An Application of Intelligent Algorithms in Solving Chemistry Problems.
الموضوعات : فصلنامه ریاضی
Hossein Jafari
1
(Young Researchers and Elite Club, Arak Branch, Islamic Azad University, Arak, Iran.)
Setareh Salehfard
2
(Department of Computer Science, Arak Branch, Islamic Azad University, Arak, Iran.)
Masoumeh Danesh Shakib
3
(Department of industrial management, College of management and accounting, Qazvin branch, Islamic Azad university, Qazvin, Iran.)
الکلمات المفتاحية: Genetic Algorithm, Chemistry, Reaction Equilibrium, Mathematics and Computer,
ملخص المقالة :
Chemistry is undoubtedly the most practical science in our life, if we pay attention to the nature around us from the moment we wake up until the day ends, we will find that at the moment of the day and night, we are surrounded by different chemicals. And we have work. In fact, many of our daily activities are related to chemical processes. This has caused the expansion of chemistry and has caused the emergence of various problems. This study aims to analyze a classical chemistry problem known as the chemical reaction equilibrium, which has no uniform solution in different scenarios. In other words, different types of chemical reactions may require diverse methods for establishing equilibrium. This paper proposes a simple system for each chemical reaction through the law of conservation of mass (LCM) and basic mathematical concepts. Optimization algorithms (e.g., the genetic algorithm) are then employed to find a solution to this system.
M. Amirfakhrian and S. Fayazzadeh/
, xx -xx (201x) xxx-xxx.
An Application of Intelligent Algorithms in Solving Chemistry Problems
Received: 3 March 2011; Revised: 18 December 2011; Accepted: 11 January 2012.
Abstract. Chemistry is undoubtedly the most practical science in our life, if we pay attention to the nature around us from the moment we wake up until the day ends, we will find that at the moment of the day and night, we are surrounded by different chemicals. And we have work. In fact, many of our daily activities are related to chemical processes. This has caused the expansion of chemistry and has caused the emergence of various problems. This study aims to analyze a classical chemistry problem known as the chemical reaction equilibrium, which has no uniform solution in different scenarios. In other words, different types of chemical reactions may require diverse methods for establishing equilibrium. This paper proposes a simple system for each chemical reaction through the law of conservation of mass (LCM) and basic mathematical concepts. Optimization algorithms (e.g., the genetic algorithm) are then employed to find a solution to this system.
Keywords: Chemistry, Reaction Equilibrium, Mathematics and Computer, Genetic Algorithm.
1.Introduction 2.Problem Statement 3.Operations Research 4.Phases of Operations Research 5.Genetic Algorithm 6.Presentation the Proposed Approach 7.Conclusion |
1.Introduction
Chemistry is a branch of science that analyzes elements, compounds composed of atoms, molecules, and ions, chemical structures, properties and behaviors of substances, and their mutual effects as well as changes of a substance in reactions with other substances [1]. A chemical reaction is a process that results in the interaction between chemical substances (atoms). The substances participating in the chemical reaction are called reactants, whereas the substances produced during the reaction are referred to as products [2].
Since chemical reactions are typically characterized by a specific chemical change, the products are generally different from the reactants [3]. Both reactants and products are indicated by their chemical formulas. Reactants are usually placed on the left side, whereas products are on the right side. As an example, the combustion of methane in the presence of oxygen is expressed as below [4]:
(1)
This equation represents an irreversible reaction in which one methane molecule reacts with two oxygen molecules to generate one carbon dioxide molecule and two water molecules. In the first step of introducing a chemical equation, the equation is typically not balanced [5]. Consider the following chemical equation as an example:
(2)
Evidently, the above equation is not balanced. For instance, there is one carbon atom on the right side, whereas there are seven atoms on the left. In fact, the number of atoms in the reactants is not equal to the number of atoms in the products [6].
2.Problem Statement
There is no uniform method for balancing chemical reactions. In simple terms, when it comes to balancing specific reactions, specific algorithms should be tailored to those reactions (similar reactions), something which is not particularly desirable [7].In this regard, a powerful tool is the utilization of mathematical optimization techniques of operations research (OR). In fact, this study aims to propose a unified approach to balancing all chemical reactions through a mathematics-based system and the genetic algorithm (GA), which will be further discussed.
3.Operations Research
Operations research (OR) is a field of applied mathematics and a key tool for engineering sciences, focusing on the study of problem analysis and solutions. The process of operations research can be divided generally into the following five stages [8]:
1. Problem definition
2. Mathematical modeling (expressing variables of the real problem in a mathematical language)
3. Model implementation
4. Testing solutions and assessing their success or failure
5. Real-world problem solving based on valid model outputs
Operations research shares significant similarities and overlaps with other decision-making methodologies such as statistical analysis, management science, game theory, optimization theory, artificial intelligence, and network analysis.
All operations research studies have three common features [9]:
Optimization: The objective of operations research is to achieve the best possible performance under arbitrary conditions. An optimization process includes comparing and constraining the number of possible solutions.
Simulation: In order to analyze potential solutions, a model of the problem is constructed prior to execution on the real problem.
Statistics and Probability: Mathematical algorithms and data are analyzed to better perceive the problem and its probable risks. Statistical and probabilistic processes enhance the credibility of predictions and potential solutions.
The significance of operations research lies in its high efficacy in solving complex problems across various fields. Operations research equips managers and decision-makers in organizations with several powerful decision-making tools. Experts in this field can assist different companies in collecting more comprehensive data for problem solving, considering all available options, exploring all probable outcomes, and estimating risks [10]. The capabilities of operations research surpass those of ordinary data analysis software and tools. These capabilities benefit from high flexibility in adapting to processes across different domains. Hence, the applications of operations research are not limited to a particular field and are very broad in scope [11].
4.Phases of Operations Research
In operations research, there are always three subsequent phases that must be undertaken:
Phase One: Problem Definition
The first stage of operations research is dedicated to defining the objectives and scope of the target problem. This stage involves the participation of all members of the operations research team. The main objective is to identify three crucial elements in the decision-making problem [12]:
1. Describing decision-making methods and alternative options
2. Determining the objective function
3. Specifying the constraints
Phase Two: Modeling
The modeling phase is aimed at transforming the real-world problem into mathematical relations. If the resultant model conforms to one of the standard models (e.g., linear programming), the problem can be solved through existing algorithms. In cases where the mathematical relationships are complex, simplification techniques or simulation methods are employed to solve the problem. In some instances, a combination of mathematical models, heuristics (empirical), and simulation models is employed to reach a solution [12].
Phase Three: Model Solution
The simplest phase of operations research involves solving the model through optimization algorithms. In fact, a key aspect of this phase is sensitivity analysis conducted to gather additional information regarding how the optimal solution changes with variations in different parameters. If it is impossible to estimate the model parameters accurately, sensitivity analysis becomes crucial. Therefore, it is essential to study the behavior of an optimal solution in the vicinity of estimated parameters [12].
5.Genetic Algorithm
The genetic algorithm is a search technique in computer science. It is employed to find approximate solutions to optimization and search problems. The genetic algorithm is a special evolutionary method that utilizes the evolutionary biology principles such as inheritance and mutation. This algorithm was initially introduced by John Henry Holland. In fact, genetic algorithms use the principles of Darwinian natural selection to find an optimal formula for prediction or pattern matching [13]. In artificial intelligence, the genetic algorithm is a programming technique that utilizes genetic evolution as a problem-solving pattern. The problem to be solved has some inputs that are transformed into solutions through a process patterned from genetic evolution. The solutions known as candidates are then evaluated with an evaluation function. The algorithm ends once the termination conditions are met. Generally, a genetic algorithm is an iterative method with many of its components selected as random processes [14].The operators of this algorithm are presented as below.
5.1.Evaluation Mechanism
The fitness function is obtained by applying appropriate transformations to the objective function, which is the function to be optimized. This function evaluates each string and assigns it a numerical value that indicates its quality. As the quality of the solution string increases, both the fitness value and the probability of participating in generating the next generation will increase [15].
5.2.Crossover Mechanism
The most important operator in the genetic algorithm is the crossover operator. Crossover is a process whereby the chromosomes of the old generation are mixed and combined to generate a new generation of chromosomes. The pairs selected as parents in the selection process exchange their genes in this step, generating new members [16].
5.3.Mutation Mechanism
Mutation is another operator that generates other possible solutions. In the genetic algorithm, when a member is created in the new population, each of its genes undergoes mutation with a certain probability. In mutation, a gene may be removed from the set of population genes, or a gene that has not existed in the population yet may be added [16].
5.4.Different Steps in the Genetic Algorithm
Figure (1) demonstrates the flowchart of the main steps in the genetic algorithm.
Figure (1): Genetic Algorithm Flowchart [16].
Figure (2) illustrates the structure of a chromosome. Figure (3) depicts an example of a crossover operator, and Figure (4) presents an example of a mutation operator.
Figure (2): Structure of a Chromosome [17].
Figure (3): Example of a Crossover Operator [17].
Figure (4): Example of a Mutation Operator [17].
6. Presentation the Proposed Approach
The proposed approach in this research involves the use of a genetic algorithm and a new fitness function for balancing chemical reactions. The different stages of this approach are outlined below step by step:
Step (1): Start.
Step (2): Define a suitable fitness function for the chemical reaction.
Step (3): Create an initial population of chromosomes (at this stage, genes are initialized randomly with natural numbers).
Step (4): Generate a new population of chromosomes using crossover and mutation operators and the current generation.
Step (5): Select the top chromosomes and remove the rest from the new population.
Step (6): If the fitness function value is zero, proceed to Step (7), otherwise, go back to Step (4).
Step (7): Display the optimal solution.
Step (8): End.
In the following discussion, the proposed approach will be presented and analyzed through several numerical examples. The solution process will then be described through the genetic algorithm (GA).
Numerical Example (1)
In this example, the goal is to balance the chemical reaction of heptane (
) with oxygen through the genetic algorithm.
First, the unknown coefficients of the reaction are assigned as follows:
(3)
The goal is to find non-zero values for 
so that the chemical reaction under investigation can be balanced.
The number of carbon atoms (
) must be equal on both sides of the reaction, which is expressed mathematically as below:
(4)
The number of hydrogen atoms (
) must be equal on both sides of the reaction, which is expressed mathematically as below:
(5)
The number of oxygen atoms (
) must be equal on both sides of the reaction, which is expressed mathematically as below:
(6)
Now, a descriptive system for the problem is presented as follows:
(7.1)
(7.2)
(7.3)
(7.4)
To solve the above-mentioned descriptive system, a fitness function can be expressed as:
(8)
The genetic algorithm is aimed at finding suitable values for the variables 
that minimize the value of 
(or more precisely, equal to zero).
Adjusting the Parameters of the Genetic Algorithm:
The initial population size for the genetic algorithm was set to 25.
The crossover percentage for the genetic algorithm was set to 50.
The mutation percentage for the genetic algorithm was set to 50.
The stopping criterion for the algorithm is the attainment of a zero value for .
Execution of the Genetic Algorithm:
Figure (5) shows the performance of the genetic algorithm in balancing the chemical reaction under investigation. Accordingly, the GA managed to balance the mentioned reaction in the 10thgeneration (10thiteration).
Figure (5): Performance of the Genetic Algorithm in Balancing the Chemical Reaction
The chromosome associated with the optimal solution is 
. Hence, the balanced reaction can be written as follows:
(9)
To check the validity of the answer obtained from the genetic algorithm, the number of atoms on the left and right sides of the chemical reaction under investigation and comparison are placed in Table(1).
Table(1): Number of atoms on the left and right sides of the chemical reaction
Atom | Number of atoms on the left side of the chemical reaction | Number of atoms on the right side of the chemical reaction | Is the balance in place? |
C | 7 | 7 | Yes |
H | 16 | 16 | Yes |
O | 22 | 22 | Yes |
According to Table(1), it can be said that the answer obtained is valid.
Numerical Example (2)
In this example, the aim is to balance the following chemical reaction through the genetic algorithm:
(10)
A descriptive system can be presented for the problem as follows:
(11.1)
(11.2)
To solve the above descriptive system, a fitness function can be expressed as below:
(12)
Figure (6) depicts the performance of the genetic algorithm in balancing the chemical reaction under investigation. According to this figure, the GA managed to balance the mentioned reaction in the 6thgeneration (6thiteration).
Figure (6): Performance of the Genetic Algorithm in Balancing the Chemical Reaction
The chromosome associated with the optimal solution is 
. If these numbers are divided by three, the balanced reaction can be written as follows:
(13)
To check the validity of the answer obtained from the genetic algorithm, the number of atoms on the left and right sides of the chemical reaction under investigation and comparison are placed in Table(2).
Table(2): Number of atoms on the left and right sides of the chemical reaction
Atom | Number of atoms on the left side of the chemical reaction | Number of atoms on the right side of the chemical reaction | Is the balance in place? |
Fe | 2 | 2 | Yes |
Cl | 6 | 6 | Yes |
According to Table(2), it can be said that the answer obtained is valid.
Numerical Example (3)
In this example, the aim is to balance the following chemical reaction through the genetic algorithm:
(14)
To solve the above descriptive system, a fitness function can be expressed as below:
(15)
Figure (7) shows the performance of the genetic algorithm in balancing the chemical reaction under investigation. Accordingly, the GA managed to balance the mentioned reaction in the 11thgeneration (11thiteration). The GA parameters in this example are the same as in the Numerical Example (1).
Figure (7): Performance of the Genetic Algorithm in Balancing the Chemical Reaction
The chromosome associated with the optimal solution is 
. Hence, the balanced reaction can be written as follows:
(16)
To check the validity of the answer obtained from the genetic algorithm, the number of atoms on the left and right sides of the chemical reaction under investigation and comparison are placed in Table(3).
Table(3): Number of atoms on the left and right sides of the chemical reaction
Atom | Number of atoms on the left side of the chemical reaction | Number of atoms on the right side of the chemical reaction | Is the balance in place? |
Al | 2 | 2 | Yes |
O | 18 | 18 | Yes |
H | 12 | 12 | Yes |
S | 3 | 3 | Yes |
According to Table(3), it can be said that the answer obtained is valid.
Numerical Example (4)
In this example, the aim is to balance the following chemical reaction through the genetic algorithm:
(17)
To solve the above descriptive system, a fitness function can be expressed as below:
(18)
Adjusting the Parameters of the Genetic Algorithm
The initial population size for the genetic algorithm was set to 90.
The crossover percentage for the genetic algorithm was set to 30.
The mutation percentage for the genetic algorithm was set to 70.
The stopping criterion for the algorithm is the attainment of a zero value for 
.
Execution of the Genetic Algorithm
Figure (8) shows the performance of the genetic algorithm in balancing the chemical reaction under investigation. Accordingly, the GA managed to balance the mentioned reaction in the 10thgeneration (10thiteration).
Figure (8): Performance of the Genetic Algorithm in Balancing the Chemical Reaction
The chromosome associated with the optimal solution is 
. Hence, the balanced reaction can be written as follows:
(19)
To check the validity of the answer obtained from the genetic algorithm, the number of atoms on the left and right sides of the chemical reaction under investigation and comparison are placed in Table(4).
Table(4): Number of atoms on the left and right sides of the chemical reaction
Atom | Number of atoms on the left side of the chemical reaction | Number of atoms on the right side of the chemical reaction | Is the balance in place? |
Ca | 6 | 6 | Yes |
P | 4 | 4 | Yes |
O | 28 | 28 | Yes |
Si | 6 | 6 | Yes |
According to Table(4), it can be said that the answer obtained is valid.
7.Conclusion
Balancing a chemical equation requires the selection of suitable coefficients for reactants and products in order to ensure an equal number of atoms for each element on both sides of the equation. However, it is not ideal for chemistry researchers to lack a standardized algorithm for balancing all reactions in the literature. This paper proposes a relatively straightforward approach by utilizing mathematical systems and genetic algorithms to establish a complete balance in chemical reactions.
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