Hybrid Genetic Programming with Local Search Operators for Dynamic Force Identification Yaowen Yang 1 ; Chao Wang 2 ; and Chee Kiong Soh 3 Abstract: In this paper, based on the Darwinian and Lamarckian evolution theories, three hybrid genetic programming GP algorithms integrated with different local search operators LSOs are implemented to improve the search efficiency of the standard GP. These three LSOs are the genetic algorithm, the linear bisection search, and the Hooke and Jeeves method. A simple encoding method is presented to encode the GP individuals into the expressions that can be recognized by the different LSOs. The implemented hybrid GP algorithms are applied to identify the excitation force acting on the structures from the measured structural response, which is an important type of inverse problem in structural dynamics. Illustrative examples of a frame structure and a multistory building structure demonstrate that, compared with the standard GP, the hybrid GP algorithms have higher search efficiency which can be used as alternate global search and optimization tools for other engineering problem solving. DOI: 10.1061/ASCE0887-3801200721:5311 CE Database subject headings: Programming; Hybrid methods; Optimization; Construction management. Introduction Genetic programming GPKoza 1992 is one of the most use- ful, general-purpose problem-solving techniques. It has been used to solve a wide range of engineering problems, such as symbolic regression, data mining, and structural optimization. It is one in- stance of the class of techniques called evolutionary computation, which are based on insights from the study of natural selection and evolution. GP is an extension of the conventional genetic algorithm GAHolland 1975; Goldberg 1989. GP is good at searching a functional space whereas GA is good for searching a parameter space. GA involves encoded strings that represent par- ticular problem solutions, whereas GP breeds executable com- puter programs. The standard GP is inspired by the Darwinian natural selection theory. In the 19th century, the Darwinian theory was challenged by Lamarck, who proposed that environmental changes through- out an organism’s life cause the internal variations of the organ- ism that are transmitted to the offspring. Lamarckian theory hypothesizes how the organisms pass down the knowledge and experience they acquired and is essentially a theory of directed variation. Although Lamarckian theory has not been observed in biological history, its convincing power is illustrated by the evo- lution of our society whereby knowledge and idea are passed from one generation to another through culture and language Gen and Cheng 1997. However, GP, the artificial organisms, can certainly benefit from the advantages of the Lamarckian theory. By letting some individuals’ good “experience” pass down to the offspring, GP’s ability to focus on the most promising areas can be improved. The Lamarckian theory has been introduced into GAs by Grefenstette 1991, and Kennedy 1993 gave an expla- nation for this hybrid. In this paper, the proposed hybrid GPs incorporating, respectively, three local search operators LSOs, i.e., the GA, the linear bisection search LBS, and the Hooke and Jeeves method HKJ, are implemented based on both the Dar- winian and Lamarckian theories. Essentially, these hybrid GPs made use of a two-prong approach whereby the standard GP per- forms the global search in the problem domain based on the Dar- winian theory while the LSOs vary a number of selected good GP individuals before they are injected into the next generation, imi- tating the directed variation in the Lamarckian theory. It is di- rected variation because the LSOs improve the fitness of the selected individuals by moving them to the local optima. When solving problems that we do not know in advance the size and structure of its best solution, the ability of GP to examine different size solutions is very important. When standard GP is used, the generated GP individuals may include a number of in- ternal parameters. These randomly generated parameters can have significant effects on the performance of the GP individuals. Gen- erally, GP is good at global search for the structure of the solution of the given problem; however, for the problems that need “fine- tuning” of solution parameters, GP is not as good as GA Yang and Soh 2002. These inspire our attempt to integrate GA with GP. In this integration, GA is employed as a LSO to alter the solution parameters. The other two LSOs, LBS and HKJ, are also studied to examine the performance of the hybrid GPs with dif- ferent LSOs. Chellapilla et al. 1998 embedded various LSOs into the self- adaptive evolutionary programming EP and the fast EP to inves- tigate the effectiveness of LSOs in EP. They observed that the LSOs can statistically and significantly enhance the performance 1 School of Civil and Environmental Engineering, Nanyang Technological Univ., 50 Nanyang Ave., Singapore 639798, Singapore. 2 School of Civil and Environmental Engineering, Nanyang Technological Univ., 50 Nanyang Ave., Singapore 639798, Singapore. 3 School of Civil and Environmental Engineering, Nanyang Technological Univ., 50 Nanyang Ave., Singapore 639798, Singapore corresponding author. E-mail: csohck@ntu.edu.sg Note. Discussion open until February 1, 2008. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and pos- sible publication on September 23, 2005; approved on November 16, 2006. This paper is part of the Journal of Computing in Civil Engineer- ing, Vol. 21, No. 5, September 1, 2007. ©ASCE, ISSN 0887-3801/2007/ 5-311–320/$25.00. JOURNAL OF COMPUTING IN CIVIL ENGINEERING © ASCE / SEPTEMBER/OCTOBER 2007 / 311