Cost and Density Evaluation Function Application, for Optimal

Biodiesel Mixtures by Genetic Algorithm Implementation

VASILEIOS VASILEIADIS1, MARIOS-ERRIKOS KYRIKLIDIS2,*, CHRISTOS KYRIKLIDIS1,

EIRINI TERZOPOYLOY1, CONSTANTINOS G. TSANAKTSIDIS1

1Department of Chemical Engineering,

University of Western Macedonia,

Kila, GR-50100, Kozani,

GREECE

2Department of Regional Development and Cross Border Studies,

University of Western Macedonia,

Kila, GR-50100, Kozani,

GREECE

*Corresponding Author

Abstract: - The current document presents a fresh method for addressing the optimization challenges

concerning fuel mixtures in the production of Biodiesel. Given the rising concerns over diesel emissions and

the associated expenses, there's a growing interest in exploring alternative fuel options. Traditional

desulphurization methods are time-consuming and require substantial financial investments. Conversely,

Biodiesel offers a promising solution as it's derived from renewable resources and is environmentally

sustainable. This study introduces an enhanced genetic algorithm that assesses the proportions of components

within a fuel mixture blend, aiming to create optimal combinations for Biodiesel production. Apart from cost

considerations, the density of the fuel, a key physicochemical characteristic, is pivotal in determining its

suitability for widespread use and commercialization. Rigorous experimentation has resulted in highly precise

Biodiesel blends, suggesting an optimal fuel solution for each specific set. For instance, in Set 1, Biodiesel was

composed of 75.031% diesel and 24.969% biodiesel, with a mixture cost of 1.6975 €/l and a density of 0.8355

g/ml. In Set 2, the fuel mixture consisted of 75.016% diesel and 24.984% biodiesel, with a cost of 1.6977 €/l

and a density of 0.8366 g/ml. Notably, the new Biodiesel fuels are significantly cheaper, costing 15.13% less

(Set 1) and 15.12% less (Set 2) than diesel (priced at 2.0000 €/l) and are proposed between 1.5 * 109 evaluated

biodiesel mixtures.

Key-Words: - Ideal combinations of biodiesel blends, challenges in finding the best solutions, algorithms based

on genetic principles, computational methods inspired by evolutionary processes, optimization

problems, environmentally friendly biodiesel, experimentation through simulations.

Received: June 27, 2023. Revised: March 21, 2024. Accepted: April 23, 2024. Published: May 27, 2024.

1 Introduction

Over recent decades, as society has progressed,

there has been a steady rise in energy demands. The

dwindling availability of diesel reserves, coupled

with the environmental repercussions of diesel

consumption such as harmful emissions, alongside

global crises, have prompted extensive exploration

into alternative fuel sources by numerous

researchers, [1], [2]. Biodiesel emerges as a

renewable energy option, offering several

environmental benefits: it is non-toxic,

biodegradable, and clean, devoid of aromatic

compounds. Furthermore, it reduces noticeably

emissions such as sulfur dioxide, carbon monoxide,

and hydrocarbons that remain unburnt and

suspended of fine particles originating from diesel

engine combustion, as various testifies reports, [3],

[4], [5], [6], [7]. On the contrary, the use of diesel

entails the presence of sulfur, which mainly

contributes to harmful oxide emissions. Although

her process of Diesel removal is time-consuming

and requires significant investment, the most

effective approach to reducing emissions is to boost

fuel by blending diesel with biodiesel. This

approach ensures that the fuel maintains its quality

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Vasileios Vasileiadis, Marios-Errikos Kyriklidis,

Christos Kyriklidis, Eirini Terzopoyloy,

Constantinos G. Tsanaktsidis

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as long as it significantly reduces sulfur content.

Another critical aspect regarding fuel characteristics

is density, which has a decisive role in determining

fuel performance in compression engines (CI), [7],

[8], [9]. The experimental reduction process of these

mixes in the labs is time-consuming and accurate, as

the researchers reported at-length analyses to

achieve the optimal balance between fuel quality

and cost, [10].

Advanced methodologies such as sophisticated

methods, approaches inspired by natural processes,

algorithms for learning by machines, and

computational strategies influenced by evolution

offer sophisticated solutions to complex

optimization challenges, yielding near-optimal

outcomes of high quality. Consequently, operational

research (OR) endeavors heavily rely on the

utilization and advancement of these techniques,

[11], [12], [13], [14], [15].

Although many studies are concerned with

improving the biodiesel production process, none

emphasize finding the best combination of raw

materials for its production. The current study deals

with the optimal combination of the basic raw

materials (Diesel and biodiesel are comprised of an

equal combination of animal-derived fats and plant-

derived oils, with each contributing 50% to the

overall composition).

The effectiveness of this approach is contingent

upon two main factors: a) innovative modeling

techniques, particularly in terms of function

evaluation modeling enhancements, and b) the

precise definition and fine-tuning of the genetic

algorithm. The current approach has yielded

significant results through experimental simulations,

including 1) minimizing experimental costs, 2)

reducing experiment durations, 3) enhancing both

cost and density through minimization of the

evaluation function, and 4) promoting the

development of ecologically sustainable fuels.

Now, laboratory researchers have access to this

innovative tool for decision-making, facilitating the

advancement of optimal fuel formulations.

Employing a genetic algorithm, it rapidly generates

optimal fuel mixtures for laboratory

experimentation, sifting through a vast array of

approximately 750 million different combinations

tested in each experimental set. The benefits of this

method or strategy are evident in streamlining the

mixture production process, particularly when the

newly developed biodiesel proves to be more

appealing than competing fuels.

The rest of the document follows this structure:

In Section 2, the mathematical groundwork is laid

out for addressing the fuel blending challenge.,

detailing the constraints imposed by ingredient

availability. Section 3 covers the key

methodological aspects of the suggested approach

and aims to provide a deeper insight into the

operational principles of the algorithm employed.

Lastly, the concluding segment offers a summary of

key findings and noteworthy observations.

2 Fuel Mixture Problem

The issue or challenge concerning fuel blends is a

subject of extensive investigation within the

research community due to its complex and

dynamic nature. Given the practical challenges

associated with this practical or tangible issue, it's

impractical to physically generate every conceivable

combination via laboratory experimentation

experiments due to their sheer volume, which would

incur significant costs and lengthy execution times.

The current approach offers a solution by allowing

for flexible management of mixture production

through simulation processes, thereby mitigating the

challenges posed by experimentation.

With the implementation of the current

Evolutionary Algorithm (GA), each formulation

undergoes a full analysis of its performance,

ensuring the identification of specific and high-

quality fuel mixtures. This approach to work

effectively suggests an excellent solution within a

concise experimental time frame. In the

minimization of the fuel problem fitness function,

the values are achieved through a mathematical

function that addresses multiple targets of fuel

production simultaneously.

2.1 Reducing the Overall Function Value of

the Mixture to Its Lowest Possible Level

(min TMFV)

The value of the function for the entire set mixture

of raw materials represented as "i", is calculated by

combining two weighted compositions. The first

sum (w_(1)) involves multiplying the normalized

cost per liter of each ingredient by its respective

percentage in the mixture, while the second sum

(w_(2)) is the result of multiplying the normalized

density per liter of each ingredient by its percentage

in the mixture.

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The optimization problem regarding raw

materials aims to reduce the function value to its

minimum of the new biodiesel mixture, denoted as

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Christos Kyriklidis, Eirini Terzopoyloy,

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TMFV (Total Mixture Function Value), represented

by the equation: min TMFV (2).

The constraints for the problem are as follows:

The percentage of each ingredient must fall

within the minimum and maximum allowable

values.

The cost of each ingredient, is represented by c1

for diesel and c2 for biodiesel.

The density of each ingredient, is indicated by

d1 for diesel and d2 for biodiesel.

The weights assigned to the ingredients, ensure

that their sum equals 100%.

3 Algorithmic Framework

Various industries have adopted nature-inspired

methodologies, yielding superior outcomes. Genetic

algorithms, a prominent example, draw from

evolutionary computation principles, initially

introduced by [16]. In this study, a Genetic

Algorithm (GA) evolutionary approach is applied to

tackle the biodiesel mixture problem (Figure 1).

These algorithms employ choice, crossover, and

mutation operations to gradually develop the genetic

material of individuals within a group over

successive generations through iteration.

Fig. 1: Genetic Algorithm Approach

3.1 Reducing the Overall Sum of the

Function's Values Across the Mixture

(min TMFV)

Consider an illustration of a chromosome

representing a mixture composed of two ingredients.

In such examples, the total percentage of ingredients

always sums up to 100%. For instance, Diesel might

constitute 76.22% of the mixture, while Biodiesel

makes up the remaining 23.78%.

3.2 Reducing the Overall Sum of the

Function's Values Across the Mixture

(min TMFV)

The generation process is split into two phases.

Firstly, the initial generation is formed by randomly

creating feasible mixtures. Secondly, for subsequent

generations in the second phase, chromosome

production comprises three separate steps.

a) Part 1: The top 10% of chromosomes from the

present iteration of the population, deemed as the

best mixtures (TOP Mixtures), are directly

transferred toward the succeeding iteration.

b) Part 2: The following 70% of solutions are

comprised of chromosomes generated through the

crossover operator, which combines genetic

information from two parent chromosomes.

c) Part 3: The remaining 20% of chromosomes are

generated through mutation, introducing small

random changes to the genetic makeup of

chromosomes, akin to how the initial population

was formed.

The process involves creating fuel mixtures by

assigning percentages of diesel and biodiesel to each

chromosome. Subsequently, a fitness function is

applied to assess each mixture (chromosome) based

on criteria such as cost and density, allowing for the

ranking of all mixtures. Solutions generated through

crossover and mutation operators adhere to specific

ingredient percentage ranges (minimum % to

maximum %), ensuring that the total percentage of

ingredients always equals 100%. Importantly, the

proposed approach only yields feasible solutions,

ensuring that every potential solution is considered

in the evaluation process.

Following the creation of the initial population,

a framework known as ± IPLS, derived the

proportions derived from the top-performing

chromosome have been included. This framework,

introduced by [14], enhances the optimization

process by centering it around the best chromosome

from the previous generation. A specific range of

values for IPLS (e.g., 5% - 10%) a value called

IPLS is established, and for every generation, a

fresh IPLS value is chosen at random (for instance,

Generation 1, IPLS: 6%; Generation 2, IPLS: 9%; ...

Generation 100, IPLS: 10%). Through extensive

experimentation, involving over 100,000

simulations, all Genetic Algorithm (GA) parameters

have been meticulously selected by [12]. These

parameters have proven to be highly effective and

remain competitive today, consistently yielding

superior results.

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3.3 Benchmark Experiments

Assessing the effectiveness of the proposed Genetic

Algorithm (GA) method was conducted through two

distinct sets of experiments, categorized based on

the temperature of the mixtures: 5°C, 10°C, 15°C,

20°C, and 25°C (referred to as sets hereafter):

(a) Set 1 - Priority on Cost: The importance

assigned to the weight value (w_(1)) assigned to the

cost aspect in the Evaluation Function TMFV was

set to 50% or higher.

(b) Set 2 - Priority on Density: The significance

attributed to the weight value (w_(2)) attributed to

the density aspect in the Evaluation Function TMFV

was also set to 50% or higher.

150 individuals, evolving over 200 generations. The

ingredient costs were predetermined: diesel priced at

2.0000 €/liter and biodiesel at 0.7901 €/liter.

Furthermore, the ingredient densities were

established at diesel 0.8191 g/ml and biodiesel

0.8855 g/ml at 5°C. The ingredient densities varied

depending on temperatures ranging from 5°C to

25°C.

(d) In each subsequent generation, the top 10% of

chromosomes from the previous generation, based

on their performance, were directly carried over.

(e) The crossover operator produced 70% of the

population, with the IPLS value selected randomly

for each generation, fluctuating within a range of

±5% to 10%.

(f) The mutation operation was implemented on the

remaining 20% of the chromosome set.

(g) Every experiment involved conducting 1000

separate simulations for each Set and temperature

variation (for instance, Set 1 - 5°C - 1000 iterations,

Set 1 - 10°C - 1000 iterations, ..., Set 2 - 25°C -

1000 iterations).

Biodiesel, functioning as the secondary

component, is sourced equally from two primary

origins: The mixture contains an equal amount of fat

from animal and plant origins. The expenses

associated with plant sources, specifically rapeseed

oil and sunflower oil, can be accessed globally

through the [17], as well as locally in Greece via the

[18].

Within Greece, 15 companies are tasked with

collecting animal fat and processed olive oil. The

prices of these components are shaped by refinery

demands, consequently impacting the ultimate price

of biodiesel.

The groups of experiments are categorized

according to temperature ranging from 5°C to 25°C.

Set 1 emphasizes cost (w1 ≥ 50%), while Set 2

emphasizes density (w2 ≥ 50%). For instance, when

w1 equals 70% and w2 equals 30%, the focus is on

cost, indicating that cost is considered more

significant than density.

 Set 1: Half and half (50% / 50%), Sixty-

forty (60% / 40%), Seventy-thirty (70% /

30%), Eighty-twenty (80% / 20%), Ninety-

ten (90% / 10%)

 Set 2: Equal split (50% / 50%), Forty-sixty

(40% / 60%), Thirty-seventy (30% / 70%),

Twenty-eighty (20% / 80%), Ten-ninety

(10% / 90%)

Additional experimental details are provided:

Diesel is priced at 2.000 €/l, while biodiesel costs

0.7901 €/l. Additionally, the density ranges from

0.8191 g/ml to 0.8855 g/ml, varying with

temperature. Moreover, the percentages of

ingredients in mixtures are specified, with diesel

ranging from 1% to 99% and biodiesel from 1% to

30%. These values reflect the availability and actual

prices during the laboratory experimentation period.

3.4 Experiments Results

Initially, the performance of the suggested Genetic

Algorithm (GA) was assessed in Set 1. This

involved conducting 25,000 independent

simulations for each combination of temperatures

(ranging from 5°C to 25°C) and weights (w1 and

w2). The total duration of these simulations

amounted to 3,536.29 seconds (equivalent to

approximately 59.41 minutes or roughly 1 hour).

Figure 2 contains information about the

biodiesel evaluation criteria of Set 1 and Set 2

experiments at a temperature of 5°C. For all w1 and

w2 combinations of priority on cost (w1 ≥ 50%) and

for all w1 and w2 combinations of priority on

density (w2 ≥ 50%) are presented the cost and the

density of the evaluated fuel mixtures. For example,

in group w1 = 90% and w2 =10%, the blue column

refers to the cost criterion = 1.6981€/l, which is part

of Set 1 (priority on cost). On the other hand, the

yellow column (w1 = 10% and w2 =90%) concerns

the cost criterion = 1.7787 €/l, as part of Set 2

(priority on density).

The ideal fuel blend in Set 1, at a temperature of

5°C with weights distributed evenly between w1

and w2, consists of 75.031% diesel and 24.969%

biodiesel. The Total Mixture Function Value

(TMFV) is recorded at -0.0727, with the mixture

costing 1.6975 €/l and having a density of 0.8355

g/ml (Figure 2).

Set 2 provides details regarding the optimal

mixture derived from 1000 independent simulations,

resulting in a total of 25 optimal mixtures. The

evaluation is centered on minimizing the Total

Mixture Function Value (TMFV). With an increase

in the value of w2, the TMFV also increases,

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Vasileios Vasileiadis, Marios-Errikos Kyriklidis,

Christos Kyriklidis, Eirini Terzopoyloy,

Constantinos G. Tsanaktsidis

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indicating an emphasis on the density criterion over

the cost criterion. Although the ingredients'

percentages, optimal mixture costs, and densities

vary slightly, they remain within proximity as

indicated earlier.

Figure 3 contains information about the

biodiesel evaluation criteria of Set 1 and Set 2

experiments at a temperature of 20°C. For all w1

and w2 combinations of priority on cost (w1 ≥ 50%)

and for all w1 and w2 combinations of priority on

density (w2 ≥ 50%) are presented the cost and the

density of the evaluated fuel mixtures. For example,

in group w1 = 80% and w2 =20%, the blue column

refers to the cost criterion = 1.6979€/l, which is part

of Set 1 (priority on cost). On the other hand, the

yellow column (w1 = 20% and w2 =80%) concerns

the cost criterion = 1.7037 €/l, as part of Set 2

(priority on density).

The best fuel blend identified in Set 2, at a

temperature of 20°C with a distribution of 10% for

w1 and 90% for w2, comprises 75.016% diesel and

24.984% biodiesel. The Total Mixture Function

Value (TMFV) is recorded at -0.8146, with the

mixture costing 1.6977 €/l and having a density of

0.8366 g/ml (Figure 3).

4 Conclusion

This paper introduces a genetic algorithm approach

aimed at offering the best possible resolutions for

the fuel-related matter blending issue. The key

novelty lies in determining viable proportions for

diesel and biodiesel, sourced equally from 50%

animal fat and 50% vegetable sources, are

determined, resulting in enhanced fuel formulations.

The efficiency of the IPLS mechanism enables

decision-makers to explore the vicinity of optimal

ingredient percentages effectively.

Moreover, the Total Mixture Function Value

(TMFV) is utilized to evaluate the new biodiesel

mixtures to signify the creation of competitive fuel,

taking into account the accessibility of ingredients.

This evaluation process emphasizes two crucial fuel

parameters: cost and density. The priorities assigned

to "Emphasis on Cost" and "Emphasis on Density"

during the evaluation of experimental fuel are

determined by the weights w1 and w2, respectively.

The investigation of the new ideal biodiesel

blend involved extensive experimentation, covering

150 million mixtures. Two sets were identified, each

spanning temperatures ranging from 5°C to 25°C:

Set 1, focused on cost optimization, and Set 2,

prioritizing density optimization.

Fig. 2: The cost and density of the optimal mixtures

at a temperature of 5°C

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Christos Kyriklidis, Eirini Terzopoyloy,

Constantinos G. Tsanaktsidis

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Fig. 3: The cost and density of the optimal mixtures

at a temperature of 20°C

In Set 1, at a temperature of 5°C with equal

emphasis on cost and density (w1 = 50%, w2 =

50%), the optimal mixture comprised 75.031%

diesel and 24.969% biodiesel, with a TMFV of -

0.0727, a cost of 1.6975 €/l, and a density of 0.8355

g/ml. In Set 2, at a temperature of 20°C with an

emphasis on density (w1 = 10%, w2 = 90%), the

optimal mixture consisted of 75.016% diesel and

24.984% biodiesel, yielding a TMFV of -0.8146, a

cost of 1.6977 €/l, and a density of 0.8366 g/ml.

Compared to diesel priced at 2.0000 €/l, the new

biodiesel fuels are approximately 15.13% (Set 1)

and 15.12% (Set 2) cheaper, offering competitive

pricing, lower sulfur content, and reduced pollutant

emissions upon consumption.

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Constantinos G. Tsanaktsidis

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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DOI: 10.37394/232015.2024.20.23

Vasileios Vasileiadis, Marios-Errikos Kyriklidis,

Christos Kyriklidis, Eirini Terzopoyloy,

Constantinos G. Tsanaktsidis

E-ISSN: 2224-3496

232

Volume 20, 2024