Intelligent Optimization for Logistics

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Intelligent Optimization for Logistics
Gamze Guler
Dept. of Logistics
Usak University – Karahalli Vocational School
Usak, Turkey
Utku Kose
Computer Sciences App. and Res. Center
Usak University
Usak, Turkey
Abstract—Optimization has been a remarkable problem solution
approach for especially real-world based cases. Since first use of
classical optimization techniques, many different fields in the
modern life have benefited from them. But after a while, more
advanced optimization problems required use of more effective
techniques. At this point, Computer Science took an important
role on providing software related techniques to improve the
associated literature. Today, Artificial Intelligence based
intelligent optimization techniques are widely used within
optimization problems. Objective of this paper is to provide a
brief look at to the use of intelligent optimization in Logistics
field. It is clearly known that Logistics operations and
managerial aspects of this field often deal with optimization
based problems. So, it is thought that use of alternative, recent
optimization techniques may give a light to further optimization
problem solutions for the Logistics field. In this context, the
authors believe that this paper will be an interesting reference for
the literature of both Computer Science and Logistics.
Keywords- optimization, logistics, artificial intelligence,
computer science
I. INTRODUCTION
Mathematics is a key factor on shaping the world of actual
time and future. It is important that the world finds its roots
within Mathematics. Because of that, Mathematics has been a
vital element for humankind in order to understand the
dynamics of the world and finding effective solutions for
encountered real-world based problems. Since the ancient
times, mathematical discoveries have made it easier to change
the world and achieve many technological developments. It is
clear here that technological developments have also made it
possible to improve the field of Mathematics and employ more
advanced approaches, methods, and techniques for solving
problems of different fields. Today, we have many different
kinds of mathematical approaches that can be applied in a wide
spectrum of real-world based cases / problems. Optimization is
one of these approaches.
Briefly, optimization means “selection of a best element
(with regard to some criteria) from some set of available
alternatives” [1, 2]. In a mathematical manner, a typical
optimization problems comes with one or more functions to
optimize and possibly some rules and constraints specific for
the objective optimization problem. We can clearly express
that optimization has been a remarkable problem solution
approach for especially real-world based cases. Since first use
of classical optimization techniques, many different fields in
the modern life have benefited from them. But after a while,
more advanced optimization problems required use of more
effective techniques. At this point, Computer Science took an
important role on providing software related techniques to
improve the associated literature. Today, Artificial Intelligence
based intelligent optimization techniques are widely used
within optimization problems.
Objective of this paper is to provide a brief look at to the
use of intelligent optimization in Logistics field. It is clearly
known that Logistics operations and managerial aspects of this
field often deal with optimization based problems. So, it is
thought that use of alternative, recent optimization techniques
may give a light to further optimization problem solutions for
the Logistics field. It is known that some Logistics operations
like Supply Chain has strong relations with optimization
oriented solution needs. On the other hand, it is of course
possible to define many different optimization problems
associated with different mechanisms / works of Logistics. In
this context, the authors believe that this paper will be an
interesting reference for the literature of both Computer
Science and Logistics.
In the context of objectives of the paper, next sections are
organized as follows: The next section is devoted to some brief
explanations about fundamentals of Artificial Intelligence
based optimization techniques, which is associated with the
term: intelligent optimization as used within this paper. With
this section, the readers are enabled to have some essential
ideas about how Artificial Intelligence and those intelligent
mechanisms are used for getting the most recent effective
optimization solutions. After that section, the third section is
about potential role of intelligent optimization in Logistics. In
this section, it is aimed to give ideas about improving works of
Logistics, thanks to Artificial Intelligence based optimization
processes. Following the third section, the paper is ended by
providing a discussion on conclusions and future work.
II. INTELLIGENT OPTIMIZATION WITH ARTIFICIAL
INTELLIGENCE
Artificial Intelligence is a great research field, which has
affected almost all fields of the modern life, with its flexible,
effective, and efficient mathematically – logically structured
solution ways. Day by day, this field gains more popularity and
becomes more advanced with the support of developments
within also other remarkable fields / technologies like
computer, electronics, communication…etc. When the field of
Artificial Intelligence is examined in detail, it can be seen that
it is also divided into some specific sub-research areas like
Machine Learning, Swarm Intelligence…etc. On the other
hand, it is also possible to classify Artificial Intelligence
approaches, methods or techniques according to their objective
application / solution problems. In this paper, the subject of
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optimization, which can be defined as also intelligent
optimization as a result of using Artificial Intelligence roots, is
taken into consideration.
A. How to Make Optimization Intelligent?
As different from classical optimization techniques or at
least alternative solution ways like Hill Climbing, Artificial
Intelligence techniques are generally based on employment of
collective, intelligently-like moving particles trying to find the
optimum in the context of some iterative algorithmic steps. At
this point, such algorithmic structures also employ some
specific solution steps making the whole solution process more
heuristic, collective behavior oriented or at least more focused
on mathematical steps making logically more intelligent sense.
Basically, it is possible to give more emphasis to some
essential factors that researchers generally employ in order to
achieve intelligent algorithmic structures and so finally
intelligent optimization. These are:
 Collective particles: Because the optimization is about
something like trying to find the best, it is better to
benefit from power of a group whose objective is
technically using mathematical / logical steps for
interacting each other and trying to find the best (most
optimum) for their common problem. This is achieved
by programmatically defining some (N number of )
particles, which are able to move within a solution
space (having solution candidates) by interacting with
other particles and determining their each move within
the solution space according to changing positions of
other particles. At this point, these movements can be
done by taking position of the best particles so far
(which has the most optimum solution so far) and
enabling other particles to follow the best particle
along their travel limited with a stopping criterion,
which is associated with finding a desired value or
reaching to a total number of iteration.
 Improving the better / Eliminating the worse: Some
Artificial Intelligence based techniques employ
specific algorithmic steps, which are for improving
some particles having better solutions or / and
eliminating some particles, which are worse according
to other ones. The most common examples of such
mechanisms can be seen in algorithms like Genetic
Algorithm, Artificial Immunity based algorithms, some
Swarm Intelligence oriented algorithms like Particle
Swarm Optimization, Firefly Algorithm, Artificial Bee
Colony…etc.
 Iteration / error or desired value based steps:
Because the mentioned Artificial Intelligence
techniques are almost all algorithmic structures,
solution logic provided by them should be repeated
until the desired solutions are obtained (This is
necessary for also ensuring the collective behavior of
particles and also improvement / elimination
approaches mentioned before). So, algorithmic steps
within such techniques are run until a specific total
number of iteration is met. In addition to this approach,
there is also another running criteria based on error or
desired value. According to this criteria, the related
algorithmic steps are run always until a specific error
value (error value is i.e. the difference between desired
and current value of the objective / fitness function) or
a desired value (i.e. a desired optimum value for the
objective / fitness function) is obtained.
 Inspiration from the Nature: This is actually not a
direct / applicable function but the nature is an
important factor on development of intelligent
optimization techniques and even all Artificial
Intelligence approaches, methods, and techniques.
Generally, nature includes many dynamics, intelligent
behaviors shown by living organisms or just natural
sources. It is always accepted that all these dynamics
and behaviors can be figured out or simulated with
mathematical and logical connections. So, it has been
always a remarkable research interest to design and
develop nature inspired optimization algorithms, which
are associated with intelligent, Artificial Intelligence
oriented techniques.
Figure 1. Essential factors employed for achieveing intelligent optimization.
B. Some Examples of Intelligent Optimization Algorithms
It is clear that the foremost use of Artificial Intelligence for
optimization is associated with specially developed algorithms.
In this context, such algorithms are generally known as Swarm
Intelligence oriented solution tools. Currently, there is a
remarkable effort on development of newer and more effective
optimization algorithms. But in order to give enough idea about
the literature, it is possible to express the following intelligent
optimization algorithms (For more information, readers are
referred to: [3]):
 Particle Swarm Optimization (PSO) Algorithm:
Particle Swarm Optimization (PSO) algorithm is an
optimization approach, which simulates social
behavior related to the actions and movement of
organisms in a bird flock or fish school [4-7]. PSO
employs a population (swarm) of candidate solutions
(particles) formed for the specific problem. In PSO, the
particles move in the search space by taking into
account some mathematical equations. Particle
movements are affected by their own best known
Collective particles
Improving the better
/ Eliminating the
worse
Iteration / error or
desired value based
steps
Inspiration from the
nature
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position within the search space as well as the entire
swarm's best known position [4-7]. Calculated
positions are used in new iterations to determine new
movements while searching for the best solution of the
problem. All process is repeated in a cycle until an
appropriate solution is found.
Algorithm of the PSO is shown in Figure 2 [8].
Figure 2. Algorithmof the PSO [8].
 Ant Colony Optimization (ACO) Algorithm: Ant
Colony Optimization (ACO) algorithm was introduced
by Dorigo in his Doctorate thesis [9, 10]. As general,
the algorithm is based on a searching operation for the
most optimal path in some kind of solution space. At
this point, the graph data model is used for defining the
solution space. ACO can be evaluated as a simple
simulation for behaviors of ants seeking a path
between the colony and a food source. Because of this,
natural aspects of ant behavior should be known in
order to understand the algorithm structure better.
According to the natural behavior, ants start to wander
randomly and when an ant finds a food source, it
returns back to the colony while laying down the
„pheromone‟ trails. If other ants find such a path, they
start to follow trail and if they eventually find food,
they return and reinforce it.
Figure 3 represents the pseudo-code of the ACO [11].
Figure 3. Psuedo code of the ACO [11].
 Artificial Bee Colony (ABC) Algorithm: Artificial
Bee Colony (ABC) algorithm is another Artificial
Intelligence based optimization algorithm and it
simulates the intelligent foraging behavior of honey
bee swarm. ABC has been introduced by Karaboga
[12]. Generally, algorithm structure is inspired from
roles of honey bees within a swarm. But working
mechanism is structured according to only three honey
bee groups, which are: onlooker bees, scouts and
worker bees. In ABC, a colony of onlooker bees search
for rich food sources. In other words, they try to find
good solutions for the problem. At this point; in order
to ensure the ABC algorithm mechanism, the problem
should be converted to the problem of finding the best
parameter vector minimizing an objective function.
After this operation, bees randomly discover a
population of initial solution vectors and try to
iteratively improve the vectors by moving to better
solutions via neighbor search mechanism [13]. In more
detail, each worker bee goes to its food source (the
food source initially associated with the related bee)
and return to the swarm for performing some kind of
„dance‟. The worker bee whose food source has been
abandoned transforms into a scout and it starts
searching for finding a new food source. On the other
hand, onlooker bees see the dances of the worker bees
and choose food sources according to effect of the
dances [12, 13]. All of these processes are done via
mathematical approaches.
Figure 4. shows general algorithm of the ABC [14].
Figure 4. Algorithmof the ABC [14].
 Firefly Algorithm: Firefly algorithm (FA) is another
Swarm Intelligence based algorithm, which was
introduced Yang [15, 16]. Working mechanism of the
algorithm is based on flashing behavior of fireflies. FA
is suitable for especially multimodal optimization
problems. In the algorithm, following factors and acts
are taken into consideration [15, 16]:
• The brightness level of fireflies is used to define the
„attractiveness‟ factor.
• The attractiveness level of each firefly is proportional
to its brightness. At this point, the brightness is
associated with the objective function related to the
problem.
• For any two fireflies, the one with less brightness will
be attracted by the brighter one.
• If there is no any brighter one than the firefly, it will
start to move randomly. Otherwise – if the firefly is
attracted, it will start to move towards to the one
attracted by.
• It is important that brightness levels of fireflies can be
decreased if the distance between them increases.
Figure 5. represents the pseudo-code of the algorithm
[15].
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Figure 5. Psuedo code of the FA [15].
 Cuckoo Search (CS) Algorithm: Cuckoo Search
algorithm (CS algorithm) is a Swarm Intelligence
based optimization algorithm introduced by Yang and
Deb [17]. It simulates the obligate brood parasitism of
some cuckoo species. In the nature, cuckoos lay their
eggs in the nests of other host birds. Here, some host
birds may engage direct conflict with the intruding
cuckoos. As a typical reaction; if the host bird
discovers some eggs, which are not its own, it will
either throw these eggs away or abandon its nest and
form a newer nest on a different place [17]. In the CS,
the following points are taken into consideration [17]:
• Each egg in a nest represents a solution whereas a
Cuckoo egg points to a new solution.
• General objective is using new and potentially better
solutions to replace worse solutions in the nests.
• As default, each nest includes only one egg (It is also
possible to use multiple eggs for different types of
problems).
• Along the algorithm steps, each Cuckoo lays one egg
at a time and dumps its egg in a randomly chosen nest.
• The best nests including high quality of eggs are taken
to the next generation.
• Number of available host nests is defined with a
constant value.
• The egg laid by a Cuckoo is seen by the host bird;
according to a probability value.
Figure 6. represents a pseudo-code for the CS [17].
Figure 6. Psuedo code of the CS [17].
III. POTENTIAL ROLE OF INTELLIGENT OPTIMIZATION IN
LOGISTICS
In Logistics, optimization is an important approach from
different perspectives. It can be said that successful and
effective simple optimization operations may result to bigger
improvements for a Logistics company at the final. Because of
this butterfly effect, almost all successful Logistics companies
decide to employ effective optimization processes along their
works.
Briefly, benefits of an optimization process for Logistics
works can be listed as follows:
 Lowered costs,
 Increased incomes,
 Increased effectiveness in works,
 Increased efficiency in works,
 Improved quality in works,
 Increased benefits (in terms of staff and the company),
 Better supply chain process,
 Better management / control on risks, costs,
works…etc.,
 Better products / services,
 Better analyze of works.
By taking the related list into consideration, it is possible to
figure out more positive effects of optimization approaches in
terms of Logistics. On the other hand, it is also important to
understand how an intelligent optimization can be applied in
Logistics oriented works.
A. Applying Intelligent Optimization in Logistics
The subject of optimization can be examined in detail, from
many different perspectives. But here, it is aimed to eliminate
details specific for the field and focus on how to run intelligent
optimization within Logistics. Simply it can be said that any
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problem that can be mathematically or logically formulated
(and regarding to works in a Logistics) can be used within
intelligent optimization processes. In order to achieve that it is
also important to know where to apply optimization in
Logistics. Some typical application ways that Artificial
Intelligence based, intelligent optimization techniques are
employed can be explained as follows:
 Applying as direct solution way: For problems,
which has specific features and has a limited problem
space, it is possible to apply an intelligent optimization
technique directly. Of course it is possible to use the
outputs from performed optimization process within
another sub-work/process. Such application way is
something modular that is an essential element under
the big Logistics system / model and can be changed,
modified if desired.
 Applying as a step: Some problems of Logistics are
wider and has optimization problems at only specific
points. In such cases, intelligent optimization
techniques can be used as supportive step elements of
the whole work. In such case, it is possible to draw i.e.
a flow chart of the solution flow. Like applying as a
direct solution way, the related step technique can be
modified or changed if desired.
 Applying in an already formed system: Some
Logistics oriented systems (specific for an objective
work or i.e. whole management process, work-flow)
are already designed and applied. But in such systems,
there may need for better cases (like benefits
mentioned at the start of this section) and this situation
can be solved by employing intelligent optimization
within the system. It is something like a modification
and similar to using as a step, but in this case the
optimization is something located deeper within the
system and can be figured out when the system is
examined in detail.
Figure 7. Typical application ways that Artificial Intelligence based,
intelligent optimization techniques are employed in Logistics.
When an optimization problem is taken into consideration,
it is important to understand how to define it mathematically /
logically as appropriate to an intelligent optimization
technique. At this point, depending on essential features of a
technique, it is possible to define a Logistics optimization
problem with an objective / fitness function or a graph
structure. As it can be understood, an objective / fitness
function regarding to Logistics optimization may be in the
form of different combinations of several variables and
constants. Here, it is important to create a function, which
provides an accurate / true calculation for the objective
minimization / maximization problem (i.e. costs, incomes).
A simple structure of an objective / fitness function for
calculating balance between costs and incomes may be in the
following forms:
       
 
     

It is possible to figure out many more different forms of
objective / fitness functions:
               (2)
            

 (3)
According to the samples provided, the aim is to find the
related variables (values) maximizing or minimizing the
obtained value. On the other hand, it is also possible to find the
optimum variables (values) keeping the output of the function
at a certain value or below / above it.
Another important use of intelligent optimization
algorithms can be found in especially supply chain in Logistics.
Along supply chain management processes, it is possible to use
already defined functions or form specific functions. But it is
also use graph based algorithms like ACO in order to i.e.
model a supply chain map according to conditions in hand and
objective travelling points. It is already a common way to test
graph based intelligent optimization algorithms with a well-
known problem: Travelling Salesman Problem (TSP). In this
problem, the objective is to find the most optimum distance
that can be followed through some number of cities (solution
points) separated in the solution space.
Figure 8 shows an example of solved TSP problem. This
can be thought as an optimum objective supply chain map
found for a Logistics company, by an intelligent optimization
algorithm.
Applying as direct
solution way
Applying
as a step
Applying in
an already
formed
system
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Figure 8. A solved TSP problem by a graph based intelligent optimization
algorithm.
Whether an optimization problem is related to function
based or graph based algorithm, we can still draw a general
flow chart for a possible optimization problem solving
processes within problems of Logistics. We can briefly said
that it is important firstly to define the problem with its all
aspects. It is important to understand if the problem is a
specific one, employ (or not) constraints, a follower of a
previous calculation…etc. and figure out an objective / fitness
function or graph structure depending on the problem. Of
course it is still possible to use a pre-defined function if the
problem is a well-known one in the Logistics. After that it is
the point to determine the intelligent algorithm(s) that will be
employed for the related problem. Following that, there is a
need for testing the optimization solution and adjust / modify
the general problem frame and testing again if needed.
Figure 9 represents a general flow chart regarding to
Logistics optimization problem solving process explained
briefly.
Figure 9. A general flow chart regarding to Logistics optimization problem
solving process.
IV. CONCLUSIONS AND FUTURE WORK
In this paper, the concept of intelligent optimization for
Logistics has been examined. In order to achieve that roots of
Artificial Intelligence oriented optimization techniques have
been explained briefly and an essential introduction to applying
intelligent optimization in works of the Logistics field has been
provided. It can be expressed that many different Logistics
works may require optimization solutions and such solutions
can be done via different ways depending on general features
of the optimization problem that is taken into consideration.
Comparing to classical optimization solutions, intelligent
optimization has the power of achieving more effective and
efficient solutions for the objective problems and as general
desired optimization results lead to better Logistics works.
When we examine applications of intelligent optimization in
Logistics, we can see that there are different ways of applying
such optimization techniques and designing an optimization
problem environment for the Logistics by thinking about
structure of the objective optimization problem. Eventually,
this paper has been a typical reference for anyone, who is new
STEP - 1: Defining the problem: the
application way, possible constraints
STEP - 2: Defining the problem: function
based or graph based?
STEP - 3: Defining the problem:
objectives - variables, contants...etc.
STEP - 3: Defining the problem:
determining the function / graph
STEP - 4: Determining the objective
intelligent algorithm
STEP - 5: Testing the optimization
STEP - 6: If the results are OK use that
structure; otherwise adjust / modify the
problem frame and return to STEP - 5
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to the subject of intelligent optimization and its application in
Logistics.
In addition to this work, the authors also think about some
additional future contributions to the associated literatures. In
this context, it is aimed to set detailed sample Logistics
problems and focus on intelligent optimization processes on the
related problems. In this way, practical sides of intelligent
optimization for Logistics will be discussed in more detail.
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