**5. References**

252 Genetic Programming – New Approaches and Successful Applications

respectively).

time period.

**Author details** 

Josep Dolz

J.M. Eaton

R. Val and K. Rodríguez

M.L. Arganis and R. Domínguez

simulate physical variables.

results from new models that can be obtained.

model the water temperature providing more accurate equations.

*PUMAGUA, Universidad Nacional Autónoma de México, México* 

*Universidad Politécnica de Cataluña, Barcelona, España* 

Comparing measured data with calculated data, for the year 1998, led to only minor errors in estimating the average water temperature using the genetic programming algorithm. When equations (4) and (5) were applied to another year, 1999, minor mean quadratic error in estimating water temperature was obtained using the multiple linear regression equation (5). The mean quadratic error associated with the multiple linear regression equation (5) for 1999 was 1.375 ºC; whereas with the genetic programming equation (4) was 2.248 ºC. This error can be considered acceptable if one takes in account the average temperature from January to June 1998 was 12.54 ºC, whereas the average temperature in 1999 for the same period was 11.62 ºC. The residuals obtained with equations (4) and (5) using data for the year 1999 had average values of 1.04 ºC and 0.43 ºC, respectively and with this criteria, multiple linear regression model can be considered better than the GP. However, reviewing the standard deviations, both models had almost the same value (1.09 ºC and 1.08 ºC,

The described procedures are then useful because equations similar to (4) or (5) can estimate important water quality characteristics, such as water temperature, using previously measured climatic data, predicted climatic data, and hydrological parameters for a given

Engineer's criteria and common sense must be considered before to apply any model to

Some standardization procedures to the involved data are suggested in order to improve the

The methods here applied are undoubtedly useful in several areas of knowledge, and can led us to new approaches to physical phenomena by considering measured field data.

Future work is focuses on the use of NARMAX (Non-linear Autorregressive Moving Average with eXogenous inputs) model combined with genetic programming in order to

*Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Coyoacán, D.F. México* 

*Centre for Hydrology, Micrometeorology and Climate Change, Department of Civil and Environmental Engineering, University College Cork, Cork, Republic of Ireland* 


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**Chapter 12** 

© 2012 Khatibi et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Khatibi et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Inter-Comparison of an Evolutionary** 

**Time-Series with Other Local Models** 

M. A. Ghorbani, R. Khatibi, H. Asadi and P. Yousefi

Additional information is available at the end of the chapter

the role of physical problems in the foreground.

into local management tools and it is a focus of this chapter.

http://dx.doi.org/10.5772/47801

**1. Introduction** 

**Programming Model of Suspended Sediment** 

The experience of applying evolutionary computing to time series describing local physical problems has benefited the modelling culture by showing that many different mathematical formulae can be produced to describe the same problem. This experience brings into the focus the roles of pluralism in the modelling culture as opposed to searching for the best model, where physical problems provide relevance and context to the choice of modelling techniques. Both of these roles are often overlooked and do not directly influence research agenda. Although the focus of this paper is on evolutionary computing, it also promotes a pluralistic modelling culture by studying other modelling techniques, as well as by keeping

Estimating suspended sediment loads is a problem of practical importance and includes such problems as changing courses in rivers, loss of fertile soil, filling reservoirs and impacts on water quality. The study of these problems in the short-run are referred to as sediment transport and erosion for those in the long-run. Past empirical capabilities remain invaluable but are not sufficient on their own as management and engineering solutions often require an insight into the problem. Empirical knowledge has been incorporated into the body of distributed modelling techniques giving rise to sophisticated modelling software tools but their applications require a great deal of resources. There remains a category of problems, often referred to as time series analysis, which uses the sequences of time variations and predicts the future values. This category of models provides useful information to management of local problems. For instance, such models may be used to schedule dredging requirements or other maintenance activities. Time series analysis is developing
