“Why Genetic Algorithms Are More Suited to Solve Certain Types of Optimization
Problems”

An Honors Thesis
by

Leslie E. Peters

California, Pennsylvania
2020

Acknowledgements
I would like to thank the Honors Program for the opportunity to work on this thesis project and
to expand my knowledge. I would also like to thank my committee for their cooperation and
help with this project; Dr. Brenton Wilburn, Dr. Jennifer Wilburn, and Prof. Loring Prest. A
special thanks to Dr. Jennifer Wilburn for the patience and time she put into holding meetings
and helping me understand certain aspects of this project.

Abstract
Some technical optimization problems that have been normally solved manually or with other
traditional techniques, can be optimized by using different advanced techniques. Techniques
have evolved to include artificial intelligence (AI) algorithms to get better results. Genetic
algorithms are a great example of one of these optimization techniques that uses AI. While
these techniques are designed to solve problems more efficiently than before, there are some
problems that are better suited to these algorithms compared to others. By analyzing
experimental data, it is possible to discern what types of problems are better solved using
genetic algorithms are better at solving. Studies that have isolated genetic algorithmic
applications have been chosen to better compare the solutions that were found, straying away
from hybridizations of any kind that could influence results and blur the line of responsibility.
Five optimization problems were analyzed to find the problems that had the best improved
results and the style best suited for genetic algorithms. These optimization problems that were
studied include: PID control tuning; traveling salesman shortest path; generation of machine
turning code; design of a wind turbine tower; and A-Mazer, a maze-solving algorithm. By
breaking down these problems and how genetic algorithms are used to enhance solutions, a
comparison can be made. It was found that problems that would have multiple trials within
traditional techniques are more suited for genetic algorithms over other optimization problems.

Table of Contents
Background ....................................................................................... Error! Bookmark not defined.
PID Control ........................................................................................ Error! Bookmark not defined.
Traveling Salesman ........................................................................... Error! Bookmark not defined.
Optimization of Machine Parameters for Tuning Operations .......... Error! Bookmark not defined.
Wind Turbine Tower ......................................................................... Error! Bookmark not defined.
A-Mazer............................................................................................. Error! Bookmark not defined.
Conclusions ....................................................................................... Error! Bookmark not defined.
References ........................................................................................ Error! Bookmark not defined.

Background
Genetic algorithms (GA) are numerical algorithms which are inspired by the biological process of
natural selection. They are designed after the biological method of how genes are passed on
throughout generations. Potential solutions to the problem represent individuals in the
population. These are simply strings of data that indicate the key parameters to define a
solution. A set of solution criteria behaves as the environment to define which solutions are
better - “more fit”. The evolutionary process consists of three primary processes: selection,
crossover, and mutation. The selection process is where the fitness of each individual is
evaluated. These strings of data progress over to the crossover stage, where individuals are
chosen at random to produce new individuals composed to shared parts of both “parents”. The
resulting string is made from the selected pair; sharing data from both. The population will then
enter the mutation phase where bits of that data will be randomly altered to create variety in
the code. With this step, new possibilities may be considered that might never have shown up
with only the selection and crossover stages. Some of these mutations may be beneficial, others
may not. The better solutions will be selected to start the selection, crossover, and mutation
process over again. These steps will be repeated until a convergence criterion is met or the
simulation is manually stopped. At times, the engineer will not be satisfied with the results after
numerous tries with the optimization and a new initial population will be constructed for reoptimization.
PID Control
One optimization problem that can be solved by genetic algorithms is PID control. Traditionally,
PID control can be tuned by an engineer to get the desired results in a system response. While
this is often an effective method, other methods were discovered to generate faster and more
accurate results, such as the genetic algorithm. PID comes in three forms of systems;
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Proportional(P), Proportional Integral (PI), and Proportional Integral Derivative (PID). PID
systems have gains that need to be adjusted to create a stable system response. P systems have
𝐾𝑝 gains, PI systems have 𝐾𝑝 and 𝐾𝑖 gains, and PID systems have 𝐾𝑝 , 𝐾𝑖 , and 𝐾𝑑 gains.
A system response is the output of a system, which has already been given a desired state by
the engineer. This desired point, the setpoint, is represented as a horizontal line across the
output graph of the system. The overshoot and undershoot of the graph, as represented below
in Figure 1, should be as small as possible for optimal results. The rise time, the time it takes to
rise from 10% to 90% of the stability condition, indicates the speed of the response. This should
also be minimized. The oscillations after reaching the setpoint should also remain bounded near
the setpoint to maintain stability and can be measured as settling time. Shorter settling time
indicates better response.
The way that a system response behaves is like a thermostat. The desired temperature would be
the setpoint and once set, the temperature would try to reach that setpoint. The temperature
might go higher than what was desired, which would be the overshoot. If it dips lower than the
desired temperature, that would be the undershoot. The thermostat shuts off and turns back on
to remain at the desired temperature, which would be the steadying oscillations that is
measured as the settling time.

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Figure 1: System Response Definitions
(Champak, Avendano, & Figueras, 2010)

For the gains in a system to be optimized, the values must be adjusted within the written code,
which is then updated in the equation. The governing equation is split off into one, two, or three
equations respectively for the different P, PI, and PID systems.
PID Original Equation:
𝑡

𝑢(𝑡) = 𝑀𝑉 (𝑡) = 𝐾𝑝 𝑒(𝑡) + 𝐾𝑖 ∫ 𝑒(𝜏)𝑑𝜏 + 𝐾𝑑
0

𝑑
𝑒(𝑡)
𝑑𝑡

Mjahed, Mostafa created a study on PID control with genetic algorithms to analyze the effects
of before and after the implementation. All three gains; 𝐾𝑝 , 𝐾𝑖 , and 𝐾𝑑 , were gathered in one
string and implemented within the genetic algorithm’s selection, crossover, and mutation

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processes. By doing this, the solution that was optimized was composed of the gains. These
gains were fed into the system to test the system response for each individual, at each iteration.
When only using traditional techniques, the results are as shown below in Figure 2. When using
the genetic algorithm, the system response is as shown below in Figure 3. The overshoot had
decreased by 14.7%, the settling time decreased by 137.7 seconds, and the rise time decreased
by 43.3 seconds. This indicates that the algorithm was capable of finding a better solution than
could have been found using traditional means.

Figure 2: Traditional Technique System Response

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Figure 3: GA System Response
Traveling Salesman
For the traveling salesman optimization problem, the goal is different than PID control. In this
problem, there are multiple locations which a salesman must visit. The best path taken to hit all
these stops in the quickest fashion is the goal. This problem would normally need to be solved
using “brute force” – checking all possible solutions. This is obviously cumbersome, so a method
capable of finding the optimal solution without having to check all possible solutions is
beneficial.
In this experiment by Hazim, Ziyad & Al-Jabbar, Abid, researchers looked at comparing the
relative time and number of operations needed to solve the problem using the genetic
algorithm versus traditional methods. Points of Duhok City were used as the locations, and the
shortest path was to be found to hit all indications regardless of roads or other obstacles.

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Excel was used to store the locations of Duhok City that were to be used to come up with
possible paths to start the genetic algorithms process. Locations without a path for Duhok City
Areas have the longitudes and latitudes shown in Figure 4. MATLAB served as the environment
for the genetic algorithm.

Figure 4: Selected Locations

Results for this genetic algorithm showed that the algorithm was capable of converging to the
same global optimum solution for each trial, even though each trial started from a different
population of solutions, and ultimately took a different number of generations to converge.
Time to converge ranged from 2.49 seconds to 7.43 seconds – vastly shorter than a brute force
approach, while yielding the equivalent result. The optimal solution obtained in each trial is
shown in Figure 5 below.
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Figure 5: Optimal Path Result

Optimization of Machine Parameters for Tuning Operations
One common production machine for manufacturing is a lathe. A lathe is used to rotate material
into which a cutting tool is driven to remove material. This is also called machine turning. The
machines are often automated using Computer Numerical Cutting (CNC) technology. When
performing CNC cutting, the machine must be programmed as to where and how to cut the
material. How the material is cut is as important as what cuts to make. Proper tool positioning,
selection of appropriate spindle speed, feed rate, and other cutting parameters have a strong
impact on the quality of the finished part, the speed at which the part can be produced, and
how long the tooling will last. These economic factors make proper selection of these
parameters extremely important.
Traditionally, “rules of thumb” guidelines are used to select these parameters, based on the
material being cut, the type of cut being performed, etc. If this is instead preformed using a
genetic algorithm, a more efficient result can be achieved.
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A series of constraints for the cutting parameters based on minimizing machining cost are
mathematically derived and used within the genetic algorithm to provide the environment.
MATLAB was used to solve as a programming base. The goal is to acquire more accurate
boundaries for the cutting process in machining. This saves money, cuts down time, an allows
the tools to last longer.

𝐶 = 0.3 +

4.6
+ 1.72 ∗ 10−11𝑉𝑐4.55𝑓 0.67
𝑉𝑐 𝑓

The C stands for machining cost measured in euros and 𝑉𝑐 𝑓 are the constraints. By using these
variables, an equation for machine turning can be found. The code for the genetic algorithm will
enforce the constraints.
𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐶 = 𝑡𝑢𝑟𝑛𝑖𝑛𝑔_𝑐𝑜𝑠𝑡(𝑥)
𝐶 = 0.3 +

4.6
+ 1.72 ∗ 10−11 ∗ 𝑥 (1)4.55 𝑥(2)0.67 ;
(
)
𝑥 1 ∗ 𝑥(2)

𝑒𝑛𝑑
The nonlinear constraints also need to be taken into consideration.

Once this code is made, MALAB can be used to execute and go through the genetic process to
find the optimization solution.

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The genetic algorithm takes 60 seconds to generate results for a total of 8 trials. The solution
created was 𝐶𝑚𝑖𝑛=0.335519 (euros), 𝑣𝑐=14.395 m/min and f=9.0 mm/rev.
Wind Turbine Tower
Genetic algorithms can also be used to reduce the size of the wind turbine towers. This is valued
because it, in turn, lowers cost. Shigeo Yoshida experimented to create an optimization program
from the genetic algorithm which determines the diameter of the whole tower, thickness of the
wall, and position of flanges and doors to the navigation lights when facing certain factors.
When creating a wind turbine tower, many factors and guidelines are made that interfere with
the design and make of the tower. To determine new guidelines to go by, using the genetic
algorithm, there are a few steps that had to be taken. The materials, structure, Building
Standard Law of Japan (BSL) force conditions, general guidelines, genetic algorithm limits, and
other needs had to be considered along with the calculated load that was determined from the
original tower and the aeroelastic. From this, IEC61400-1/Germanischer Lloyd (IEC/GL) forces
from the design and safety variables were found.
These can then find the elements of the optimization program, which includes multiple factors
of the tower. The genetic algorithm uses a solution domain that has be converted to biological
terms and a fitness equation to use on this domain. This equation, along with modal analysis for
1st to 3rd bending forms, BSL forces, stability, fatigue damage, diameter distribution, and location
of flanges and doors to navigation lights are what are considered for the optimization program
and help with the design. The program can now find the necessary limits for the new tower.

Shown in Figure 6, is the relationship that the progress of iterations in the genetic algorithm had
on fitness.
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Figure 6: Performance of Model per Generation

The genetic algorithm was able to take different parameters in the tower and adjust to find the
optimal results for each specific variation. Tower A; as shown in Figure 7, and Tower G; in Figure
8, are the first and last results respectively. Tower A through Tower G have different
parameters.

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Figure 7: Tower A Results

Figure 8: Tower G Results

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A-Mazer
For this optimization problem, it is much like the traveling salesman in that the best route is to
be determined. The difference being, there are only two location points. More thought is
needed for this experiment on the part of the genetic algorithm, in the sense that there are
walls in place that act as barriers to be eliminated in one spot. Meaning, one wall needs to be
removed to make the maze functionable and the best option needs to be determined by the
genetic algorithm.
Mazes are generated with random entry and exit locations for each new maze. The Genetic
Algorithm must analyze the possible routes and find the shortest path.
Like in the previous problems, the solution goes through selection, crossover, and mutation
processes. The GA also has the specific, tailored, fitness equation that is applied. Genetic
algorithms can accommodate different types of problems.
An example of a finished maze completed with genetic algorithms is shown below in Figure 8.
While the genetic algorithm does not always find the best solution, it finds better paths
compared to other tried applications.

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Figure 10: Maze Solution Example

Conclusions
While genetic algorithms can often be used to optimize at least one element of a problem, they
have various strengths and limitations. Genetic algorithms have an evolutionary design that
makes optimization problems a good match, there are some optimization problems that are
better suited for genetic algorithms. Other “decision making” algorithms might be better suited
for the other optimization problems. Genetic algorithms show promising results when facing
these optimization problems, but some are more complex than others. Genetic algorithms are
better suited for optimization problems that are harder to determine using traditional analytic
techniques.

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References
•

Choubey, Nitin. (2012). A-Mazer with Genetic Algorithm. International Journal of
Computer Applications (0975 – 8887). 58. 48-54. 10.5120/9378-3886.

•

Hazim, Ziyad & Al-Jabbar, Abid. (2020). Using Genetic Algorithm to Solve Travelling
Salesman Optimization Problem Based on Google Map Coordinates for Duhok City
Areas.

•

Mjahed, Mostafa. (2013). PID Controller Design using Genetic Algorithm technique.

•

PETKOVIC, D., & RADOVANOVIC, M. (2013). Using Genetic Algorithms for Optimization
of Turning Machining Process. Journal of Engineering Studies & Research, 19(1), 47–55.

•

Shigeo Yoshida. (2006). Wind Turbine Tower Optimization Method Using a Genetic
Algorithm. Wind Engineering, 30(6), 453.

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