The Proposed Chemical Reaction Algorithm

Abstract This chapter introduces the chemical reaction algorithm it describes the main characteristics and definitions. In this work, the main objective is to introduce a novel optimization algorithm based in a paradigm inspired by nature, the chemical reactions. 

Keywords Chemical reactions Optimization algorithm Chemical algorithm 

This chapter introduces the chemical reaction algorithm it desalbes the main characteristics and definitions. 

A novel set of intensifier/diversifier mechanisms will be introduced in order to allow the population to converge to an optimal solution within a determined search space. Comparisons with other nature inspired optimization techniques will be made in order to prove good performance of the proposed algorithm. 

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The proposed chemical reaction algorithm is a metaheuristic strategy that performs a stochastic search for optimal solutions within a defined search space. In this optimization strategy, every solution is considered as an element (or compound), and the fitness or performance of the element is represented by the final energy (which is determined according to the objective function). The general flowchart of the algorithm is shown in Fig. 4.1. 

From Tables 6.3, 6.4 and Tables A.l to A.3 in the annex A section, it can be observed that the proposed chemical reaction algorithm was able to reach values very close to the global minimum compared with other optimization approaches. 

The main difference of the proposed chemical optimization algorithm with respect to the previous mentioned approaches is that it has a simpler parameter representation and yet it is proven to be efficient. Since only the general schema of the chanical reactions is taken into consideration, the initial set of elements is simply represented and no extra parameters (such as mass, kinetic coefficient, etc.) are added. 

In order to have a better picture of the general schema for this proposed chemical reaction algorithm (CRA), a comparison with other nature inspired paradigms is shown in Table 4.1. 

We describe in Chap. 3 a brief overview of the basic concepts from chemical methods needed for this work. In this chapter, some definitions of the chemical reactions are offered as a basis for understanding the proposed chemical optimization algorithm. 

For Case 1, the minimum error value found by the chemical reaction algorithm was 0.89855. Figure 6.13 shows the resulted input membership functions found by the proposed optimization algorithm for the linear and angular velocity errors. 

Several algorithms have been proposed to solve the model equations with chemical reactions (Holland, 1981 Saito et al., 1971 Tierney et al., 1982). Venkataraman et al. (1990) applied the two-tier method for this purpose. 

Another significantly faster procedure for solving the Newton-Raphson equations, called the Broyden-Bennett method, was proposed by Hess et al.10 The Broyden-Bennett algorithm may be used to solve the equations for an absorber-type column accompanied by a chemical reaction in the following manner. 

At first sight, chemical theory and its definitions may seem complex and none or few related to optimization theory, but only the general schema will be considered in proposing the chemical reaction optimization algorithm. 

Dittrich et al. [1], described the basic terms to characterize and classify artificial chemistries. Given the statistical and qualitative features of the reaction laws and element/component representation, our proposed algorithm is an abstraction of the chemical reaction process and can be described as a constructive dynamical... 

Analog to some other nature inspired algorithms for example, genetic algorithms, where genes are the basic units and are encoded as strings or chromosomes, in this proposed chemical algorithm, the basic units or candidate solutions are represented by elements or/and compounds, and the metaphor of chemical reactions is used as a procedure to approximate the solution to a desired optima. 

In this book, a novel optimization method inspired by a paradigm from nature is introduced. The chemical reactions are used as a paradigm to propose an optimization method that simulates these natural processes. The proposed algorithm is described in detail and then a set of typical complex benchmark functions is used to evaluate the performance of the algorithm. Simulation results show that the proposed optimization algorithm can outperform other methods in a set of benchmaik functions. 

Another general problem, the development of an algorithm for the construction of kinetic models for the quasi-stationary state of the evolution of non-equilibrium chemical system, is solved by the method of linear routes as simple cycles of a graph assigned to sets of elementary reactions and intermediate substances (see Chapter 2). A general algorithm for construction of kinetic models for the linear catalytic and un-branched radical-chain processes, including a free radical polymerization, is proposed. 

There is a number of references [1-13] in which an algorithm of the kinetic models construction is described, but mainly two widely used methods are applied, namely linear algebra [1, 2, 7, 10-13] and the theory of graphs (5, 6, 8, 9]. In the most of the proposed algorithms the main attention is paid into obtaining the expression for the rate of an elementary reaction. Principally, it suffices to use the vector of a rate of an elementary reaction to determine the vector of the rate of a composite substance s formation and in such a way to describe the evolution of a chemical system s composition. In particular cases, however, the expressions for the final reactions rates are retained, since in complicated systems with a set of final reactions the knowledge of an elementary reaction rate does not mean knowledge of the final reactions rates. 

Phase and chemical equilibrium calculations are essential for the design of processes involving chemical transformations. Even in the case of reactions that cannot reach chemical equilibrium, the solution of this problem gives information on the expected behaviour of the system and the potential thermodynamic limitations. There are several problems in which the simultaneous calculation of chemical and phase behaviour is mandatory. This is the case, for example, of reactive distillations where phase separation is used to shift chemical equilibrium. Also, the calculation of gas and solid solubility in liquids of high dielectric constants requires at times the resolution of chemical equilibrium between the different species that are formed in the liquid phase. Several algorithms have been proposed in the literature to solve the complex non-linear problem however, proper thermodynamic model selection has not received much attention. 

Mechanism. The thermal cracking of hydrocarbons proceeds via a free-radical mechanism (20). Siace that discovery, many reaction schemes have been proposed for various hydrocarbon feeds (21—24). Siace radicals are neutral species with a short life, their concentrations under reaction conditions are extremely small. Therefore, the iategration of continuity equations involving radical and molecular species requires special iategration algorithms (25). An approximate method known as pseudo steady-state approximation has been used ia chemical kinetics for many years (26,27). The errors associated with various approximations ia predicting the product distribution have been given (28). 

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