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Knowledge-based evolution method for optimizing refrigerant circuitry of fin-and-tube heat exchangers.

Article Excerpt
INTRODUCTION

Fin-and-tube heat exchangers are widely applied in refrigeration and air conditioning systems and often must be quickly designed and show good performance. We have developed a three-dimensional distributed-parameter model to assist the design of fin-and-tube heat exchangers (Liu et al. 2004). This model predicts the performance of a fin-and-tube heat exchanger with parameters given by the designer. For the purpose of choosing a heat exchanger with good performance, the designer should repeat the process of giving parameters and waiting for the simulation results many times, which is still not convenient. Therefore a method for optimizing fin-and-tube heat exchangers is needed.

Optimization of refrigerant circuitry (RC) is very important in designing a fin-and-tube heat exchanger because RC has an obvious effect on performance (Wang et al. 1999; Bigot et al. 2000; Liang et al. 2001), and optimal RC is affected by many factors (Domanski et al. 2005; Casson et al. 2002). The exhaustive searching method is an easy-understanding optimization method but is not suitable for RC optimization. Taking a 36-tube heat exchanger as an example, there are 2x[10.sup.45] possible solution candidates, and an exhaustive search could take as long as 6.34x[10.sup.26] years on a 100 GHz CPU computer for even the simplest model. Therefore practical optimization methods should be developed.

The method using knowledge-based, structure-modifying operators and symbolic learning has been used for RC optimization (Domanski et al. 2004; Kaufman and Michalski 2000). However, the process of generating the rules for symbolic learning in this method is complicated, and the generated rules may limit the diversity of the solutions because they fix some tube connections in the RC. Therefore, simpler and more effective methods for RC optimization are needed.

To develop simpler methods for RC optimization, the GA can be considered because it is easy to operate (Goldberg 1989), is effective in finding the global optimal solution (Holland 1975), and can provide good results for many combinatorial optimization problems (Androulakis and Venkatasubramanian 1991; Loomans and Visser 2002; Rong 1997; Ravindra et al. 2000).

The following three problems must be solved in order to develop simpler and more effective RC optimization method based on the GA:

1. Coding the RC. The RC must be coded to apply the GA for RC optimization, but no suitable genetic coding method is available.

2. Avoid infeasible RC solutions during the genetic evolution process. Infeasible RC solutions are easily generated in the conventional random initialization process and genetic operation (mutation and crossover) process, which may abnormally break the optimization process.

3. Improve the efficiency of the optimization process. The conventional genetic operators have lower efficiency because they only use random operations, which leads to the low convergence rate of the GA for a large-scale optimization problem (Srinivas and Patnaik 1994) and easily traps it in a local-optimal solution.

To solve these three challenges to obtaining a simpler RC optimization method that has higher efficiency, the present work develops a knowledge-based evolution method (KBEM) for RC optimization by integrating an improved genetic algorithm (IGA) with some knowledge-based RC search methods. This paper first describes the RC optimization problem and the KBEM scheme and then presents the IGA for RC optimization and describes how to apply the knowledge-based RC search methods for RC optimization.

DESCRIPTION OF THE RC OPTIMIZATION PROBLEM

As the RC for a heat exchanger is usually optimized to achieve the maximum heat exchange capacity, this paper uses the maximum heat exchange capacity as the optimization objective to illustrate the method. All of the working conditions and the structural parameters are fixed during optimization except for the RC. The RC optimization problem can be described as follows:

max Q(X), X is the variable of refrigerant circuitry that needs to be optimized.

s.t.[L.sub.b][less than or equal to][L.sub.adj]; [n.sub.p,in][less than or equal to]n;[n.sub.p,out][less than or equal to]n;[DELTA][p.sub.r]
where Q is the heat exchange capacity related to X; [L.sub.b] and [L.sub.adj] are the length of single joint tube on the far side of the heat exchanger and the maximum length of single joint tube between two adjacent tubes of the same row or adjacent rows, respectively; [n.sub.p,in], [n.sub.p,out] and n are the number of inlet paths, the number of outlet paths, and the maximum number of inlet paths or outlet paths, respectively; [DELTA][p.sub.r] is the refrigerant-side pressure drop; and z is the maximum value for [DELTA][p.sub.r].

SCHEME OF THE KBEM FOR RC OPTIMIZATION

The present KBEM for RC optimization is an integration of a developed IGA and knowledge-based methods for searching new RC. It consists of two parts: IGA and knowledge-based optimization model (KOM). Figure 1 shows the schematic framework of the KBEM.

[FIGURE 1 OMITTED]

The IGA in the KBEM is an improved version of the conventional GA (Goldberg 1989). The improvements in the IGA include the tailor-made RC coding method, specific RC initialization method, and improved RC genetic operators (crossover, mutation, and correction). RC correction operators are added in the IGA to absolutely avoid infeasible RC solutions. The IGA is the basis of the KBEM because it generates the initial solutions and controls the whole optimization process.

The knowledge-based RC search methods are applied to increase the optimization efficiency by reducing the search space according to the domain knowledge without losing optimal solutions. The main reason for the low efficiency of the conventional genetic operators is that they neglect the inner characteristics of the optimization object and only use random operations to blindly search the solutions on a wide solution space. Applying the domain knowledge to generate better solutions by considering the inner characteristics of the optimization object may help to make up the deficiency of the conventional genetic operators and improve the efficiency of the optimization process. In the KBEM, the knowledge-based RC search methods are integrated into one module of KOM, and the KOM is used after the genetic operations of the IGA during the optimization process.

IMPROVED GA FOR RC OPTIMIZATION

A GA is successfully applied to solve many combinatorial optimization problems; however, the existing RC coding method has low efficiency and is not suitable for RC optimization. Moreover, infeasible RC solutions, which may abnormally break the optimization process, are easily generated with the existing initialization method and genetic operators (crossover and mutation). Therefore, new methods to improve the efficiency of RC coding, specific RC initialization methods, and improved RC genetic operators, as well as methods to avoid infeasible RC solutions are needed for RC optimization.

New RC Coding Method Using One-Dimensional Integer String

The existing RC coding methods (Liu et al. 2004, Jiang et al. 2006, Kuo et al. 2006) have low efficiency for RC optimization. The new method applied in the GA should satisfy the following three requirements: (1) the coding method should be able to describe...

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