A fuzzy genetic algorithm for the discovery of process parameter settings using knowledge representation

Abstract

In this paper, we propose a fuzzy genetic algorithm (Fuzzy-GA) approach integrating fuzzy rule sets and their membership function sets, in a chromosome. The proposed approach consists of two processes: knowledge representation and knowledge assimilation. The knowledge of process parameter setting is encoded as a string with a fuzzy rule set and the associated membership functions. The historical process data forming a combined string is used as the initial knowledge population, which is then ready for knowledge assimilation. A genetic algorithm is used to generate an optimal or nearly optimal fuzzy set and membership functions for the process parameters. The originality of this research is that the proposed system is equipped with the ability to take advantage of assessing the loss which is caused by discrepancy with a process target, thereby enabling the identification of the best set of process parameters. The approach is demonstrated by the use of an experimental example drawn from a semiconductor manufacturer and the results show us that the suggested approach is able to achieve an optimal solution for a process parameter setting problem.

Introduction

In both industrialized countries and newly industrialized countries, manufacturing firms are facing significant change resulting from mass customization and shortening product life cycles (Prajogo, Laosirihongthong, Sohal, & Boon-itt, 2007). There are various intelligent and information systems to explore the artificial intelligence (AI) techniques in optimizing the processes with better finished product quality or service performance (Huang, Trappey, & Yao, 2006; Tsai, 2006; Tsaih & Lin, 2006).

Hybrid architecture for intelligent systems has become a new field of AI research, operating in concert with the development of the next generation of intelligent systems. Current research in this field concentrates mainly on the marriage of genetic algorithms (GA) and fuzzy logic (Caputo et al., 2006, Feng and Huang, 2005). Exploring the similarities of the essential structures of these two knowledge manipulation methods is where intelligent hybrid systems can possibly play an important role. However, such hybrid systems have not shown great significance in the manufacturing industry. To extend the application of specifically the above hybrid approach, a knowledge framework integrating fuzzy rule sets and their associated membership function sets in a GA chromosome has been proposed, assisted with the mathematical evaluation in terms of the chromosome fitness. This innovative research approach is intended to accentuate integrating the GA and fuzzy logic so that the related crisp and fuzzy values could coexist in simply one chromosome, while the unavoidable performance trade-off phenomenon occurring in the manufacturing process is to be also taken into consideration.

The proposed approach consists of two processes: knowledge representation and knowledge assimilation. In the stage of knowledge representation, the expertise of process parameter setting is encoded as a string with fuzzy rule sets and the associated fuzzy membership function. The historical process data are also included into the strings mentioned above, contributing to the formulation of an initial knowledge population. Then in knowledge assimilation, GA is used to generate an optimal or nearly optimal fuzzy set and membership functions for the entitled process parameters. The approach is demonstrated by the employment of an experimental example, the reactive ion etching (RIE) process, drawn from a semiconductor manufacturer.

Two objectives have been set in this paper. Firstly, a comprehensive discussion of scientific control of parameter-based operations with investigation into previously used methods has been conducted. Ideally such an argument can be useful to the improvement of any process with various parameters, since many researchers may not fully realize the importance of the research on process parameters or of performance trade-off issues. Secondly, a set of methodologies by means of numerical analysis for determining the optimal process parameters has been provided. This can be thought of as a guide to achieve the purpose of manufacturing optimization in a comprehensive way, and furthermore, as an inspiration showing how appropriate mathematical tools can be adopted to conquer various manufacturing problems.

This paper is organized as follows: Section 2 presents a literature review of GA, fuzzy logic, and related applications in the manufacturing domain. The formal description of the problem and model about parameter settings are presented in Section 3. Section 4 provides the details of GA and the performance trade-off function. Section 5 provides a case example for the proposed Fuzzy-GA approach. In Sections 6, the numerical analysis and conclusions are addressed.