Experimental Genetic Algorithm And Its Applications In The Water System Problems

With the continuously rapid growth of population and economy, water demand has been substantially increasing which leads to the global problems of water resource shortage and water quality deterioration. Since 1990s, as the largest developing country, China has faced severe water problems such as lack of water resources, worsening of water circumstances and increase of flooding disasters, which were sometime called water security problem as a whole. Nowadays water resource system is a huge and complex system exhibiting multi-stage, multi-objective, multi-level, multi-attribute and multi-functioning characteristics. System engineering and system analysis has been becoming one of the most dominating tools for analysis of water resource system. However, as the extent and depth of system research grow, the conventional theories and methods are not suitable to deal with the problems of modern water resource system which are high dimensional, non-linear and non-convex. In recent years, with the fast development of applied mathematics and computer techniques, the methods of artificial computational intelligence (CI) have been proposed to treat the complex system problems. Some of the frequently used CI theories and methods include genetic algorithms (GA), artificial neural networks (ANN), fuzzy sets (FS) etc. The applications of CI have helped the development of system analysis techniques, and have proposed new solutions for the water resource problems.Due to its self-adaptivity, global optimum, probability search, latent parallel process and easy operation, GA has been widely applied to the problems of modern water resource system. However, there are still some shortages for GA, such as searching algorithms in solution space, convergence of solutions and selection of controls parameters. Thus GA has been a hot research topic for a relatively long time. The operation of crossover and integration is one of the main technical and scientific innovation nowadays, which is also the vital kernel of GA. Consequently combining the conventional or intelligent mathematical methods with GA becomes an important way to improve the performance of the latter. In this study we briefly discuss the feasibility of integration of experiment design and GA, including:①t he theoretic foundation of the integration of experiment design with GA-the generalized experimental method;②the application foundation of integration of experiment design and GA - great complementarities between each other. As a result we propose a novel way of integrating the following two methods: GA based experiment design (GA orthogonal design, GA uniform design), experiment design based GA (immune GA, experimental GA). The experiment designs obtained by sub-GA were imbed into GAs in the following way:①u niform generation of forerunner individuals;②uniform searching in solution space;③utilizing uniform designs to make evolution experiment;④utilizing normal random distribution to make evolution experiment;⑤utilizing variable perturbation to make evolution experiment. Thus the so-called self-adaptive experimental genetic algorithms (EGA) based on the experiment design is developed. Digital test showed that, as a new hybrid intelligent method, EGA owns characters of fine optimizing efficiency and good precision adaptivity. It also has the ability to accelerate the individual variety to obtain the global solutions, and gives good values in area of complex water resource system.System optimization is the core of modern water resources system. In this dissertation, EGA is applied to solve the water resource system optimization problems such as:①C anal transect design is transformed into a non-linear optimization problem by constructing a relevant optimizing mathematical model. The design of trapezoid transect and U-shaped transect canals are taken as examples to illustrate the procedure of using EGA to get the optimal solution.②For the interval design of drains which control the level of ground water, a non-restraint model with the objective of minimum project is proposed, and for interval design of hidden pipes which govern the seepage of rice field, a non-linear model is set up with the objective of minimum cost and restraints of seepage, the results given by EGA are very favorable.③A multi-variable-mixed non-linear optimization model is built during designing the structure of underground stiffened penstock of hydraulic power station, solutions given by EGA turns out to be superior to those based on the conventional methods.System forecasting for water resource is a highly demanding technical issue. Forecasters are required to comprehensively master, as well as synthesize many methods or techniques. Because of its outstanding performance on fault-tolerance and nonlinear mapping, artificial neural nets (ANN) have been one of the most popular model-construction methods used in water resource system. In this dissertation, the application of BP-ANN to modeling and forecasting of water resource system contains:①after a brief introduction on the principle and method of BP-ANN, a hybrid artificial neural networks based on EGA is proposed to improve its ability to get the global solution;②the improved BP-ANN is utilized to form the method of nonlinear combination forecasting, which successfully avoids the tedious computation of the model weights;③according to the principle of best selection, the combined forecasting model is wisely transformed into a problem of 0 and 1 pattern recognition, and is solved by the method of improved BP-ANN with strong ability of non-linear mapping. The given example shows that, the so called selecting-best forecasting model (ANN-SFM) not only successfully avoids computing the weights of the combined forecasting models, but also owns the properties of clear concept, easy operation. As a special case of variable-weighting CFM, ANN-SFM has high values in practical applications.The key point of water resource system assessment is the rational construction and effective optimization of the assessment model. Conventional methods based on general model construction and optimization are not fit for the requirements of comprehensive assessment of complex water resource system which involves problems of multi-attribute, multi-levels and multi-factors. In this dissertation, the following works are presented to improve the overall assessment on water resource system:①in order to solve the incompatible problem resulting from the comprehensive evaluation on the quality of agricultural irrigation water, a new evaluation method-projection pursuit model based on the technology of data exploring, and optimized by EGA, is proposed to evaluate the irrigation water quality. Compared with the traditional water quality evaluation methods, for example the gray association analysis, the mathematical concept of IGA-PP method is much simpler and clear. The results using IGA-PP are also more reasonable and precise;②large errors occur when the general attribute recognition model based on linear measure function(LMF-ARM) is employed to do assessment on virtual samples drawn randomly from the criterion of water quality. Therefore, an improved attribute recognition model based on non-linear measure function (NLMF-ARM) is also developed. The results given by the later model are much better than those from the former, according to the tests on virtual samples selected by the random method as well as the orthogonal design approach. It indicates that the measure function could play an important role during the process of utilizing attribute recognition model to do comprehensive assessment. Thus from the case study on a river water quality assessment, it can be concluded that the non-linear measure function, compared to the linear one, has better capability to describe the natural attribute degrees of assessment indexes. Also due to its higher reliability than that of LMF-ARM, NLMF-ARM has broad applicability in the comprehensive assessment of water quality.