,

Ftempmj

Ftempmj f

step3:Caculate benefit(w,v) for

Dbenefit = Dbenefit1+ Dbenefit2+ Dbenefit3

all arc(w,v).

Scost = Scost1+ Scost2+ Scost3

FLOWkm

Dcost= Dcost1 + Dcost2 + Dcost3 The variable adopted in here is summarized in Appendix A. step 4:Find the most approprate load route, search step5 :If

t d 100 ,return step2;

otherwise,find and record the optimal load flow and route. step6:

Update transport route,

flow of each arc, cost of each

benefit (w* , v* ) STEP (t * , 4) ,v

max benefit ( w, v)

( w,v )A

max STEP (t , 4) , w t 1:n

STEP(t * , 2) , f

STEP(t * ,3) f

IF

arc

Yijik

STEP(t * ,1)

STEP(t * ,3) ! 0

Yijik f , Yijkm

Yijkm f , Yijwv

then

Yijwv f

The variable adopted in here is summarized in Appendix B km

In the programm above, we will increasely load Yij

/100 each time to caculate the most

optimal load flow. In step3 , Dbenefit1,Dbenefit2,Dbenefit3 denote that flow of arc exceed threshold when loading flow f,although it is obtain a saving of

lower than threshold. Consequently ,cost of other od pairs along the arc will

cost with parameter a.

In the formular Dbenefit3, to avoid repeatly caculating flow benefit of

arc

w-i of

route i-w-w-i


,we add the constraint (v,j)(i,w). For example , arcs 1-3 appear twice in route 1-3-3-1, the benefit of arc 1-3 will be caculate twice without the constrain (v,j)(i,w) . In

the formular Scost1, Scost2, Scost3, if the flow of arc is larger than threshold but smaller than

threshold when reducing f ,then

unit cost of other od flow

across the

arc will be increased with

parameter a. Other approaches for parallel algorithms that have proven useful on discrete optimization problems,such as branch and bound or branch and cut,may also prove useful for hub arc problems.However,implementation of these approaches is more complex.A parallel implementation of the smart enumerate algorithm is facilitated by the independence of the cost evaluations using a set of q hub arcs(one iteration of steps 3–5 of the algorithm).

4.

Experimental analysis This section presents computational results for the ROASWSN problems,using two very different

optimal solution approaches.The first is to use the commercial MILP solver LINGO 9.0 to solve the formulations described in§2.The second approach is the smart enumerate algorithm described in§3. These problems were solved using the SE algorithm coded in matlab on a personal computer with a 2 GHz Intel Intel Core2

Dou

processor operated under Windows XP Professional with 1.0 GB

DDR2-SDRAM memory. The experiment flat use AP(Australia Post) data set which include

distance ,flow of od pare

etc.We use data of AP set with 5 nodes,6 nodes, 7 nodes, 8 nodes in computational tests to test how the parameter a,b affect

whole

cost and computation time with ROASWSN.

We assume unit cost of non-hub arc

cij

3dij , the discount of scale is parameter a.

In Tables 4-1,we provide results for solving the MILP formulations ROASWSN using LINGO 9.0. Table 4-1 Test Using Lingo Based On AP Data Set(N= 6,7,8,9) n

a

b

Direct transport cost

Object value

Time cost(second)

6

0.6

1.5

88419

53262

1

6

0.6

2

88419

53735

2

6

0.8

1.5

88419

71014

4

6

0.8

2

88419

71596

2

7

0.6

1.5

150240

91860

8

7

0.6

2

150240

93698

40

7

0.8

1.5

150240

122474

7

7

0.8

2

150240

124937

11

8

0.6

1.5

229860

140619

81

8

0.6

2

229860

142950

64

8

0.8

1.5

229860

187493

27

8

0.8

2

229860

190600

88

9

0.6

1.5

237960

166330

127

9

0.6

2

237960

168967

274

9

0.8

1.5

237960

221774

301

9

0.8

2

237960

225289

216

433

434

Luo youlong and Nie guihua / Systems Engineering Procedia 5 (2012) 427 – 436 *UHHGDOJRULWKPWHVWEDVHGRQ$3GDWDVHW1 n

a

b

cost caculated by greedy algorithm

Result gap

Time cost(second)

6

0.6

1.5

54270

0.018925

3.6

6

0.6

2

54464

0.013567

2.7

6

0.8

1.5

72381

0.01925

3

6

0.8

2

72095

0.00697

2.7

7

0.6

2

94243

0.025942

6

7

0.6

1.5

99227

0.058964

5

7

0.8

1.5

129210

0.054948

5

7

0.8

2

127540

0.020835

5

8

0.6

1.5

151490

0.077308

9.2

8

0.6

2

152570

0.067296

9.3

8

0.8

1.5

195200

0.041106

5.7

8

0.8

2

199360

0.04596

7.6

9

0.6

1.5

181090

0.070703

14.8

9

0.6

2

182210

0.078376

16.6

9

0.8

1.5

230310

0.03849

18.1

9

0.8

2

237370

0.053624

17.8

WLPHFRVWE\OLQJR WLPHFRVWE\*UHHG\$OJRULWKP

5-1 time cost difference between lingo and greedy algorithm For the enumeration of hub arc combinations,we considered the following orderings of potential arcs: From quality of consider

solution ,heuristic algorithm has not get the optimal solution . It is that we don’t

all combination of od flow route even route has been alternated.Morever,

the optimal load

route and load flow we caculated each step is only based on one route without considering other route. Howerver,gap between

the solution of Heuristic algorithm and optimal solution of LINGO is limited

to 7 percent. It is that the quanlity

of solution is satisfied. From graph 5-1,we can find time cost by

LINGO is much more than greedy algorithm when caculating corphn optimization model.Wth increase of nodes,the differece of time cost between LINGO and greedy algorithm increase greatly. The result tables show clearly that for all of the formulations,the problems become much harder as the increases. Under condition of advantage in time cost. 5.

Conclusion

ensuring accuracy ,we had better use greedy algorithm which has


This paper provides a model and results for new hub-and-spoke design,ec. ROASWSN. A arc will be acclaimed as a hub arc when flow aggregated on a arc exceeded a fix value and it get discount a(0=