AMEBA - Evolutionary Computation Method: Comparison and Toolbox Development

Evolution algorithms are optimization methods that mimic a process of the natural evolution. Their stochastic properties result in a huge advantage over other optimization methods, especially regarding solving complex optimization problems. In this paper, several types of evolutionary algorithms are tested regarding a dynamic nonlinear multivariable system modelling and control design. We have defined three problems: the first one is the so-called grey box identification problem where the characteristic of the system’s valve is under investigation, the second one is a black box identification where the goal is a dynamic system’s model development using system’s measurements data, while the third one is a system’s controller design. The efficacy of solving presented problems was compared to the usage of the following optimization methods: genetic algorithms, differential evolution, evolutionary strategies, genetic programming, and a developed approach called AMEBA algorithm. All methods have proven to be very useful for grey box identification and design of a system’s controller, but AMEBA algorithm has also been successfully used in a black box identification, where it generated a corresponding dynamic mathematical model. Introduction Corn et al. AMEBA-Evolutionary Computation Method: Comparison and Toolbox 230 SNE 26(4) – 12/2016 TN 1 Three Coupled Tanks System Figure 1: System of three coupled tanks. 1.1 Model structure V3 Valve V3 u2(t) u1(t) Part model h1(t) h2(t) h3(t) Izh(t) Pumps vh 1(t) vh 2(t) Figure 2: Block diagram of the three coupled tanks system structure. Corn et al. AMEBA-Evolutionary Computation Method: Comparison and Toolbox SNE 26(4) – 12/2016 231 T N Figure 3: Input signals u1(t) and u2(t). Figure 4: Responses of the system to chosen input signals. 1.2 Controller design u2(t) u1(t) Process h1(t) h2(t) h3(t) vh1(t) vh2(t) Pumps h2ref (t) h1ref (t) e1(t) e2(t) Controller Figure 5: Closed-loop system operation href1 href2 e1 e2 h1 h3 href1 href2 u1 u2 wopt Figure 6: Reference signals. 2 Modelling Results 2.1 Parametrical evolutionary algorithms a1 a2 a3 a4 Corn et al. AMEBA-Evolutionary Computation Method: Comparison and Toolbox 232 SNE 26(4) – 12/2016 TN Met. Error identification [%] Error validation [%] DE 1.77 3.27 ES 1.79 3.58 GA 1.88 4.57 Table 1: Evaluation of modelling results of parametrical algorithms. Figure 7: Comparison of measurements with the response of the model generated by the DE method. Figure 8: Average convergence of parametrical methods 2.2 Structural evolutionary algorithms Algorithm Error ident. [%] Error valid. [%] GP 1.62 3.12 AMEBA valve 3.57 4.65 AMEBA full model 5.63 7.23 Table 2: Evaluation of modelling results when using structural algorithms. Corn et al. AMEBA-Evolutionary Computation Method: Comparison and Toolbox SNE 26(4) – 12/2016 233 T N Figure 9: Solution generated with the GP method. Figure 10: Graph representation of model of the valve generated with AMEBA algorithm. Color Node Color Node Input Amplification Output Exponent Low pass filter Delay High pass filter Derivative Multiply Integral Divide Add Table 3: Color-legend of different types of nodes. Figure 11: Graph representation of system’s model generated with the use of AMEBA algorithm. 3 Results of the Controller Design 3.1 Parametrical evolutionary algorithms Corn et al. AMEBA-Evolutionary Computation Method: Comparison and Toolbox 234 SNE 26(4) – 12/2016 TN Kp Ki Algorithm Error Energy used DE 2.04 % 35.9% GA 2.04 % 36.5% ES 2.48 % 35.3% Table 4: Evaluation of controller optimization results calculated with parametrical methods. 3.2 Structural evolutionary algorithm Algorithm Error Energy used AMEBA 1.5 % 34.1 % GP 9.3 % 35.5 % Table 5: Results of controllers generated by structural evolutionary methods. Figure 12: Graph representation of controller generated by the AMEBA algorithm. 4 Toolbox development Figure 13: Settings of simulation environment. Corn et al. AMEBA-Evolutionary Computation Method: Comparison and Toolbox SNE 26(4) – 12/2016 235 T N Figure 14: General setting. Figure 15: Agent settings. Figure 16: Node settings. Figure 17: Reproduction settings. Figure 18: Additions functionalities of Toolbox. Corn et al. AMEBA-Evolutionary Computation Method: Comparison and Toolbox 236 SNE 26(4) – 12/2016 TN 5 Conclusions References Optimal multivariable control design using genetic algorithms Genetic Algorithms in Search, Optimization and Machine Learning The Theory of Evolution Strategies (Natural Computing Series) Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces Clever Algorithms: Nature-Inspired Programming Recipes Genetic Programming On the Programming of Computers by Means of Natural Selection Grammatically-based Genetic Programming Artificial Intelligence through Simulated Evolution Indoor-environment simulator for control design purposes Cell based Genetic Programming Toolbox (CGP Toolbox) A Graph-Based Evolutionary Algorithm : Cell Based Genetic Programming AMEBA – Structural evolutionary optimization: method and toolbox development Multivariabilni sistemi, Zbirke kompleksnejših problemov Grey-box model identification via evolutionary computing