Transportation Network Optimization
A. Ogunbanwo, Brunel University, United Kingdom
A. Williamson, Brunel University, United Kingdom
M. Veluscek, Brunel University, United Kingdom
R. Izsak, Brunel University, United Kingdom
T. Kalganova, Brunel University, United Kingdom
P. Broomhead, Brunel University, United Kingdom
INTRODUCTION
The longevity of transportation networks dates back to the age of ancient civilization, since that time
the main objective has in essence remained the same: to facilitate the transportation of goods from
one location to another using the most cost effective mean available. To rephrase that in modern
vernacular, the management and optimization of transportation networks in meeting business
objectives. While the forces driving the interpretation of most cost effective means available have
changed overtime with the introduction of new technologies, global trade links and governmental
policies; the general expectation of a transportation network has remained constant. These driving
forces have impacted on the perception of optimality; cost is not necessarily the sole objective these
days. Optimization objectives such as energy costs and their variability, time, environmental impact
but to name a few have growing in importance of late. Many of the existing approaches to supply
chain management take a multi-objective optimization approach, combining several (possibly
competing) objectives and optimize the network. As such there is a growing trend to perform
balanced optimization across a number of objectives. Transportation networks are rapidly expanding
due to the globalization of business and supply chains; as such the size and complexity of
transportation networks has increased considerably in the last decade. Transportation network
optimization is known to be a difficult and complex problem to solve, a deterministic solution is often
not applicable or indeed available for such problems and the problems themselves are therefore
categorized as NP-hard problems. In response to the failure of deterministic algorithms to solve NPhard problems, other optimization techniques have been developed and applied.
The purpose of the paper is to review the current state of art in transportation network
optimization. The paper is organized in five sections. In the Background section, we introduce the
transportation problem, consider its theoretical aspects and implications, and perform a detailed
analysis of the main contributions made in the field. In the Main Focus section, we present a critical
analysis of the algorithms used, the objectives optimized and the complexity of the networks analyzed
in the literature, and discuss the main problems that as yet remain to be addressed. In the Solutions
and Recommendations section, we propose ideas, and possible solutions to these outstanding
problems. Finally, in the Future Research Directions section, we discuss future and emerging trends.
BACKGROUND
A transportation or distribution network is a dynamic, stochastic and complex system that can be
modeled as a graph where the nodes (vertices) represent entities that can in general can be categorized
as representing producers, distribution centers and end customers (Ding, Benyoucef, & Xie, 2009) or
in the more specialist case of manufacturing enterprises as manufacturing and distribution sites that
procure raw material, process them into finished goods, and distribute the finish goods to customers
(Ganeshan, 1999) (Figure 1 shows an example of a transportation network).
2
Figure 1 – Example of Transportation Network, where 𝑺𝒊 are sources, 𝑫𝒋 destinations/dealers, and 𝑺𝑷𝒌 and 𝑫𝑷𝒍 are
possible intermediate ports
The optimization of transportation networks is a specialization of the minimum-cost flow
problem, a well-known optimization model, where the goal is to find a feasible flow of minimum cost
in a network with capacity constraints and edge costs (Goldberg & Tarjan, 1987). As a specialization
of a linear programming problem, it may be solved by applying the common algorithms from linear
programming theory, e.g. the simplex method, branch and bound/cut, etc. Such methods are exact in
the sense that they always terminate with a feasible solution, a solution that is also optimal. While it is
desirable to have a solution that is theoretically guarantee to be the best, such exact methods are not
always applicable. When the problem difficulty is high or the model is too complex (i.e. NP-Hard
problems cannot always be solved exactly), or perhaps time or indeed the resources available are
limited, then using an exact method is not always possible or a feasible solution strategy. In scenarios
where it is not possible to apply exact methods, then finding an approximate solution could well be an
acceptable tradeoff, particularly if the solution found is close to the optimal and the time/resource
employed are reasonable.
In the case of many optimization problems it is often possible to design specific heuristics,
heuristics that take advantage of specific problem properties and/or employ historical knowledge
acquired from past experience. Clearly the qualities of such heuristic are heavily dependent on the
level of domain knowledge and experience available in the design of the algorithm. In recent years
there has been a growing interest in approaches based on general heuristics. This approach is
applicable across a range of problem domains and often results in better performance than that
achieved using specific heuristics, particularly in terms of solution quality and execution time. In the
literature it is possible to detect a trend towards the use of meta-heuristic approaches as the solution
basis for solving transportation networks problems. The most common approaches include (Multi
Objective) Genetic Algorithm, (Fuzzy-) Ant Colony Optimization, and Swarm Particle Optimization.
One example of transportation network optimization is the trans-shipment problem of crossdocking networks where the goods are transferred from suppliers to retailers through cross-docking
facilities, without storing them in distribution centers. Here the objective function is to minimize the
transportation costs in the network by loading trucks in the supplier locations and routing them to
customers directly or indirectly using cross-docking facilities where loads are consolidated (Musa,
Arnaout; & Jung, 2010). The most common objective in transportation network optimization is in
finding the shortest distant distribution on a given network i.e. to determine an optimal set of routes
3
between suppliers and customers (Han & Ji, 2010). However there is growing interest in using
optimization factors such as profit, energy, service level or resilience etc., possibly competing factors
that result in an optimal solution that itself is possibly a tradeoff amongst these parameters.
An example of supply chain optimization based on multi-objective criteria can be found in
(Ding, et al., 2009). H. Ding et al. addressed the design of production-distribution networks that
includes both supply chain configuration and related operational decisions such as order splitting,
transportation allocation and inventory control (Ding, et al., 2009). They developed a simulation
framework based on Multi-Objective Genetic Algorithm (MOGA). Evolutionary algorithms have also
been shown to be flexible. In (Chang, 2010), the author proposes a combination of the coevolutionary mode with constraint-satisfaction mode to narrow down the possible solutions, as a
means of reducing the exploration space. The co-evolutionary mode can adjust evaluation constraints
dynamically to match a complex reality (Chang, 2010). See Figure 2 for an overview of Evolutionary
Strategy variants used in supply chain optimization.
Another interesting approach is the ant colony optimization algorithm, which mimics the
optimal way in which ants find their food. Ants deposit evaporating pheromone along their search
paths that attracts other ants and influences the way in which they choose pathways. The ‘fastest’
routs tend to be those with the highest pheromone density, more ants that pass down a particular
pathway then greater is the quantity of pheromone deposited, the strength of this marker increases the
probability that other ants will travel along the same pathways. The deposited pheromone evaporates
as a function of time; the degradation rate is faster on longer paths than on shorter ones.
Consequently, after a number of tours to and from the nest, there is a higher concentration of
pheromone on shorter paths than on the longer ones. In ACO, artificial ants work as simple computer
agents within a network to probabilistically build solutions. While the ant colony algorithm in its
original form has been successfully applied to transportation optimization problems (Musa, et al.,
2010), some subsequent variants have improved the convergence behaviors (Han & Ji, 2010). See
Figure 3 for details of Ant Colony Optimization variants.
Particle Swarm Optimization (PSO) has its roots in two main component methodologies.
Perhaps the more obvious is its ties to artificial life (A-life) and in general to bird flocking, or fish
schooling, and swarming theory in particular. However it is also related to evolutionary computation,
and has ties to both genetic algorithms and evolutionary programming (Kennedy & Eberhart, 1995).
PSO-based strategies can and have been applied to the solution of multi-objective transportation
network optimization problems. M. Huang et al. (Huang, Li, & Wang, 2011) designed a Fourth-Party
Logistics (4PL) network optimization model based on resilience and used a PSO method to solve the
problem. Che Z. (Che, 2012) implemented a similar strategy in developing a decision methodology
for the production and distribution planning of a multi-echelon unbalanced supply chain. In (Zhao &
Dou, 2011), Zhao X. et al. proposed an improvement PSO approach. The authors embedded into the
PSO algorithm a reduced variable neighborhood local search, in order to reduce the complexity of the
solution space and enhance explorability.
Figure 2 - Transportation Network Optimization approaches and Evolutionary Algorithms variants
Xiang et al, 2012
Number of ants: n/a
ρ: 0.3
α: 1
β: 2
τ: n/a
Generations: 100
Largest problem size: 50 nodes within the
Hong Kong island
Ant Colony
Optimisation
Multi
Objective
Single
Objective
Ant
Han et al, 2010
System
Number of ants: 16
ρ: 0.3
α: 1
β: 2
τ: n/a
Generations: 10
Largest problem size: 1 logistics centre,
8 customers, 2 distribution vehicles
with a load capacity of 8 tons
Ant Colony
System
Fu et al, 2007
Max-Min
Number of ants: 20
Ant System
ρ: 0.3
α: 0.1
β: 0.5
τ0: n/a
Generations: 100
Largest problem size: 30 ports
connected with unilateral cargo flow
Caldeira et al, 2007
for container transportation
Number of ants: 10
ρ: 0.2
α: 0.5
β: 0.5
τ: 0.5
Generations: 40
Largest problem size: 1 logistics
centre, 1 distributor and 2
suppliers
Ant Colony
System
‘Two-phase’
ACO
Musa et al, 2010
Number of ants: 10
ρ: 0.1366
α: 1
β: 1.5
τ: 0.5
Generations: 5000
Largest problem size: 75 origins,
50 cross docking facilities and 75
destinations
Wang, 2007
Number of ants: 50
ρ: 0.5
α: 5
β: 5
τ: n/a
Generations: 300
Largest problem size: A 4–3–4–3
defective supply chain network
Rizzoli et al, 2007
Number of ants: 10
ρ: n/a
α: n/a
β: n/a
τ: n/a
Generations: n/a
Largest problem size: Distribute
52000 products to 6800 customers
over a period of 20 days
Anghinolfi et al, 2011
Number of ants: n/a
ρ: n/a
α: n/a
β: n/a
τ: n/a
Generations: 900
Largest problem size: 100 orders, 50
vehicles, 20 trains and 8 carriers
Ghoseiri et al, 2010
Number of ants: 900
ρ: 0.99
α: 2
β: 4
τ: n/a
Generations: 100
Largest problem size: 4000 nodes and 61783 edges
‘Fuzzy’ ACO
Utama et al, 2011
Number of ants: n/a
ρ: n/a
α: n/a
β: n/a
τ: n/a
Generations: n/a
Largest problem size: 10 farmers, 5
collectors, 5 CPO factories, 2 bio
energy factories, 2 customers
Figure 3 - ACO Variants
Max-Min
Ant System
Chan and Kumar, 2009
Number of ants: 100
ρ: 0.5
α: 1
β: 1
τ: n/a
Generations: 2000
Largest problem size: 7 distribution centres,
21 potential customer sites across the USA
Lin and Wang, 2008
Number of ants: 40
ρ: 0.2
α: 1.3
β: 1.2
τ: 0.5
Generations: 40
Problem Size: A 5 stage network with 20 nodes in each stage
MAIN FOCUS
Increasing Transportation Network Complexity
The field of transportation network optimization has been studied for a number of years, yet it remains
a problem that is of great interest to both the industrial sector and the research community. The early
transportation network optimization problems involved models based on a single objective function,
and had small set of constraints. These networks also had a tendency towards lower complexity.
These days the data and networks for transportation optimization problems usually comes from the
industrial sector and are often multi-objective with a large and complex network topology.
Table 1 - Objectives investigated and algorithms used in existing approaches to Transportation Network
Optimisation
Author, year
Objective(s)
Algorithms
Distance Cost Resilience Time
(Xiang, Li, Huang, & Li, 2012)
(Bevilacqua, Costantino, & Dotoli, 2012)
(Che, 2012)
(Sadjady & Davoudpour, 2012)
(Zhao & Dou, 2011)
(Boudahri, Sari, & Maliki, 2011)
(Huang, et al., 2011)
(Utama, Djatna, Hambali, Marimin, & Kusdiana,
2011)
(Anghinolfi, Paolucci, Sacone, & Siri, 2011)
(Yeh & Chuang, 2011)
ACO
MOGA
PSO
MILP
PSO
ILP
PSO
ACO
IP and ACO
MOGA
MILP and
(Georgiadis, Tsiakis, Longinidis, & Sofioglou, 2011)
B&B
(Zhao, Kumar, Harrison, & Yen, 2011)
PSO
(Musa, et al., 2010)
ACO
(Han & Ji, 2010)
ACO
(Ying-Hua, 2010)
GA
(Ghoseiri & Nadjari, 2010)
ACO
(Che & Chiang, 2010)
MOGA
(Jiang, Zhao, & Sun, 2009)
MOGA
(Ding, et al., 2009)
MOGA
(Lin, Gen, & Wang, 2009)
GA
(Chan & Kumar, 2009)
ACO
(Lau, Chan, Tsui, & Ho, 2009)
GA
Service Product Environmental
level
quality
issues






































In graph theory, several means exist to measure the complexity of a graph or network. Such
measures are usually based on either the length of the whole network, the length of the shortest path,
the number of cycles in the graph, or its level of connectivity.
Here we choose to measure the complexity of analyzed networks based on their beta index and
the number of cycles measures. The beta index measurement take into account the level of
connectivity of a graph, and requires prior knowledge of the number of graph vertices (nodes) and
edges. Let 𝑒 be the number of edge in a graph, and let 𝑣 be the number of vertex in the same graph,
𝑒
the beta index is define as: 𝛽 = 𝑣. The number of cycles measure is based on the maximum number of
independent cycles in a graph, and again requires prior knowledge of the number of vertices, edges,
and sub-graphs. Let 𝑒 be the number of edge in a graph, let 𝑣 be the number of vertices, and let 𝑝 be
the number of sub-graph. The number of cycles measure is defined as: 𝑢 = 𝑒 − 𝑣 + 𝑝. Table 2 reports
7
the beta index and the number of cycle’s complexity measures for a number of networks as extracted
from the literature
Table 2 - Network Complexity Analysis
Author, Year
Algorithms
(Syarif, Yun, & Gen, 2002)
GA
(Yu, 2005)
ACO
(Chen, Subprasom, & Ji, 2006)
ES
(Lin, et al., 2009)
ES
(Jiang, et al., 2009)
MOGA
(Ghoseiri & Nadjari, 2010)
ACO
(Ying-Hua, 2010)
GA
(Zhao & Dou, 2011)
PSO
(Huang, et al., 2011)
B&B
(Sadjady & Davoudpour, 2012)
M-ILP
(Bevilacqua, et al., 2012)
MOGA
No
Nodes
124
2300
4
35
20
4000
80
1000
14
150
9
No
No SubEdges
graph
188
1
3200
61
10
1
210
1
64
1
61783
1
120000
1
1815
1
40
1
3600
1
18
1
Betaindex
1.52
1.40
2.5
6
3.2
15.46
1500
1.815
2.86
24
2
No of
Cycles
65
961
7
176
45
57784
119921
816
27
3451
10
We can deduce from this analysis, that the current trend is towards problems that are based on
multiple-objective functions, larger data sets and higher complexity networks. From an industrial
standpoint there is increased interest in including variability and uncertainty into the optimization
models, so that they are more representative of real-world applications.
4%
6%
Distance
5% 6%
Cost
20%
Resilience
51%
8%
Time
Figure 4 - Frequency of appearance % of each objective
8
2%
2%
2%
Ant Colony Optimisation
5%
2%
5%
30%
7%
Genetic Algorithm
Particle Swarm
Optimsation
Branch & Bound
12%
33%
Benders’ decomposition
Figure 5 - Frequency of appearance % of each algorithm
Approaches from the domain of linear programming theory are not always well suited to solve
large problems that involve multiple-objective functions and uncertainty. As such growing interest
exists in the application of meta-heuristic methods. Although a preference by some researchers in the
adoption of a (mixed) integer/linear programming technique, such as dual method, simplex method, or
branch and bound/cut can still be observed, there is great preference and interest in adopting
approximated methods (see Table 1 and Figure 5). The most frequently adopted methods are
evolutionary strategy, genetic algorithm, ant colony system, and particle swarm optimization.
In general the literature analyzed discusses the solution to optimization problems that in the
main relate to networks which are constrained to or operate in confined geographic locations/areas,
which typically are no larger than a region or state. There is a growing interest from the logistics field
to address problems that operate at a global level. In such cases the supply chains are complex, and
their optimization is critical. Possible solutions to such problems are considerably less: it becomes
difficult to build a distribution plan; at a global level more factors affect the solution. To address such
problems, the underpinning mathematical models must include a greater number of constraints. The
complexity of the problem increases such that for certain scenarios even approximated methods are
difficult to be applied.
Many of the developed algorithms from the literature require a large amount of time to
converge to an optimal or near optimal solution. Many authors identified the converging speed as a
drawback of their algorithms. There is general agreement that future work should focus on reducing
the convergence time required to achieve a good solution.
A recurring problem relates to how the general quality of the proposed algorithm/method is
assessed. A more comprehensive supply chain simulation benchmarking framework should be
established to apply proposed algorithms to a set of comparable test cases. Another important research
direction is to account for risk related issues in the supply chain design. The approaches presented in
the literature cannot be easily extended due to prohibitive computation time. Future research could be
focused at establishing robust models that can accommodate changes to the parameters of the
business environment for the life-time of the logistics network. Addressing demand uncertainty is a
promising research avenue with significant practical relevance to the industrial sector.
Solutions and Recommendations
With the inevitable increases in problem complexity, the efficiency and scalability of the proposed
solutions are key aspects. Meta-heuristic methods have already been proved to be scalable and
effective when faced with large problems, but this may not always be sufficient. There is possibly
some value in attempting to add specific domain knowledge from the field of transportation network
optimization into these general methods. The availability of more specific information could very well
help in trimming the solution/search space and hence allow better/faster convergence of the solution.
9
The idea of specializing meta-heuristic methods could be implemented by applying hyperheuristics. Hyper-heuristics are general heuristic methods that have the capability to automatically
specialize to the problem at hand by the inclusion of artificial intelligence and machine learning
techniques in the search process. Research in the field of hyper-heuristic is at an early stage, and, at
the time of writing, there are very few studies that relate to the application of hyper-heuristic as a
solution strategy for the transportation optimization problem.
Several approaches can be used to speed-up the convergence and reduce the computation time
of metaheuristic algorithms. In (Tseng, Tsai, Chiang, & Yang, 2010), S. Tseng et al. modified ACO
for the travel salesman problem to track the past iterations for the purpose of reducing redundant
computations. In (Zhou & Deng, 2009), P. Zhou et al. developed a hybrid ACO with a taboo search to
quickly reduce the solution search space.
From a technical point of view, there is undoubtedly value in introducing parallelization in
meta-heuristic algorithms to allow the exploitation of current trends in multi-core hardware, and
concurrent and distributed architectures. In (Randall & Lewis, 2002), M. Randall et al. developed a
simple parallel version of the ACO algorithm for the travel salesman problem. Their parallelization
strategy is based on the well-known master/slave approach. A master ant is used to coordinate the
activities of the colony. The results showed an acceptable speed-up. However, one of the main
disadvantages of this architecture is the large amount of communication required to maintain the
pheromone matrix. Future work should concentrate on minimizing (both absolutely and relatively) the
amount and frequency of this communication. Distributed agent based concurrency with its optimized
message system is worthy of consideration.
When considering changes to the parameters of the business environment during the life-time
of the logistics network, a promising first step would be the addition of stochastic simulation. A
Monte Carlo simulation for instance could be used to update the parameters describing the
transportation network with their sampled estimates. Instead of testing a proposed solution on a
snapshot of the business, the simulations would cover a set of possible scenarios. These results would
be of broader interest.
FUTURE RESEARCH
The solution to transportation network optimization will become key component in the field of
logistics management. With the embracement of global supply chains it is unlikely that the business
model of medium to large-size companies will be geographically constrained to localized areas.
Developments in communication and transportation technologies have more than exceeded the limits
that were common place just few years ago. The size and complexity of transportation problems will
continue to increase, and the planning of resources distribution, production facilities and goods
sourcing will inevitably become a more critical factor in the success of any business. Faster, accurate
and more scalable solutions will undoubtedly be required. All the studies so far considered have in the
main focused on the optimization of one or a few static features. To the knowledge of the authors,
there has not been any proposal reported in the literature that relate to methods capable of including
the dynamic behavior of external parameters, such as energy cost, transportation cost, and inventory
cost fluctuation directly in the optimization model. The introduction of dynamic factors is important
in bridging the gap that currently between research studies and the needs of real-world applications.
Real-world problems are complex in nature, dynamic, and often involve stochastic parameters. Even
the application of the best known methods requires certain simplification to be made in order to
ensure they successfully converge to a solution. The problem is usually reduced in complexity to a
much simpler one by ignoring certain factors or making assumptions about the operating
environment. Consequently, the results produced by such models are not always of great interest to
the actual stakeholders. What undoubtedly would be of interest is for future research directions that
develop models and techniques capable of accommodating dynamic and stochastic factors.
In the near future, there is little doubt that logistic operations will be increasingly influenced by
environmental factors. Environmental factors that currently affect the logistics sector are the
increasing costs and taxes associated with non-green transportation technologies. Existing models
may accommodate such factors by simply adding variables, and constraints. However, the resultant
10
profit will inevitably be lower. Models should be changed to consider the possibility of investment in
environmentally friendly technologies. This is not a straight forward strategy, since such investments
could potentially lead to negative profits in the short term. Adopting such technologies is usually
expensive and requires time before a positive return on any investment is made. Future research
should focus on allowing higher tolerance and increasing the ‘line-of-sight’ of the models, such that
the advantages resulting from the adoption of these technologies may be adequately taken into
account. More options may ultimately be considered and eventually the simulation of such models
could potentially lead to more desirable long term solutions.
CONCLUSION
Because of the increasing importance and complexity of supply chain management and logistic
activities, this paper has presented the state of the art in studies relating to the field of transportation
network optimization. Initially we presented the mathematical formalization of the problem, and
discussed its reduction to the well-known problem of minimum cost flow optimization. We then
investigated the most common approaches used to reach either an exact or an approximated solution.
These methods included Mixed-Integer Linear Programming, Branch and Bound, (Multi Objective)
Genetic Algorithm, (Fuzzy-) Ant Colony Optimization, and Swarm Particle Optimization.
In the remainder of the paper, we discussed research trends and the limitations of the currently
proposed solutions. We commented on the trend in the need to have more complex models that truly
represent the global transportation situation. On the failure of current algorithmic approaches in terms
of their scalability, we suggested the exploration of more scalable methods, such as hyper-heuristics,
and the exploration of parallelization techniques.
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spanning tree-based genetic algorithm approach. Computers & Industrial Engineering, Jul,
43(1-2), 299-314.
Tseng, S.-P., Tsai, C.-W., Chiang, M.-C. & Yang, C.-S. (2010). A fast Ant Colony
Optimization for Traveling Salesman Problem. IEEE Congress on Evolutionary
Computation.
Utama, D. N. et al. (2011). Multi Objectives Fuzzy Ant Colony Optimization of Palm Oil
Based Bioenergy Supply Path Searching. Advanced Computer Science and Information
System (ICACSIS), 177-182.
Xiang, Q., Li, H., Huang, B. & Li, R. (2012). Improved Ant Colony Optimization for Multiobjective Route Planning of Dangerous Goods. 8th International Conference on Natural
Computation (ICNC 2012), 772-776.
Yeh, W.-C. & Chuang, M.-C. (2011). Using multi-objective genetic algorithm for partner
selection in green supply chain problems. Expert Systems with Applications, Apr, 38(4),
4244-4253.
Ying-Hua, C. (2010). Adopting co-evolution and constraint-satisfaction concept on genetic
algorithms solve supply chain network design problems. Expert Systems with Applications,
37, 6919-6930.
Yu, B. (2005). Optimizing Bus Transit Netwrok with Parallel Ant Colony Algorithm.
Proceedings of the Eastern Asia Society for Transportation Studies, 5, 374-389.
Zhao, K., Kumar, A., Harrison, T. P. & Yen, J. (2011). Analyzing the Resilience of Complex
Supply Network Topologies Against Random and Targeted Disruptions. IEEE Systems
Journal, 5(1), 28-39.
Zhao, X. & Dou, J. (2011). A Hybrid Particle Swarm Optimization Approach for Design of
Agri-food Supply Chain Network. IEEE International Conference on Service Operations and
Logistics and Informatics (SOLI), 162-167.
Zhou, P. & Deng, Q. (2009). Hybridizing fast taboo search with ant colony optimization
algorithm for solving large scale permutation flow shop scheduling problem. 2009 IEEE
International Conference on Granular Computing.
13
ADDITIONAL READING SECTION
Additional reading about linear programming:

Chen, J., Lu, J., & Qi, S. (2010). Transportation network optimization of import crude oil in
China based on minimum logistics cost. Emergency Management and Management Sciences
(ICEMMS), 2010 IEEE International Conference, 335-338.

Bidhandi, H. M., Yusuff, R. M., Megat Ahmad, M. M. H., & Abu Bakar, M. R. (2009).
Development of a new approach for deterministic supply chain network design. European
Journal of Operational Research, 198(1), 121-128.

Creazza, A., Dallari, F., & Rossi, T. (2013). Applying an integrated logistics network design
and optimisation model : the Pirelli Tyre case. International Journal of Production Research,
37-41.

Taylor, C., & Weck, O. d. (2006). Integrated transportation network design optimization. 47th
AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference,
May, 1-16.
Additional readings about evolutionary strategies:

Lianshuan, S., & Zengyan, L. (2009). An improved pareto genetic algorithm for multiobjective TSP. Fifth International Conference on Natural Computation, 585-588.

Dong, Y., Gu, J., & Li, N. (2007). Combination of genetic algorithm and ant colony algorithm
for distribution network planning. Proceedings of the Sixth International Conference on
Machine Learning and Cybernetics, Hong Kong, August, 19-22.

Wang, L., Kowk, S. K., & Ip, W. H. (2011). Design of an improved quantum-inspired
evolutionary algorithm for a transportation problem in logistics systems. Journal of Intelligent
Manufacturing, 23(6), 2227-2236.

Syarif, A., Yun, Y., & Gen, M. (2002). Study on multi-stage logistic chain network: a
spanning tree-based genetic algorithm approach. Computers & Industrial Engineering, 43(12), 299-314.

Oliveira, F., Hamacher, S., & Almeida, M. R. (2009). Process industry scheduling
optimization using genetic algorithm and mathematical programming. Journal of Intelligent
Manufacturing, 22(5), 801-813.

Liu, Q. (2008). Study on multi-object optimization of logistics network based on genetic
algorithm. International Conference on Computational Intelligence and Security, 210-214.

Ko, H. J., & Evans, G. W. (2007). A genetic algorithm-based heuristic for the dynamic
integrated forward/reverse logistics network for 3PLs. Computers & Operations Research,
34(2), 346-366.

Hosseinzadeh, M., & Branch, A. (2012). An Optimization model for reverse logistics network
under stochastic environment using genetic algorithm. International Journal of Business and
Social Science, 3(12), 249-264.
14

Chen, A., Subprasom, K., & Ji, Z. (2006). A simulation-based multi-objective genetic
algorithm (SMOGA) procedure for BOT network design problem. Optimization and
Engineering, 7(3), 225-247.
Additional reading about ant colony optimization strategies:

Yan, Y., Zhao, X., Xu, J., & Xiao, Z. (2011). A mixed heuristic algorithm for traveling
salesman problem. Third International Conference on Multimedia Information Networking
and Security, 229-232.

Stutzle, T., & Hoos, H. (1997). MAX-MIN Ant System and local search for the traveling
salesman problem. Proceedings of 1997 IEEE International Conference on Evolutionary
Computation (ICEC '97), 309-314.

Dorigo, M., Maniezzo, V., & Colorni, A. (1996). Ant system: optimization by a colony of
cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics. Part B,
Cybernetics: a Publication of the IEEE Systems, Man, and Cybernetics Society, 26(1), 29-41.

Blum, C. (2005). Ant colony optimization: Introduction and recent trends. Physics of Life
Reviews, 2(4), 353-373.

Korukoglu, S., & Ball, S. (2011). An improved Vogel's approximation method for the
transportation problem. Mathematical and Computational Applications, 16(2), 370-381.

Yu, B. (2005). Optimizing bus transit network with parallel ant colony algorithm.
Proceedings of the Eastern Asia Society for Transportation Studies, 5, 374-389.
Additional reading about particle swarm optimization:

Huang, Y., Qiu, Z., & Liu, Q. (2010). Supply chain network design based on fuzzy neural
network and PSO. Machine Learning and Cybernetics (ICMLC), 2010 International
Conference, September, 2189-2193.
Additional reading about memetic algorithms:

Pishvaee, M. S., Farahani, R. Z., & Dullaert, W. (2010). A memetic algorithm for bi-objective
integrated forward/reverse logistics network design. Computers & Operations Research,
37(6), 1100-1112.
Monte Carlo hyper-heuristic:

Ayob, M., & Kendall, G. (2003). A Monte Carlo hyper-heuristic to optimise component
placement sequencing for multi head placement machine. Proceedings of the International
Conference on Intelligent Technologies, InTech.
KEY TERMS & DEFINITIONS
Optimization Problem: The problem of finding the best value for a given max/min
functions according to a set of constraints on the function variables.
Transportation Network: A given set of connections between producers and
dealers/customers which may be used by the producers to transport finished goods to the
dealers.
15
Linear Programming: A mathematical technique used to solve optimization
problem. Linear programming require the problem to be define as a mathematical model
consisting of an objective function relative to a set of variables, and a set of constraints over
those variables. Linear programming may only be applied if all the relationships in the model
are linear.
Multi-Objectives: An objective function of an optimization model is defined as
multi-objectives if it models more than one entity is to be optimized; the optimization
problem has to be solved in more than one dimension. For instance, an objective function that
includes variables of profit and time is multi-objectives.
Evolutionary Strategy: A strategy that mimics evolutionary models defined by
Darwin’s laws of evolution. Evolutionary strategies require the definition a population, a
crossover operator and fitness metric. The strategy used is to combine elements of the
population, evolve them, and keep only the fittest/best ones. After a number of iterations,
evolutionary strategy should produce a stronger population that represents a set of
approximated solutions.
Ant Colony Systems: A system that mimics the behavior of ants in their search of
food. Some experiments and observations of ant colonies have shown that ants very often are
able to find the shortest path between the colony and their food source. It is the
characterization of this behavior in a stochastic algorithm, and its application in finding the
shortest path between a source and a destination or as in the case of transportation networks,
between the producer and the dealer that defines the method.
Particle Swarm Optimization: A search strategy that starts from an initial set of
candidate solutions (the particles) and try to improve them by looking at their neighbors in
the solution spaces. A solution, or particle is moved according to a local criteria (i.e. the
particle moves to the local best), in combination with a criteria based on the situation of all
other particles (i.e. the particle moves to the best known position of the other particles).