A modified ant colony system for solving the travelling
salesman problem with time windows
Chi-Bin Cheng, Chun-Pin Mao
Mathematical and Computer Modelling, accepted 29 November 2006
Table 1
Applications of ant colonyoptimization (ACO)
Problem domain
Traveling salesman problem
Quadratic assignment
problem
Scheduling
Vehicle routing problem
Literature
Algorithm
year
Colorni et al. [1]
Dorigo et al. [14]
AS
AS
1991
1996
Gambardella and Dorigo [15]
Ant-Q
1995
Dorigo and Gambardella [16]
ACS
1997
Bullnheimer et al. [17]
ASrank
1999
St¨utzle and Hoos [18]
MMAS
2000
Gambardella et al. [3]
AS-QAP
1999
Maniezzo [4]
ANTS-QAP
1999
St¨utzle and Hoos [18]
MMAS-QAP
2000
Talbi et al. [19]
Parallel Ant Colonies
2001
Solimanpur et al. [20]
ACO
2004
Colorni et al. [9]
St¨utzle [21]
AS-JSP
AS-FSP
1994
1998
McMullen [10]
ACO
2001
T’kindt et al. [11]
ACO
2002
Gravel et al. [12]
ACO
2002
Ying and Liao [13]
ACS
2004
Shyu et al. [22]
ACO
2004
Blum [23]
Beam-ACO
2005
Bullnheimer et al. [5]
Gambardella et al. [24]
AS-VRP
MACS-VRPTW
1999
1999
Bell and McMullen [25]
ACO
2004
Schoonderwoerd et al. [7]
Di Caro and Dorigo [8]
ABC
AntNet
1996
1998
Gambardella and Dorigo [26]
HAS-SOP
2000
Costa and Hertz [6]
ANTCOL
1997
Solnon [27]
Ant-P-solver
2000
Classification
Shelokar et al. [28]
ACO classifier system
2004
Clustering
Shelokar et al. [29]
Kuo et al. [30]
ACO
Ant k-means
2004
2005
Yang and Kamel [31]
Multi-ant colonies
2006
Network routing
Sequential ordering
Graph colouring
Constraint satisfaction
References
[1] A. Colorni, M. Dorigo, V. Maniezzo, Distributed optimization by ant colonies, in: Proceedings of ECAL91 — European
Conference on Artificial Life, Paris, France, 1991, pp. 134–142.
[2] W. Gutjahr, A graph-based ant system and its convergence, Future Generation Computer Systems 16 (2000) 873–
888.
[3] L.M. Gambardella, E. Taillard, M. Dorigo, Ant colonies for the quadratic assignment problem, Journal of Operational
Research Society 50 (1999) 167–176.
[4] V. Maniezzo, A. Colorni, The ant system applied to the quadratic assignment problem, IEEE Transactions on
Knowledge and Data Engineering 11 (1999) 769–784.
[5] B. Bullnheimer, R.F. Hartl, C. Strauss, An improved ant system algorithm for the vehicle routing problem, Annals of
Operations Research 89 (1999) 319–334.
[6] D. Costa, A. Hertz, Ants can colour graphs, Journal of Operational Research Society 48 (1997) 295–305.
[7] R. Schoonderwoerd, O. Holland, J. Bruten, L. Rothkrantz, Ant-based load balancing in telecommunications networks,
Adaptive Behavior (1997) 169–207.
[8] G. Di Caro, M. Dorigo, AntNet: Distributed stigmergetic control for communications networks, Journal of Artificial
Intelligence Research 9
(1998) 317–365.
[9] A. Colorni, M. Dorigo, V. Maniezzo, M. Trubian, Ant system for job-shop scheduling, Belgian Journal of Operations
Research 34 (1994)
39–53.
[10] P.R. McMullen, An ant colony optimization approach to addressing a JIT sequencing problem with multiple objectives,
Artificial Intelligence
in Engineering 15 (2001) 309–317.
[11] V. T’kindt, N. Monmarche, F. Tercinet, D. Laugt, An ant colony optimization algorithm to solve a 2-machine bicriteria
flowshop scheduling
problem, European Journal of Operational Research 142 (2002) 250–257.
[12] M. Gravel, W.L. Price, C. Gagne, Scheduling continuous casting of aluminum using a multiple objective ant colony
optimization
metaheuristic, European Journal of Operational Research 143 (2002) 218–229.
[13] K.-C. Ying, C.-J. Liao, An ant colony system for permutation flow-shop sequencing, Computers and Operations
Research 31 (2004) 791–801.
[14] M. Dorigo, V. Maniezzo, A. Colorni, The ant system: Optimization by a colony of cooperating agents, IEEE
Transactions on Systems, Man
and Cybernetics 26 (1996) 29–41.
[15] L.M. Gambardella, M. Dorigo, Ant-Q: A reinforcement learning approach to the traveling salesman problem, in:
Proceedings of the 12th
International Conference on Machine Learning, ML-95, Tahoe City, CA, 9–12 July 1995, pp. 252–260.
[16] M. Dorigo, L.M. Gambardella, Ant colony system: A cooperative learning approach to the traveling salesman problem,
IEEE Transactions on
Evolutionary Computation 1 (1) (1997) 53–66.
[17] B. Bullnheimer, R.F. Hartl, C. Strauss, A new rank-based version of the ant system: A computational study, Central
European Journal for
Operations Research and Economics 7 (1) (1999) 25–38.
[18] T. St¨utzle, H.H. Hoos, MAX–MIN ant system, Future Generation Computer Systems 16 (8) (2000) 889–914.
[19] E.-G. Talbi, O. Roux, C. Fonlupt, D. Robillard, Parallel ant colonies for the quadratic assignment problem, Future
Generation Computer
Systems 17 (2001) 441–449.
[20] M. Solimanpur, P. Vrat, R. Shankar, Ant colony optimization algorithm to the inter-cell layout problem in cellular
manufacturing, European
Journal of Operational Research 157 (2004) 592–606.
[21] T. St¨utzle, An ant approach to the flow shop problem, in: Proceedings of the 6th European Congress on Intelligent
Techniques & Soft
Computing, EUFIT’98, Aachen, Germany, 7–10 September 1998, pp. 1560–1564.
[22] S.J. Shyu, B.M.T. Lin, P.Y. Lin, Application of ant colony optimization for no-wait flowshop scheduling problem to
minimize the total
completion time, Computers and Industrial Engineering 47 (2004) 181–193.
[23] C. Blum, Beam-ACO — Hybridizing ant colony optimization with beam search: An application to open shop
scheduling, Computers and
Operations Research 32 (6) (2005) 1565–1591.
[24] L.M. Gambardella, ´ E.D. Taillard, G. Agazzi, MACS-VRPTW: A multiple ant colony system for vehicle routing
problems with time windows,
in: D. Corne, M. Dorigo, F. Glover (Eds.), New Ideas in Optimization, McGraw Hill, London, UK, 1999, pp. 63–76.
[25] J.E. Bell, P.R. McMullen, Ant colony optimization techniques for the vehicle routing problem, Advanced Engineering
Informatics 18 (2004)
41–48.
[26] L.M. Gambardella, M. Dorigo, Ant colony system hybridized with a new local search for the sequential ordering
problem, INFORMS Journal
on Computing 13 (3) (2000) 237–255.
[27] C. Solnon, Solving permutation constraint satisfaction problems with artificial ants, in: Proceedings of the 14th
European Conference on
Artificial Intelligence, Berlin, Germany, 20–25 August 2000, pp. 118–122.
[28] P.S. Shelokar, V.K. Jayaraman, B.D. Kulkarni, An ant colony classifier system: Application to some process
engineering problems, Computer
and Chemical Engineering 28 (2004) 1577–1584.
[29] P.S. Shelokar, V.K. Jayaraman, B.D. Kulkarni, An ant colony approach for clustering, Analytica Chimica ACTA 509
(2004) 187–195.
[30] R.J. Kuo, H.S.Wang, T.-L. Hu, S.H. Chou, Application of ant k-means on clustering analysis, Computers and
Mathematics with Applications
50 (2005) 1709–1724.
[31] Y. Yang, M.S. Kamel, An aggregated clustering approach using multi-ant colonies algorithms, Pattern Recognition 39
(2006) 1278–1289.
[32] M. Dorigo, G. Di Caro, L.M. Gambardella, Ant algorithms for discrete optimization, Artificial Life 5 (1999) 137–172.
[33] M. Gendreau, A. Hertz, G. Laporte, M. Stan, A generalized insertion heuristic for the traveling salesman problem with
time windows,
Operations Research 43 (3) (1998) 330–335.
[34] M.M. Solomon, Algorithms for the vehicle routing and scheduling problems with time windows constraints, Operations
Research 35 (2)
(1987) 254–265.
[35] D.J. Rosenkrantz, R.E. Stearns, P.M. Lewis, An analysis of several heuristics for the traveling salesman problem,
SIAM Journal on Computing
6 (1977) 563–581.
[36] J.-Y. Potvin, S. Bengio, The vehicle routing problem with time windows—Part II: Genetic search, INFORMS Journal
on Computing 8 (1996)
165–172.
A hybrid approach for feature subset selection using
neural networks and ant colony optimization
Rahul Karthik Sivagaminathan, Sreeram Ramakrishnan
Expert Systems with Applications 33 (2007) 49–60
براي. استNP-hard يافتن زيرمجموعه بهينه اي ازويژگيها يك مساله
ارزيابي همه وضعيتها از لحاظ محاسباتي،تعداد زيادي ويژگي
ممكن نيست بنابراين به روشهاي جستجوي اكتشافي مثل روشهاي
روش نمايي شامل روشهايي مثل. ترتيبي و تصادفي نياز است،نمايي
شاخه و قيد است كه از يك مجموعه كامل شروع كرده و با استفاده
روش ديگر در اين.ويژگيها را حذف مي كند،از استراتژي اول عمق
جستجوي پرتوي است كه در آن ويژگيها براساس كيفيت به،مقوله
جستجوي پرتوي در هر مرحله.طور نزولي در صف قرار مي گيرند
تمام وضعيتهاي ممكن حاصل از افزودن يك زيرمجموعه از ويژگيها
.را ارزيابي مي كند
1
( كه روشهاي مرحله اي همSSA) الگوريتم هاي جستجوي ترتيبي
پيچيدگي نسبتا كمتري دارند و از استراتژي تپه،ناميده مي شوند
به دليل نقاط.نوردي براي يافتن راه حل بهينه بهره مي برند
با شروع از2 به دو دسته انتخاب پيشروي ترتيبيSSA ،شروع مختلف
با شروع از مجموعه كامل3يك مجموعه تهي و انتخاب پسروي ترتيبي
به طور كلي روشهاي فرااكتشافي به عنوان.ويژگيها تقسيم مي شود
.روشهاي جستجوي تصادفي شناخته مي شوند
بعدها محققين آن. مطرح شدQAP وTSP اولين بار براي مسايلACO
اين.را براي مسايل بهينه سازي گسسته زيادي به كار بردند
مختلف مانند بهينه سازي تركيبيNP-hard فرااكتشاف براي مسايل
مسايل بهينه سازي تركيبي گسسته.پويا به كار برده شد/ايستا
شامل
1
Sequential Search Algorithms
Sequential forward selection
3
Sequential backward selection
2
Job shop scheduling (Blum & Sampels, 2002; Colorine, Dorigo, & Maniezzo, 1994)
flow shop scheduling (Stu¨ tzle, 1998)
open shop scheduling (Blum, 2003)
group shop scheduling (Sampels, Blum, Mastrolilli, & Rossi-Doria, 2002)
vehicle routing problem (Bullnheimer, Hartl, & Strauss, 1998)
sequential ordering (Gambardilla & Dorigo,1997)
graph coloring (Costa & Hentz, 1997)
shortest common super sequences (Micheal & Middendorf,1999)
مسايل بهينه سازي تركيبي پويا شامل مسيريابي در شبكه هاي
و بدون
(Schoonderwoerd, Holland, Bruten, & Rothkrantz ,1996) اتصال گرا
.( استSim & Sun, 2001) اتصال
References
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intelligence (AAAI-91) (Vol. 2, pp. 547–552). Anaheim, CA: AAAI Press.
Ani, A. Al. (in press). An ant algorithm based approach for feature subset selection. In International Conference on Artificial Intelligence and
Machine Learning.
Ani, A. Al. (2005). Feature subset selection using ant colony optimization. International Journal of Computational Intelligence, 2(1), 53–58.
Blum, C. (2003). An ant-colony optimization algorithm to tackle shop scheduling problems. Tech. report, TR/IRDIA/ 2003-01, IRDIA, Universite’
Libre de Bruxelles, Belgium.
Blum, A. L., & Langley, P. (1997). Selection of relevant features and examples in machine learning. Artificial Intelligence, 245–271.
Blum, C., & Sampels, M. (2002). Ant colony optimization for fop shop scheduling: A case study on different pheromone representations. In
Proceedings of the 2002 congress on evolutionary computing (CEC’02) (pp. 1558). New York: IEEE Press.
Bonabeau, E., Dorigo, M., & Theraulaz, G. (1999). From nature to artificial swarm intelligence. New York: Oxford University Press.
Boz, O. (2002). Feature subset selection using sorted feature relevance. In The proceedings of ICMLA, international conference of machine learning
and applications, Los Angeles, USA (pp. 147–153).
Bullnheimer, B., Hartl, R. F., & Strauss, G. (1998). Applying the ant system for the vehicle routing problem. In Meta-heuristics: Advances and
trends in local search paradigms for optimizations(pp. 109–120).
Cardie, C. (1993). Using decision trees to improve case-based learning. In Proceedings of the tenth international conference on machine
learning (pp. 25–32). Los Altos, CA: Morgan Kaufmann Publishers.
Caruana, R., & Freitag, D. (1994). Greedy attribute selection. In Proceedings of the eleventh international conference on machine learning (pp. 180–
189). Los Altos, CA: Morgan Kaufmann Publishers.
Colorine, A., Dorigo, M., &Maniezzo, V. (1994). Ant system for job shop scheduling. Belgium Journal of Operations Research, Statistics and
Computer Science (JORBEL), 34, 39–53.
Corne, D., Dorigo, M., & Glover, F. (1999). New ideas in optimization. Maidenhead: McGraw Hill.
Costa, D., & Hentz, A. (1997). Ants can color graph. Journal of the Operational Research Society, 48, 295–305.
Debuse, J. C. W., &Smith, V. J. R. (1997). Feature subset selection within a simulated annealing data mining algorithm. Journal of Intelligent
Information Systems, 9, 57–81.
Desai, R., Lin, F. C., & Desai, G. R. (2001). Medical diagnosis with a Kohonen LVQ2 neural network. In Proceedings of the 8th interna- tional
conference on neural information processing, Cd-ROM, Shanghai.
Devijver, P. A., & Kittler, J. (1982). Pattern recognition: A statistical approach. Englewood Cliffs, NJ: Prentice Hall International.
Doak, J. (1992). Intrusion detection: The application offeature selection – A comparison of algorithms, and the application of a wide area
network analyzer. Master’s thesis, Department of Computer Science, University of California, Davis.
Dorigo, M., Caro, G. D., &Gambardella, L. M. (1999). Ant algorithm for discrete optimization. Artificial Life, 5(2), 137–172.
Dorigo, M., & Gambardella, L. M. (1997). Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE
Transaction on Evolutionary Computation, 1(1), 53–66.
Gambardilla, L. M., & Dorigo, M. (1997). HAS-SOP: An hybrid ant system for the sequential ordering problem. Tech. report 11-97, Lugano,
Switzerland: IDSIA.
Gorunescu, F., Gorunescu, M., Darzi, E. El., & Gorunescu, S. (2005). An evolutionary computational approach to probabilistic neural network
with application to hepatic cancer diagnosis. In 18th IEEE symposium on computer-based medical systems (CBMS-05) (pp. 461–466).
Jensen, R., & Shen, Q. (2003). Finding rough set reducts with ant colony
optimization. In Proceedings of the 2003 UK workshop on computational intelligence (pp. 15–22).
John, G., Kohavi, R., & Pfleger, K. (1994). Irrelevant features and the
subset selection problem. In Machine learning: Proceedings of the
eleventh international conference (pp. 121–129). Los Altos, CA:
Morgan Kaufmann Publishers.
Kira, K., & Rendell, L. A. (1992). The feature selection problem:
Traditional methods and a new algorithm. In Proceedings of the 10th
national conference on artificial intelligence (pp. 129–134). San Jose,
CA: MIT Press.
Kulkarni, R. S., Lugosi, G., & Santosh, V. S. (1998). Learning pattern
classification – A survey. IEEE Transaction on Information Theory,
44(6), 2178–2206.
Kulkarni, R. S., & Vidyasagar, M. (1997). Learning decision rules for
pattern classification under a family of probability measures. IEEE
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images using neural networks. IEEE Transaction on Image and Signal
Processing Analysis.
Leardi, R., Boggia, R., & Terrile, M. (1992). Genetic algorithms as a
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Merz, C. J., &Murphy, P. M. (1996). UCI Repository of machine learning
databases. Irvine, CA: Department of Information and Computer
Science, University of California. Available from http://www.ics.uci.edu/~mlearn/MLRepository.html.
Micheal, R., & Middendorf, M. (1999). An ACO algorithm for the
shortest common super sequence problem. New ideas in optimization.
Maidenhead: McGraw Hill.
Narendra, P., & Fukunaga, K. (1977). A branch and bound algorithm for
feature subset se lection. IEEE Transactions on Computing, 77(26),
917–922.
Pudil, P., Novovicova, J., & Kittler, J. (1994). Floating search methods in
feature selection. Pattern Recognition Letters Archive, 15(11),
1119–1125.
Punch, W. F., Goodman, E. D., Pei, M., Chia-shun, L., Hovland, P., &
Enbody, R. (1993). Further research on feature selection and classification using genetic algorithms. In The proceedings of 5th international conference on genetic algorithm (pp. 557–564).
Ripley, B. D., & Hjort, N. L. (1996). Pattern recognition and neural
networks. New York: Cambridge University Press.
Sampels, M., Blum, C., Mastrolilli, M., & Rossi-Doria, O. (2002).
Metaheuristics for group shop scheduling. In The proceedings of
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PPSN-VII. Lecture notes in computer science, Berlin, Germany (Vol.
2439, pp. 631–640).
Schoonderwoerd, R., Holland, O., Bruten, J., & Rothkrantz, L. (1996).
Ant-based load balancing in telecommunications networks. Adaptive
Behavior, 5(2), 169–207.
Schreyer, M., & Raidl, G. R. (2002). Letting ants labeling point features.
In Proceedings of the 2002 IEEE congress on evolutionary computation
at the IEEE world congress on computational intelligence (pp. 1564–
1569).
(2002-11) State of the Ant - Overview of ANTS2002 (SIT Seminar 20-11-2002):
Descrete Optimization
Group shop scheduling
Protein folding
Vehicle routing
Assembly line balancing
Dynamic TSP and QAP
Network design
Set partitioning
Dynamic task allocation
Continuous optimization
Simulation
Robotics
Theoretical models of ACO
Theoretical ant programming
Variations of ACO
Anti-pheromone
Candidate set
Combined GA ant algorithms
Others:
Web document classification
ACOinapplication بيشتر از پوشه
Maximum Independent Set Problems
Classification Rule Discovery
Feature Selection
Multi-Label Classification(D:\project\thesis\gecco-2006-chan)
Network Routing and Load-Balancing
Complex Multi-stage Decision Problems
Resource-Constrained Project Scheduling
Path Planning for Mobile Robots
Generalized Assignment Problem
Spatial Cluster Scheduling Problem
Mine Detection Application
Best Path Planning
Constructing Load-Balanced Clusters
Loss Minimization in Distribution Networks
vehicle routing problem
Multiple Travelling Salesman Problem
Ship Pipe Route Design in 3D Space
)Multicast Routing (IEEE3\article1
)Multiple Knapsack Problem (MKP
)Job Shop Scheduling Problem (JSP
)Generalized Assignment Problem (GAP
)Open shop Scheduling Problem (OSP
Car sequencing problem
Multiple TSP
)Probabilistic TSP (each customer has a given probability of requiring a visit
)Set Covering Problem(IEEE3\article9
تعاريف کلي مسايل کالسيک بهينه سازي
:QAPانتساب nوسيله 4به nمکان مختلف به نحوي که هزينه هاي
جريان کاالها (اجناس) بين وسيله ها کمينه شود.
:JSPتعيين ترتيب پردازش تعادي عمليات (که به کارهاي مختلف
تقسيم شده اند) روي چند ماشين که ترتيب پردازش عمليات در هر
کار ،ثابت است.
:MKPانتخاب زيرمجموعه اي از آيتمها با مقدار ماگزيمم (هر
آيتم داراي يک مقدار و ميزان نيازمندي هاي آن به منبع است) از
يک مجموعه به نحوي که محدوديتهاي بهره وري منابع ،لحاظ گردد.
:GAPانتساب هر وظيفه از nوظيفه به دقيقا يکي از mعامل که
به هر عامل مي تواند هيچ يا چند وظيفه منتسب شود ،متناسب با
قابليتهاي نسبي عاملها.
:CSPدر آن هدف قرار دادن ماشينهاي با مدلهاي مختلف در دنباله
توليد است به نحوي که جريمه جداسازي ماشينهاي يک مدل ،کمينه
شود.
:SCPهدف يافتن مجموعه اي از تسهيالت با كمترين هزينه از ميان
مجموعه متناهيي از تسهيالت است كه هر گره تقاضا حداقل با يك
وسيله پوشش داده شود.
D:\project\thesis\aco2004
Facility
4
چاپ كردم
5.3 Significant problems
In the following of this section we will present applications of ACO algorithms to
some significant combinatorial optimization problems. This is to give the reader
an idea of what is involved by the use of an ACO algorithm for a problem: even
though the last subsection presents an overview of recent application the list is by
no means exhaustive, as it becomes readily evident by searching the web under the
keywords “ant colony optimization”.
5.3.1 Sequential ordering problem
The first ACO applications were devoted to solve the symmetric and the asymmetric
traveling salesman problem. Given a set of cities V = {v1, ... , vn}, a set of
10
edges A = {(i,j) : i,j V} and a cost dij = dji associated with edge (i,j) A, the TSP
is the problem of finding a minimal length closed tour that visits each city once. In
case dij ? dji for at least one edge (i,j) than the TSP becomes an Asymmetric TSP
(ATSP). The first algorithm that applies an ACO based algorithm to a more general
version of the ATSP problem is Hybrid Ant System for the Sequential Ordering
Problem (HAS-SOP, [34]). HAS-SOP was intended to solve the sequential ordering
problem with precedence constraints (SOP). The SOP in an NP-hard
combinatorial optimization problem first formulated by Escudero [29] to design
heuristics for a production planning system. The SOP mo dels real-world problems
like production planning [29], single -vehicle routing problems with pick-up and
delivery constraints [64], and transportation problems in flexible manufacturing
systems [2]. The SOP can be seen as a general case of both the ATSP and the
pick-up and delivery problem [47]. It differs from ATSP because the first and the
last nodes are fixed, and in the additional set of precedence constraints on the order
in which nodes must be visited. It differs from the pick-up and delivery problem
because this is usually based on symmetric TSPs, and because the pick-up and
delivery problem includes a set of constraints between nodes with a unique predecessor
defined for each node, in contrast to the SOP where multiple precedences
can be defined.
HAS-SOP combines a constructive phase (ACS-SOP) based on the ACS algorithm
[36] with a new local search procedure called SOP-3-exchange. SOP-3exchange is based on a lexicographic search heuristic due to [64], on a new labeling
procedure and on a new data structure called don’t push stack inspired by the
don’t look bit [5] both introduced by the authors. SOP-3-exchange is the first local
search able to handle multiple precedence constraints in constant time.
ACS-SOP implements the constructive phase of HAS-SOP but differs from
ACS in the way the set of feasible nodes is computed and in the setting of one of
the algorithm’s parameters that is made dependent on the problem dimensions.
ACS-SOP generates feasible solutions that does not violate the precedence constraints
with a computational cost of order O(n2) like the traditional ACS heuristic.
A set of experiments based on the TSPLIB data shows that HAS-SOP algorithm
is more effective than other existing methods for the SOP. HAS-SOP was
compared against the two previous most effective algorithms: a branch-and-cut algorithm
[2] that proposed a new class of valid inequalities and Maximum Partial
Order/Arbitrary Insertion (MPO/AI), a genetic algorithm by Chen and Smith [17].
To better understand the role of the constructive ACS-SOP phase and the role
of the SOP-3-exchange local search MPO/AI was also coupled with the SOP-3exchange local search. Experimental results shows that MPO/AI alone is better
than ACS-SOP due to the use of a simple local search embedded in its crossover
operator. On the contrary, the combination between constructive phase and local
search shows that HAS-SOP is better than both MPO/AI alone and MPO/AI +
SOP-3-exchange. This is probably due to the fact that MPO/AI generates solutions
that are already optimized and therefore the SOP-3-exchange procedure quickly
gets stuck. On the contrary, ACS-SOP solution is a very effective starting point
for the SOP-3-exchange local search therefore the HAS-SOP hybridization is very
11
effective. Currently HAS-SOP is the best known method to solve the SOP and was
able to improve 14 over 22 best known results in the TSPLIB data set.
5.3.2 Vehicle routing problems
A direct extension of the TSP, the first problem AS was applied to, are Vehicle
routing problems (VRPs). These are problems where a set of vehicles stationed at
a depot has to serve a set of customers before returning to the depot, and the objective
is to minimize the number of vehicles used and the total distance traveled
by the vehicles. Capacity constraints are imposed on vehicle trips, as well as possibly
a number of other constraints deriving from real-world applications, such as
time windows, backhauling, rear loading, vehicle objections, maximum tour
length, etc. The basic VRP problem is the Capacitated VRP (CVRP): ASrank, the
rank-based version of AS, was applied to this problem by Bullnheimer, Hartl and
Strauss [7, 8] with good results. These authors used various standard heuristics to
improve the quality of VRP solutions and modified the construction of the tabu
list considering constraints on the maximum total tour length of a vehicle and on
its capacity.
Following these results, and the excellent ones obtained by ACS with TSP,
SOP and QAP problems, ACS was applied to a VRP version more close to actual
logistic practice, called VRPTW. VRPTW is defined as the problem of minimizing
time and costs in case a fleet of vehicles has to distribute goods from a depot
to a set of customers. The VRPTW minimizes a multiple, hierarchical objective
function: the first objective is to minimize the number of tours (or vehicles) and
the second objective is to minimize the total travel time. A solution with a lower
number of tours is always preferred to a solution with a higher number of tours
even if the travel time is higher. This hierarchical objectives VRPTW is very
common in the literature and in case problem constraints are very tight (for exa mple
when the total capacity of the minimum number of vehicles is very close to the
total volume to deliver or when customers time windows are narrow), both objectives
can be antagonistic: the minimum travel time solution can include a number
of vehicles higher than the solution with minimum number of vehicles (see e.g.
Kohl et al., [45]).
To adapt ACS to a multiple objectives the Multiple Ant Colony System for the
VRPTW (MACS-VRPTW [38]) has been defined. MACS-VRPTW is organized
with a hierarchy of artificial ACS colonies designed to hierarchically optimize a
multiple objective function: the first ACS colony (ACS-VEI) minimizes the number
of vehicles while the second ACS colony (ACS-TIME) minimizes the traveled
distances. Both colonies use independent pheromone trails but they collaborate by
exchanging information through mutual pheromone updating. In the MACSVRPTW
algorithm both objective functions are optimized simultaneously: ACSVEI
tries to diminish the number of vehicles searching for a feasible solution with
always one vehicle less than the previous feasible solution.
12
0. MACS-VRPTW algorithm
1. {Initialization}
Initialize ialize gb the best feasible solution: lowest number
of vehicles and shortest travel time.
2. {Main loop}
Repeat
2.1 Vehicles #active_vehicles( gb )/* The actual number of used vehicles
is computed */
2.3 Activate ACS-VEI(Vehicles - 1) /* ACS-VEI searches for a feasible solution
with always one vehicle less
by maximising the num. of visited
customers */
2.4 Activate ACS-TIME(Vehicles) /* ACS-TIME is a traditional ACS colony
that minimises the travel time */
While ACS-VEI and ACS-TIME are active
Wait for an improved solution y from ACS-VEI or ACSTIME
2.5 gb y
if #active_vehicles( gb ) < Vehicles then
2.6 kill ACS-TIME and ACS-VEI
End While
until a stopping criterion is met
ACS-VEI is therefore different from the traditional ACS applied to the TSP. In
ACS-VEI the current best solution is the solution (usually unfeasible) with the
highest number of visited customers, while in ACS the current best solution is the
shortest one. On the contrary, ACS-TIME is a more traditional ACS colony: ACSTIME,
optimizes the travel time of the feasible solutions found by ACS-VEI. As
in HAS-SOP, ACS-TIME is coupled with a local search procedure that improves
the quality of the computed solutions. The local search uses data structure similar
to the data structure implemented in HAS-SOP [36] and is based on the exchange
of two sub-chains of customers. One of this sub-chain may eventually be empty,
implementing a more traditional customer insertion.
Experimentally has been shown that the performance of the system increases in
case the best solution gb calculated in ACS-TIME is used, in combination with
the ACS-VEI best solution ACSVEI , to update the pheromone in ACS-VEI equation
(5.7).
13
ACS -VEI ACS - VEI
t ij (t) r t ij (t 1) 1 r Ly (i, j) y (5.7)
gb gb
tij (t) r t ij (t 1) 1r Ly (i, j) y
MACS-VRPTW has been experimentally proved to be most effective than the
best known algorithms in the field such as the the tabu search of Rochat and Taillard
[61], the large neighbourhood search of Shaw [71] and the genetic algorithm
of Potvin and Bengio [58]. MACS-VRPTW was also able to improve many results
in the Solomon problem set both decreasing the number of vehicle or the travelled
time.
MACS-VRPTW introduces a new methodology for optimising multiple objective
functions. The basic idea is to coordinate the activity of different ant colonies,
each of them optimizing a different objective. These colonies work by using independent
pheromone trails but they collaborate by exchanging information. This is
the first time a multi-objective function minimization problem is solved with a
multiple ant colony optimization algorithm.
5.3.3 Quadratic Assignment Problem
The quadratic assignment problem (QAP) is the problem of assigning n facilities
to n locations so that the assignment cost is minimized, where the cost is defined
by a quadratic function. The QAP is considered one of the hardest CO problems,
and can be solved to optimality only for small instances. Several ACO applications
dealt with the QAP, starting using AS [MC94] and then by means of several
of the more advanced versions [54], [66]. The limited effectiveness of AS was in
fact improved using a well-tuned local optimizer [53], but several other systems
previously introduced were also adapted to the QAP. For example, two efficient
techniques are the MMAS-QAP algorithm [71] and HAS-QAP [39]. For the testing
of QAP solution algorithms, Taillard [75] proposed to categorize instances
into four groups: (i) unstructured, uniform random (ii) unstructured, grid distance,
(iii) real-world and (iv) real-world-like. Both MMAS-QAP and HAS-QAP have
been applied to problem instances of type i and iii. The performances of these two
heuristic approaches are strongly dependent on the type of problem. Comparisons
with some of the best heuristics for the QAP have shown that HAS-QAP performs
well as far as real-world, irregular and structured problems are concerned. On the
other hand, on random, regular and unstructured problems the performance of this
technique is less competitive.
This problem-dependency was not shown by ANTS, which was also applied to
QAP. In order to apply ANTS to QAP (or any other problem), it is necessary to
specify the lower bound to use and what is a move in the problem context (step
2.2). The application described in [50] made the following choices.
As for the lower bound, since there is currently no lower bound for QAP, which
is both tight and efficient to compute, the LBD bound was used, which can be
computed in O(n) but which is unfortunately on the average quite far from the optimal
solution.
As for the moves, it was declared that a move corresponds to the assignment of
a facility to a location, thus adding a new component to the partial solution corresponding
to the state from which the move originated. Some considerations on the
move structure were used to improve the computational effectiveness of the resulting
algorithm.
ANTS was tested on instances up to n=40 and showed to be effective on all instance
types; moreover its direct transposition into an exact branch and bound was
also effective when compared to other exact algorithms.
5.3.4 Other problems
This section outlines some of the more recent applications of ACO approaches to
problems other than those listed in the previous ones. This variety is well represented
in the many diverse conference with tracks entirely dedicated to ACO and
most notably in ANTS conference series, entirely dedicated to algorithms inspired
by the observation of ants' behavior (ANTS'98, ANTS'2000 and ANTS'2002).
Many different applications have been presented: from plan merging to routing
problems, from driver scheduling to search space sharing, from set covering to
nurse scheduling, from graph coloring to dynamic multiple criteria balancing
problems. A large part of the relevant literature can be accessed online from [1].
Moreover, several introductory overviews have been published. We refer the
reader to [23], [24] and [52] for other overviews on ACO.
Among the problems not in the list above, a prominent role is played by the
TSP. In fact, TSP has been and in many cases still is the first testbed for ACO
variants, and more in general for most combinatorial optimization metaheuristics
[68]. It was already on this problem that the limited effectiveness of the first variants
emerged, and this fostered the design of improved approaches modifying
some algorithm element and possibly hybridizing the framework with greedy local
search or with other approaches, such as genetic algorithms or tabu seach [69],
[42], [73]. These variants were then applied to other problems, for example MAXMIN
ant system was applied to the flow shop problem in [63], a problem then
faced also with other ACO modifications [10], whereas in [8] a rank-based approach
for the TSP is described or in [14] a so-called best-worst variant.
More recently, different authors ([76], [77], [44]) have tackled the TSP with
hybrid variants, mainly using tabu search, but also, in the case of large TSP instances,
also with genetic evolution and nearest neighbor search, in order to improve
both efficiency and efficacy. Moreover, variations of the basic TSP, such as
the orienteering problem [49] or the probabilistic TSP where clients have to be
visited with a certain probability [4] have also been studied.
Scheduling problems provide another common area for testing the effectiveness
of ACO algorithms. An ACO approach for the job-shop scheduling is presented in
[12], whereas applications to real-world scheduling cases have been recently described
in [3] and [62].
More recently, the maturity of the field is showed by the fact that ACO approaches
began to be proposed also for problems which are not standard combinatorial
optimization testbed, but which are more directly connected to actual practice.
For example, the problem of searching and clustering records of large
databases is faced by means of ACO in [59], while an algorithm for document
clustering is described in [80]. Even more theoretical problems linked to spatial
data analysis were tackled with ACO techniques in [74] and [37].
Finally, a recent interesting research branch of ACO, not directly related to
combinatorial optimization, is about telecommunication. In fact, the area of packet
switching communications appear to be a promising field for ACO-related routing
approaches [19, 20]. Whereas a standard optimization version of the frequency assignment
problem was described in [51], an application to wavelength allocation
was presented in [57], while techniques for path adaptive search are described in
[79], [22], [9], [81] and an application to a satellite network in [67]. Moreover,
applications directly related to communication Quality of Service (QoS) have been
presented in [28], and more recently in [15], while an application which optimizes
communication systems with GPS techniques is described in [16].
D:\project\thesis\phd_thesis
SCOPs: Stochastic Combinatorial Optimization Problems
:در اين تز دو ويژگي برای فرااكتشافات تشخيص داده شده است
آنها جايگزين معتبري برای روشهاي كالسيك حقيقي جهت انجام مسايل
به عالوه.بهينه سازي تركيبي احتمالي در اندازه واقعي هستند
انعطاف پذيرند زيرا آنها مي توانند به سادگي براي حل فرمول
. ايستا و پويا تطبيق يابندSCOPs هاي مختلف
Acronym
PTSP
TSPTW
VRPSD
VRPSDC
SCP
SSP
SDTCP
SOPTC
Full SCOP name
Probabilistic Traveling Salesman Problem
Traveling Salesman Problem with Stochastic Time Windows
Vehicle Routing Problem with Stochastic Demands
Vehicle Routing Problem with Stochastic Demands and Customers
Set Covering Problem
Shop Scheduling Problem
Stochastic Discrete Time-Cost Problem
Sequential Ordering Problem with Time Constraint
Table 1.1: Explanation of acronyms used to refer to some relevant SCOPs.
D:\project\thesis\thesis-abstract
D:\project\survey\ A Review of ACO trend basis and model
5 بخش
بقيه بعدا ترجمه شوند
اولين مقاله اي كه پيدا كردمD:\project\survey\ BC.04-DorDic-NIO99
. قبال چاپ كرده ام. توضيح دارند.9 .2 زير بخش هاي
Problem name
Authors
Year
1991
1995
1996
1997
1997
1994
1997
1998
1998
1998
Main referen
ces
[16, 21, 22]
[23]
[19, 20, 24]
[48, 49]
[6]
[41]
[27]
[50]
[40]
[39]
Traveling salesman
Dorigo, Maniezzo & Colorni
Gambardella & Dorigo
Dorigo & Gambardella
StÄutzle & Hoos
Bullnheimer, Hartl & Strauss
Maniezzo, Colorni & Dorigo
Gambardella, Taillard & Dorigo
StÄutzle & Hoos
Maniezzo & Colorni
Maniezzo
AS
Ant-Q
ACS & ACS-3-opt
MMAS
ASrank
AS-QAP
HAS-QAP
MMAS-QAP
AS-QAP
ANTS-QAP
Bullnheimer, Hartl & Strauss
Gambardella, Taillard & Agazzi
Schoonderwoerd, Holland,
Bruten & Rothkrantz
White, Pagurek & Oppacher
Di Caro & Dorigo
Bonabeau, Henaux, Guerin,
Snyers, Kuntz & Theraulaz
Di Caro & Dorigo
Subramanian, Druschel & Chen
Heusse, Gu¶erin, Snyers & Kuntz
van der Put & Rothkrantz
1996
1999
1996
[9, 5, 7]
[26]
[45, 44]
AS-VRP
HAS-VRP
ABC
1998
1998
1998
[55]
[14]
[4]
ASGA
AntNet-FS
ABC-smart ants
1997
1997
1998
1998
[12, 13, 15]
[52]
[33]
[53, 54]
AntNet & AntNet-FA
Regular ants
CAF
ABC-backward
Sequential ordering
Gambardella & Dorigo
1997
[25]
HAS-SOP
Graph coloring
Shortest common
supersequence
Costa & Hertz
1997
[10]
ANTCOL
Michel & Middendorf
1998
[42]
AS-SCS
Quadratic assignme
nt
Vehicle routing
Connectionoriented network ro
uting
Connectionless network routing
a HAS-QAP
b This
is an ant algorithm which does not follow all the aspects of the ACO meta-heuristic.
is a variant of the original AS-QAP.
The references are related to page 2.
Algorithm name
Scheduling
Constraint
satisfaction
Classification
Clustering
Colorni et al. [9]
St¨utzle [21]
1994
1998
AS-JSP
AS-FSP
McMullen [10]
2001
ACO
T’kindt et al. [11]
2002
ACO
Gravel et al. [12]
2002
ACO
Ying and Liao [13]
2004
ACS
Shyu et al. [22]
2004
ACO
Blum [23]
2005
Beam-ACO
Solnon [27]
2000
Ant-P-solver
Shelokar et al. [28]
2004
ACO classifier system
Shelokar et al. [29]
Kuo et al. [30]
2004
2005
ACO
Ant k-means
Yang and Kamel [31]
2006
Multi-ant colonies
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