Optimizing an Amplifier with a Many Objective Algorithm

Published in 25 Friday

Track

Modeling, Control and Industry

In this work a Miller CMOS amplifier [1], with integrated circuit technology of 35m, is optimized using the many objective algorithm MOMBI [2] which is based in the R2 indicator. Five objectives are used: a DC gain bigger than 80 dBV, a unity gain frequency bigger than 17 MHz, a phase margin bigger than 60,slew rate bigger than 18 MV/s, and a CMRR bigger than 90 dBV. Also this problem has eight constraints[3] (all transistors must be working in saturation mode). Results are compared with the amplifier obtained in [1].

References

[1] T. Oliveira Weber and W.A.M. Van Noije. Analog circuit synthesis performing fast Pareto frontierexploration and analysis through 3D graphs.Analog Integrated Circ. Sig. Processing, 73:861–871, 2012.

[2] R. Hernandez Gomez and C.A. Coello Coello. “MOMBI: A new metaheuristic for many-objectiveoptimization based on the R2 indicator",Evolutionary Computation (CEC), 2013 IEEE Congress on,pp. 2488–2495, 2013.

[3] L. G. de la Fraga and E. Tlelo-Cuatle. “Optimizing an amplifier by a many-objective algorithm basedon R2 indicator", Circuits and Systems (ISCAS), 2015 IEEE International Symposium on, 265-268

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Local Search approach to Genetic Programming for RF-PA modeling implemented in FPGA

Published in 25 Friday

Track

Modeling, Control and Industry

In this article is presented a genetic programming (GP) with a local search heuristic (LSHS) to emulate the Radio Frequency (RF) Power Amplifier(PA) Doherty 7W @2.11 GHz conversion curves.The full data package related to the conversion curves that describe the PA behavior has a length of 122,880 data. The basic RF-PA modeling techniques involves special truncations of the Volterra Series[1-3],but for very complex nonlinear model swith wide data range is required the use of the whole Volterra Series[4-5], Fuzzy Neural Network [6-7] or GP[8-9]. By other hand, GP performs an evolutionary search within the space of possible program syntaxes, achieving the expression that best solves a given model.

GP can be viewed as a biologic evolutionary inspired algorithm where a pool of symbolic expressions are built in a synergy fashion upon a target. Each expression competes for survival at each iteration by measuring its fitness value. This is usually expressed by an error metric toward the objective. In general, each symbolic expression consist of a mathematical equation that represent a potential candidate model in the imposed problem. Standard GP can solve complex problems by searching in the syntax space, however accuracy on the solutions can be stagnated through the evolution and expressions might grow in size.

In this work we propose a similar approach as performed in other population based algorithms: a combination of explorative search by using genetic operators and an exploitative search by numerical optimization means is designed. This synergy produces better quality solutions in faster times. The numerical optimization is performed by an iterative algorithm called Trust Region which minimizes the error for a parameterized non-linear function. This deterministic optimization is usually called Local Search (LS), since the optimum usually locates closer to the actual model by searching only in the parameter space given by thecurrent symbolic expression. A set of small candidates models are picked up to be optimized during evolution. We call this approach LSHS[10-11].The Fig. 1 shows the LSHS flowchart.

Experimental results shows that LSHS’s best models accuracy outperforms Canonical GP ones. The selected model including 17 parameters shows that produced model by GP for the AM/PM conversion curve has a MSE of 0.26033 during the implementation. The implementation stage for the AM/AM conversion curve is done in DSP Development Board Cyclone III-ALTERA.The test performed on the development board in the laboratoyy indicate that the GP model accuracy is very high.

The authors wish to thank the Dr. José Raúl Loo Yauof the CINVESTAV for the support provided during the RF-PA Doherty 7W @2.11 GHz measurement. In addition, the authors would like to express their gratitude to the Dr. J. Apolinar Reynoso Hernández of the CICESE for provide the RF-PA as device under test.

References

[1] L. Ping-hui and W. Peng. Wiener-Saleh modeling of nonlinear RF power amplifiers considering memory effects.International Conference on Microwave and Milimeter Wave Technology, Chengdu, China, 1447-1449, May 2010.

[2]M. Junghwan, O. Saad, S. Jungwan, C. Fager and K. Bumman. 2-D enhanced hammerstein behavior model for concurrent dual-band power amplifiers. European Microwave Conference,Amsterdam, 1249-1252, November 2012

[3]J. Misic, V. Markovic and Z. Marinkovic. Volterra kernels extraction from neural networks for amplifier behavioral modeling. International Symposium on Telecommunications,Sarajevo, Bosnia-Herzegovina, 1-6, October 2014.

[4]J. Staudinger,J. Nanan and J. Wood. Memory Fading Volterra series model for high power infrastructure amplifiers.IEEE Radio and Wireless Symposium, New Orleans,184-187.January 2010

[5]Z. Anding and T. J. Brazil. Behavioral modeling of RF power amplifiers based on pruned Volterra series.IEEE Microwave and Wireless Components Letters,14(12):563-565, December 2014

[6] J. Zhai, J. Zhou, L. Zhang and W. Hong. Behavioral Modelling of Power Amplifiers With Dynamic Fuzzy Neural Network.IEEE Microwave and Wireless Components Letters, 20(9):528-530, 2010.

[7] F. Mkadem, M. Ben Ayed, S. Boumaiza, J. Wood and P. Aean. Behavioral modeling and digital predistortion of power amplifiers with memory using two hidden layers artificial neural networks,IEEE International Microwave Symposium, Anaheim, USA,1,May 2010.

[8]Z. Sheng, S. Xiuyuand W. Wei. An ANN model of optimizing activation functions based on constructive algorithmand GP. International Conference on Computer Application and System Modeling, 1:420-424, October 2010.

[9]A. Patelli and L. Ferariu. A regressive schema theory based tool for GP evolved nonlinear models. 201-206, September 2011.

[10]E. Z-Flores, L. Trujillo, O. Schütze, and P. Legrand. Evaluating the effects of local search ingenetic programming. In EVOLVE of Advances in Intelligent Systems and Computing, Springer International Publishing, 288:213–228, 2014.

[11] E. Z.-Flores, L. Trujillo, O. Schütze, and P. Legrand. A local search approach to genetic programming for binary classification. In Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2015, Madrid, Spain, 1151–1158, July 2015.

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Wastewater treatment modeling by means of Memetic Genetic Programming

Published in 25 Friday

Track

Modeling, Control and Industry

One of the methods used in the wastewater treatment is the adsorption process, a type of physicochemical treatment that commonly uses activated carbon as the absorbent. In this particular application, the removal of Phenol and Nitrophenol is required, and thus a prediction of adsorption removal (W%) is modeled based on a contaminant, pH and an initial concentration (Ci) for a given contact time. Given experimental data, a symbolic regression model is built with the premise of predicting reasonable well unseen data based on a well known family of techniques from the Evolutionary Computation (EC) domain,a branch of a broader Artificial Intelligence (AI) research area. Particularly, a novel framework is proposed called Memetic Genetic Programming (MGP), which essentially uses the advantages of explorative search,present on the majority of population based algorithms, and the explotative procedure using a deterministic method to build altogether a model. This model exhibit a pair of benefits: first, the interpretability is high which could be explained by an expert on account of its symbolic nature, and second, the accuracy is high enough to compete with other state-of-art techniques used in model extraction.

The MGP is designed by incorporating numerical Local Search (LS) optimization into a Canonical or Standard Genetic Programming (SGP). LS is explained in the context of the search space where the solutions are being explored, which can be in different layers of the algorithm, like syntaxis, fitness, output,etc. In our case, the LS space matches the solution output space given by SGP.

In SGP, a common representation for the solution is given by syntactic trees, which can be also viewed as mathematical expressions built during the evolutionary process by elementary units called functions. Each of these expressions or potential solutions represents an individual model in our problem, and are ranked by a fitness function that measures the error with respect to a desired output (the adsorption removal rate in our case). The evolutionary process mimics an optimization process where this fitness function is minimized to reach an acceptable value. However, this process usually takes computational resources to produce accurate solutions. This is because SGP is more eager to improve solutions by extending syntactic trees. Nonetheless, this takes more resources and there is no guarantee that significant improved solutions are ever going to be found.

The LS process is designed by optimizing a specific solution toward the target. To be able to do this,firstly, syntaxis trees are transformed by incorporating a parameter for each node. Second, a linear tree of the expression 1+2K(x)is inserted at the root node of each tree, where is the parameter set and K(x)is the tree before transformation.

The optimization is performed by a well known technique, the Trust Region, a variant of Levenberg-Marquardt, where an approximate model is found in a neighborhood during a given iteration of the algorithm. The Trust Region method excels by simultaneously finding the step size and direction toward the optimum, which could be local or global.

Not all solutions are picked up in the population to be optimized. This reduces resources and at the same time produces sufficient improvement in the overall population fitness. An heuristic method was used to choose the solutions, which is based on a ratio of the average population size and individual size. The size is expressed as the number of nodes in a given tree, an it has a direct relationship with the length of the mathematical expression. Small expressions are preferred to be optimized by this heuristic. The fitness function integrates an error measure given by the Mean Squared Error (MSE).

Data was randomly partitioned in training and testing subsets during the experimental procedure, with a 75% of total data for the former and the rest for the latter. 30 independent runs where performed for the experiment. The MGP setup was the following: 250 generations, 200 individuals, 0.9 probability of crossover, 0.1 probability of mutation, approximated 50% of population is optimized, 500 iterations for the Trust Region method, 17 maximum depth level, ramped half-and-half initialization and keep best as elitism.

Experimental statistical results shows good performance for unseen data in terms of Pearson correlation and MSE. The required correlation beforehand was to overpass= 0:96, which was successfully accomplished.In the other hand, in terms of algorithm performance, there is no evident presence of over-fitting which gives a rough idea of the model generalization capabilities. Preliminary results are shown in figures 1(a)and 1(b) for training and testing data respectively.

References

[1] Emigdio Z-Flores, Leonardo Trujillo, Oliver Schütze, and Pierrick Legrand. Evaluating the effects of local search in genetic programming. InEVOLVE, volume 288 of Advances in Intelligent Systems and Computing, pages 213–228. Springer International Publishing, 2014.

[2] Emigdio Z.-Flores, Leonardo Trujillo, Oliver Schütze, and Pierrick Legrand. A local search approach to genetic programming for binary classification. In Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2015, Madrid, Spain, July 11-15, 2015, pages 1151–1158, 2015.

[3] M. Abatal and M.T. Olguin. Comparative adsorption behavior between phenol and p-nitrophenol byna- and hdtma-clinoptilolite-rich tuff.Environmental Earth Sciences, 69(8):2691–2698, 2013.

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Multi-objective optimization of injection molding process by a hybrid of artificial neural network and NSGA-II

Published in 25 Friday

Track

Modeling, Control and Industry

This study presents a hybrid of artificial neural network and NSGA-IIfor multi-objective optimization of plastic injection molding process. The objectivesto be optimized areadimension of thefinished plastic product(product quality), processing time(productivity), and energy consumption(manufacturing cost). Thedata collection and resultsvalidation ismade in a 330 ton plastic injection machine. The design variables considered are mold temperature,material temperature, injection time, packingpressure, packingpressure time, and cooling time. Artificial neural network isused to map the relationship between design variables and output variables. Then,NSGA-IIis used to find the set of Pareto optimal solutions. The results show that the methodology gives the designer flexibility and robustness to choose different scenarios accordingto current design requirements in terms of quality, productivityand energysaving. 

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