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This research project focuses on GA-PSO LECO hybridization optimization method by comparing the performance of this model over other types of built-in optimizers in APLAC Software. The experiment is done to solve the problems with two cases studies single stage amplifier circuit and 2-stage amplifier circuit.
The parameters optimization is executed for the design variable values of the circuit components to obtain the goal as desired solutions to the problems. The optimization process is developed with the idea of multi-resolution approach to achieve a better performance by using integer values in external layer and real values in internal layer of the GA-PSO LECO modal.
Besides of capability to perform with multi-resolution approach with many combinations of different variables, the flexibility of the GA-PSO LECO model to work with multi-objective solution and goal is also extensively inspected in this research.
The general methods used to optimize the parameters are by the implementation of stochastic approaches and mathematical programming by using MATLAB software.
The APLAC circuit design optimization tool that used throughout this research does not equipped with online application for external optimizer like GA-PSO LECO optimization model. As the consequence, the optimization process becomes very tedious and cause human fatigue. But, this limitation provides the opportunity for human interactive process to assess the system data heuristically.
Multi-resolution approach in optimization is the coarse-to-fine strategy that the search is in different scales, promoting global and local optimum. Coarse-to-fine strategy has proven to be able in avoiding of convergence into local minima traps. The existence of many local minima causes the difficulty in finding global minimum (Gefen et al, 2004).
According to Ganovelli et al. (2000), multi-resolution approach improves the precision in the action focus proximity. At the same time it ensures the computation is under a desired boundary. After all, multi-resolution learning approach improves scalability in complex problem, decomposes an original learning task in systematic hierarchical way and promotes exploitation in different resolution level and different correlation structure.
3.1.2 Parameter Optimization
Parameter optimization is done in a given problem to control and improves the performance of a system. It is required to achieve a particular goal with certain accuracy in the desired output. A particular problem is characterized by multiple parameters that contribute vital impact to the input-output data relationship.
According to Peng et al. (2003), parameter setting search becomes more difficult as the higher requirement of accuracy in the proposed system. Yamashita et al. (2006) proposed that the quality of the solution achieved is highly proportionate to the estimation of parameters initial values.
The two classes in parameter optimization are deterministic and stochastic. Deterministic algorithms consume shorter execution time but they do have limitations (Chong and Zak, 1996). Least-square method unable to achieve optimal parameters solution and only may provide rough approximation (Peng et al, 2003). Linear programming and simplex met can only work with linear objective function problem. Meanwhile, non linear programming like gradient and Newton method are only efficient for unimodal objective function (Nam et al, 2001). Nam et al, (2001) suggested the implementation of evolutionary programming in stochastic algorithm to solve multi-modal non linear objective function.
Yamashita et al. (2006) claimed that genetic algorithm possibly solving problems caused by initial values. Somehow, it might not take into consideration the local distribution of the objective function.
3.1.3 Interactive Optimization
Human-computer interactive may provide better impact of performance-wise compared to automated methods that omit human expertise and intuition (Scott, Lesh and Klau, 2001). According to Parmee et al. (2001), interactive optimization exploits human knowledge and intuition within the optimization process. When there is more than one optimal solution available, human intervention may aid the searching process to avoid local minima, reduce the solution spare to be explored and reduce ambiguity (Nacimento and Eades, 2005).
In evolutionary computation, active human intervention are divided into two parts; online knowledge embedding and visualized IEC. Takegi (1998), (2001) mentioned that online knowledge and visualized IEC enhance the acceleration of evolutionary convergence and improve the genetic search.
Users are permitted to edit the gene parameters or mask the certain features of the gene directly when online knowledge embedding is applied. This may reduce the searching space and improve the convergence process.
However, IEC application possesses limitation, whereby human fatigue becomes an obvious limitation factor. Bintrup, Ramsden, and Tiwari, (2007) described human fatigue as a limitation factor for human to evaluate massive designs quantity over a huge number of generations due to psychological or physical exhaustion. Besides, human assessment process is more time consuming compared to automated computation system.
3.2 APLAC Simulation Software
APLAC offers intelligent shortcuts for components manipulation and insertion of components, simulation control objects and models and other functions and devices in the circuit simulation schematic.
APLAC software engine is capable to deliver accurate results in less time for large-scale and highly nonlinear designs, yield the increment of productivity and shorter design cycles.
APLAC high-frequency circuit simulation technology provides the benefits of harmonic balance (HB) analysis in designing complex, extremely nonlinear circuits and that method enables simulation of larger RFIC circuits gets faster with less memory. APLAC is consistently enhanced and finely tuned for more than 15 years, makes APLAC technology used extensively for IC design at Nokia and many device manufacturers over the world. Moreover, APLAC has aided in the design of more than thirty percent of the rest of mobile phone RFICs.
3.3 S-parameters in circuit design
In microwave design, s-parameters are very significant because they are simple and easy to be measured and able to work at high frequencies than other types of parameters. Besides, they¿½re analytically convenient, simple and capable to give a great insight into a design problem or measurement.
S-parameters are broadly used to design RF microwave circuits such as HP TC702 distributed traveling wave amplifier (TWA). S-parameters which are known as scattering parameters are a parameter set that correlates to the reflected or scattered travelling waves when an n-port network is inserted into a transmission line. They are the measurement of voltage wave transmission and reflection through a two-port electrical network.
S-parameter analysis is based on AC analysis. It has many similarities (runs
in the frequency domain and is a linear method) with the AC analysis. However, there are differences too.The main difference between the parameter analysis and an ordinary circuit analysis is that the circuit under inspection is defined as a multiport. The analysis multiport most typically is a 2-port, but can have any (reasonable) number of ports. The S parameter analysis returns s-parameters that describe the behavior of the structure as seen in its ports. This means that the s-parameter analysis does not reveal anything about the node voltages internal to the circuit.
The ease with the measurement of s-parameters makes them very suitable to describe transistors and other active devices. Measuring most other parameters calls for the input and output of the device to be successively opened and short circuited. This could be hard to be done mostly at RF frequencies that lead capacitance and inductance make open and short circuits hard to obtain. Typically, at higher frequencies these measurements need tuning stubs, adjusted at each measurement frequency separately, to reflect open or short circuit conditions to the terminals of device. Not only is this tedious and inconvenient condition, but a tuning stub shunting the input or output may cause a transistor to oscillate, creating invalid measurement. On the other hand, usually s-parameters are measured with the device imbedded between a 50 ohm source and load, and the possibility of oscillations to occur becomes very low.
Another advantage is that travelling waves, unlike terminal currents and voltages, the magnitude does not vary at points throughout a lossless transmission line. This indicates that scattering parameters are measureable on a device that located at some distance from the measurement transducers, as long as the measuring device and the transducers are connected by low-loss transmission lines.
S-parameters are readily measured using network analyzers and are usually tabulated by manufacturers. The stability conditions for a transistor can be found from its s-parameters, also its maximum gain. The input and output matching circuits to achieve a specified performance can be designed from s-parameters data using a Smith chart and all other circuit responses calculated from the overall s-parameters of the resulting circuit.
S11 and S22 are complex reflection coefficients and are usually shown on a Smith chart. S21 and S12 are transfer ratios and are shown on a normal polar plot. Usually S21>1 and S12<1. To preserve the same scale as the Smith chart (a circle of a unit radius) sometimes 1/S21 is plotted instead of S21. Meanwhile, S21 is the most important transistor parameter because it gives the potential gain of the device.
3.4 The GA-PSO LECO model
In this proposed GA-PSO LECO model, GA and PSO are integrated to promote exploration for global solutions through GA and to encourage the exploitation of local area solutions through directional search by using PSO. This results in hybridization of GA-PSO in which to ensure balance exploration and exploitation of search mechanism in this GA-LECO model. GA are used to determine best integer value while PSO used to find more refined solution that is in real valued solutions.
The process of GA is started with random initialization population of candidate solutions called individuals (integer values). Fitness of each individual is calculated to become parents for reproduction. The reproduction process consists of genetic operators known as selection, crossover and mutation. Reproduction process for new individuals is done repetitively. Once GA termination criterion is met, the process is stooped to end the process. Optimal or more optimal parents are ranked based on their fitness, and allowed to reproduce new offspring.
The pseudo-code description for GA is shown as follows:
Let Pc and Pm be the crossover and mutation probability respectively.
t ? 0;
Initialize a population of individuals, P(t), with size N at generation t=0;
Evaluate fitness for each individual;
while (termination condition is not attained) do
Select two parent solutions from P(t) by fitness function;
Randomly generate a number, r, 0?r?1;
Carry out crossover operation on the selected solutions to produce child solutions;
Randomly generate a number, r, 0?r?1;
Carry out mutation operation on the selected solution to produce child solution;
Evaluate fitness of child solutions
Reinsert the child solutions in the new population based on fitness;
t ? t+1;
Meanwhile, in PSO algorithm, the candidate solutions are called particles. These particles are selected from the best individual from GA to go through the process of PSO for real valued potential solutions. For each particle, position and velocity randomly generated. The best found position or coordinate of a particle is called particle and the fitness of each particle are compared to current fitness by using fitness evaluation function. Then, the pbest fitness is updated if the current fitness is better and the pbest positions or coordinates are replaced with the current positions. gbest is the best found position for all particles.
Similar steps are applied for gbest where fitness of each particle is compared with the gbest. The gbest is replaced with the current positions and current fitness is assigned as the gbest¿½s fitness if the current fitness is better then gbest.
From iteration to iteration, particle positions and velocities are repetitively updated to improve the potential solution candidates to the most optimal position until finally the termination criteria is met.
A pseudo-code description for PSO is given below:
Let iter denotes iteration number of PSO.
iter ? 0;
Initialize a population of particles, Pop (iter), with size n at iter=0;
while (termination condition is not attained) do
for each particle
Calculate fitness value;
if the fitness value is better than the best fitness value (pbest) in history
Set current value as the new pbest
Choose the particle with the best fitness value of all the particles as the gbest
for each particle
Calculate particle velocity according equation (2)
Update particle position according equation (3)
Figure 3.1: General flow of the developed multi-resolution GA-PSO LECO model
In this GA-PSO LECO model optimization is firstly done on external layer then only move on to the next internal layers as shown in Figure 3.1 (Neoh et al., 2010) above. Thousands of possible internal layers may exist for each of external layer and these methods create a cascade flow evolutionary search. Firstly, in the first layer, initialization of N individuals that consist of parameter setting in integer values is done randomly. These N individuals then go through the process of GA to determine the approximation of good parameter setting in integer value. Then, the best individuals are selected from the new generated populations to generate population that is in higher resolution real value parameter setting in the next second layer.
Then, optimization is done by using PSO to obtain the best second layer representative. This process flow is repeated until the termination criterion is met. Then finally, the best second layer representative is selected as final result based on their fitness value where those that have highest fitness value will be selected.
MATLAB programming software is used extensively to develop this hybrid GA-PSO LECO model and the pseudo-code description is shown as follows:
GA operation for lower resolution parameter setting;
while (termination condition is not attained) do
for each selected individual of GA
PSO operation for higher resolution parameter setting;
return the best second layer representative (higher resolution setting) to each first layer individual (lower resolution setting)
GA operation for lower resolution parameter setting (update first layer individuals)
3.5 Layered Encoding Structure for Single Stage and Two-Stage Amplifier Circuits Design Variables.
Conventional encoding structures are more common and popular for other problem solving. But the limitation of conventional encoding is they faced the issue of slow convergence mainly as the step or resolution of variables is small to form huge searching space. They are also computationally burden whenever optimization process is carried out offline and the values of variables have to be manually inserted to a simulation or external design.
But conversely, layer encoding structures allow both global and local search. Both global and local search updated through the communication of external layer and internal layer. Different objective and decisions are used in different multiple layers to simplify the evaluation and analysis methods. Furthermore, human intervention is also allowable where a human have the access to select the preferable external or internal layer for chromosome masking. In addition, these layers could develop visualized IEC because mapping of n-D solution to 2-D solution is not needed since layer encoding itself is a straightforward 2-D representation. Therefore, this layer encoding structure provides a direct access for evaluation and to retrieve the required information from the problem model.
Figure 3.2: Layer encoding structure: communication and optimization
Figure 3.3: The layered representation of design variables in amplifier optimization
Figure 3.2 and Figure 3.3 (Neoh et al., 2010) show a two-layered encoding structure that is utilized as solution structure for the design of single-stage and 2- stage amplifier. The structure provides different slice of layer that represents different resolution value of variables. Integer values of variables are designated in external layer whereas real-values (3 decimal place resolution) are represented in internal layer. The purpose of this structure model is to narrow down the search space by encouraging in-depth search for local optimum based on coarser resolution level. These layers are finally combined to attain global optimum after searching for the local optimum.
3.6 Interactive GA-PSO LECO Approach
According to Nishio, et al. (1997); Caldwell and Johnston, (1991); Smith, (1991); Hsu and Chen, (1999), commonly the IEC implementation of human evaluation is in defining the fitness value and chromosome masking.
For this case study, human evaluation is applied for the selection of number of individuals for reproduction process. This done intentionally to narrow down the solution search space by fastening the convergence of EC and also to minimize the human fatigue.
Hybridization of GA-PSO is selected as evolutionary mechanism and applied in the proposed interactive model because it has been proven to outperform the other hybridization techniques which had been done in previous work by Neoh et al. (2010).
Figure 3.4: The interactive GA-PSO LECO flow for MMIC circuit design
The interactive GA-PSO LECO flowchart for the single stage and two-stage amplifier circuit design is shown in Figure 3.4 (Neoh et al., 2010). The steps of procedure are demonstrated as follows:-
* Step 1: First (External) Layer Initialization
Design variables of the amplifier circuit are randomly generated and initialized in integer value. For single-stage amplifier six design variables are used and nine design variables for the two-stage circuit. The integer values are generated respectively according to the ranges given in Table 3.1 and Table 3.3. Next, GA process is utilized with population size of 50 and generations number equal to 5. The fitness value of each individual is obtained for evaluation through GA optimization method.
* Step 2: Human Intervention
In order to select the number of optimal first layer individuals to proceed for next second layer optimization process, human intervention implementation is applied by referring to the fitness of each solution.
* Step 3: Second (Internal) Layer Initialization
The selected first layer individuals are used to be produced in higher resolution real value (in 3 decimal places). PSO algorithm is then applied to search for the best second layer representative for each previously selected individual in Step 2. Particle size used for PSO is equal to 5 for single stage amplifier circuit whereas the particle size used for two-stage amplifier circuit is 2. Meanwhile, number of iterations used for both circuits is 5 in total.
* Step 4: Repetition
Step 2 to Step 3 is repeated until termination condition is fulfilled. Termination criterion is based on human evaluation on the requirement of specification and the objective fitness.
In this project research, two amplifier circuits are investigated to validate the applicability of the GA-PSO LECO hybridization. The first case study is on the single stage amplifier circuit design and the second case study is on the 2-stage circuit design.
In this project, human interaction or intervention is not applied in every GA generations process to minimize human fatigue factor. The GA and PSO parameters are decided or selected based on experience of the circuit designer expert. In GA operation, selection function is applied by using stochastic universal sampling. Genetic operator of four point crossover and two-point mutation operations are implemented with crossover probability, Pc equals to 0.8 and mutation probability set to 0.2.
While for the next operation of PSO, minimum inertia weight, Wmin and maximum inertia weight, Wmax are respectively set to 0.4 and 0.9 in range, whereas both constant factors of C1 and C2 set to 2.
3.7 Case 1: Single Stage Amplifier Circuit Design Optimization
3.7.1 Circuit Structure
Figure 3.5: Single stage amplifier circuit design
Shown in Figure 3.5 is amplifier s-parameter realization and surrounding tuning circuit. The single stage amplifier is represented by its s-parameters (file bpamp.s2p), and the component values of the surrounding tuning circuit are optimized. Referring to the single stage amplifier circuit in Figure 3.5, this circuit consists of few components for the input, output and feedback of the amplifier circuit. At input port 1 and output port 2 of the circuit, the input resistance, Rin and output resistance, Rout are fixed at value of 50 ohm.
Input resistance, Rin, inductance, L1, capacitance, Cin are basically used for input matching of amplifier circuit, while components of output resistance, Rout, inductance, L3 and capacitance, C2 are designed for output matching of the single stage amplifier circuit. Meanwhile, feedback resistance, R1 and feedback inductance, L2 play the role as the feedback network of the amplifier circuit design.
3.7.2 Components Design Variables
This single stage amplifier circuit deals with 6 component variables to for optimization with multi-objective of fulfilling the 3 goals of input and output coefficient and power gain of the amplifier circuit. The range of each design variables for optimization sweep is based on the designer¿½s experience which is of the default values as shown in Table 3.1.
Table 3.1: Synthesis setup of design variables for single-stage amplifier circuit
3.7.3 Multi-objective Specification Requirements
The single stage amplifier circuit designed in Figure 3.5 is represented by its s-parameters of S(1,1), S(2,2), S(1,2) and S(2,1) and also the component values of the surrounding tuning circuit are optimized shown in Table 3.1 and Table 3.2.
The parameters optimization goal is the reflection coefficients, S(1,1) and S(2,2) from the amplifier input and output ports that supposed to be zero with tolerance of 0.2 at frequency of 1.5 GHz, when the other port is terminated by a matched load. This means the acceptable range of reflection coefficient S(1,1) and S(2,2) are between -0.2 and 0.2. At the same time, the power gain, S(2,1) of the amplifier is considered to be met if the power gain, S(2,1) is between 9.8 and 10.2 which is 10dB power gain with tolerance of 0.2 at 1.5 GHz frequency.
The performance of this amplifier are said to be excellent when the value of power gain, S(2,1) is getting higher as the input reflection coefficient, S(1,1) and output reflection coefficient, S(2,2) getting closer to zero. This indicates that goals are to get the value of the power gain, S(2,1) is high as it can, while input reflection coefficient, S(1,1) and output reflection coefficient, S(2,2) is getting lower that is approaching value of zero.
Table 3.2: Specifications requirement for single stage amplifier optimization
3.8 Case 2: 2-Stage Amplifier Circuit Design Optimization
3.8.1 Circuit Structure
Figure 3.6: 2-Stage amplifier circuit design
In Case 2, the inspection of GA-PSO LECO applicability is done on the 2-stage amplifier circuit shown in Figure 3.6. The difference of this 2-stage amplifier circuit to the previous single-stage amplifier circuit in Case 1 is that this 2-stage amplifier circuit design is extended to another stage called second stage.
3.8.2 Components Design Variables
This second stage consists of three more additional components which are resistor, R2; inductor, L4; and capacitor, C3 while the other component variables for stage 1 are similar to the single stage in Case 1.
Similar to single stage circuit in Case 1, the range of each design variables for optimization sweep is based on the designer¿½s experience which is of the default values as shown in Table 3.3.
Table 3.3: Synthesis setup of design variables for 2-stage amplifier circuit
3.8.3 Multi-objective Specification Requirements
The purpose of having 2-stage circuit design is to obtain a bigger overall circuit power gain, S(2,1) value, at least 12 dB, meanwhile, the input and output port reflection coefficients, S(1,1) and S(2,2) must be maintained within -0.2 to 0.2. The closer the reflection coefficients to zero, the better the design is.
Table 3.4: Specifications requirement for 2-stage amplifier optimization
3.9 Relative Fitness Function Setup for Case 1 and Case 2
In this GA-PSO LECO model, weighted-sum method is applied for fitness evaluation based on specified requirement in Table 3.2 and Table 3.4. The weight is set according to the experience and expertise of these single stage and two-stage amplifier circuit designer.
Specified criteria that are not fulfilling the minimum and maximum constraint requirement as in Table 3.2 and Table 3.4, will be added by penalty value of 10. Referring to equation 3.1 ¿½ 3.3 and equation 3.4 ¿½ 3.6 below, F1, F2, F3 are fitness for circuits power gain in dB [S(2,1)], input port reflection coefficient [S(1,1)] and output port reflection coefficient [S(2,2)] respectively.
Single-Stage Amplifier Circuit:
2-Stage Amplifier Circuit:
The method of objectives normalization used in equation 3.1 ¿½ 3.3 and equation 3.4 ¿½ 3.6 are based to the method that also proposed by Morad (1997). Shown in equation 3.7 below, is the total objective value formulation based on calculation of relative fitness of individuals with respect to similar objective value.
Faverage=the average objective value of objective j at generation 1
Fj=objective value of each individual for objective j
Ftot=total objective value
?j=weight for objective j
The total summation of the rest objective value, Ftot, is calculated by using the formulas shown in equation 3.8 as follow. This calculation is adapted from previous equation 3.7 with the objective weight as given in Table 3.2 and Table 3.4.
Optimization of the single stage and two stage circuit design variables is done with the main objective of minimizing Ftot at the specified frequency of 1.5GHz.
The built-in optimizers in APLAC are Gradient Optimizer, Genetic Optimizer, Random Optimizer, Anneal Optimizer, Exhaustive Optimizer, Multidirectional Optimizer, Min-Max Optimizer and HookeJeeves Optimizer is applied to optimize the design variables of the amplifiers. Simulated Annealing and Genetic optimization belong to the category of intelligent global optimization methods, while Gradient, Conjugate Gradient, Hooke-Jeeves, Min-Max, Multidirectional Search, Nelder-Mead and Gravity Center are local optimization methods. Random and exhaustive search are robust global methods.
Due to the difficulty to plug in the MATLAB software to APLAC, the genetic search for this case study is done manually by offline. The results obtained from each built-in optimizer methods are finally compared with the interactive GA-PSO LECO model approach for performance evaluation.