Automated synthesis of 8-Output Voltage Distributor using Incremental Evolution
Yerbol Sapargaliyev, Tatana G. Kalganova School of Engineering and Design, Brunel University
Uxbridge, Middlesex, UB8 3PH, UK
{Yerbol.Sapar, Tatiana.Kalganova}@brunel.ac.uk
Abstract
The automated synthesis of the analog electronic circuit, including both the topology and the numerical values for each of the circuit’s component, is recognized as a difficult problem. This problem is aggregating considerably when the size of a circuit and the number of its input/output pins increases.
In this paper for the first time the method of automated synthesis of the analog electronic circuit by mean of evolution is applied to the synthesis of multi- output circuit, namely 8-output voltage distributor, that distributes the incoming voltage signal among the outputs in filter-like mode. Using the substructure reuse, dynamic fitness function and incremental evolution techniques the largest analogue circuit has been evolved in the area that has 138 components.
1. Introduction
The Evolutionary Electronics is one of the most promising areas of today’s electronics. It is also known as automatic design of electronic circuits with help of Evolutionary Algorithm (EA). EA together with a circuit simulation tool (or the real hardware) automatically designs the circuit for the given problem. The circuits evolved may have unconventional designs. The EA is nowadays mostly represented by Genetic Algorithm, Genetic Programming, or Evolutionary Strategy (ES).
The general idea is the EA navigated by fitness values, provides randomly created and mutated chromosomes.
Each chromosome encodes the structure for a circuit in the form of a genotype and has to be evaluated by a fitness function. The fitness function assigns each chromosome with a fitness value that defines how close the current hardware is to the target by its functional characteristics. Selecting the best chromosomes by their fitness, cloning them (and/or crossing them over), mutating and evaluating them compose the full cycle of the search process. According to the Darwinian laws of natural selection, running the cycle repeatedly will lead to the best individual. The successful circuits most of all depend on the evolutionary technique that one has worked out and applied. The evolutionary technique is a set of rules according to which, parameters of EA (e.g., mutation rate, crossover, selection), genotype length
varying strategies [3], mutation types and the circuit representation techniques are designed and managed.
Despite that recently the EA was successfully applied to the design of the range of analog circuits (low-pass filters [1], [2],[4],[6],[8],[9],[13]-[17],[20]-[22],[24],[25], high-pass filters[1],[14],[17],[20],[22], amplifiers [1],[4], [7],[11],[13],[18][19],[19],[20],[24],[26],[27], digital-to- analog and analog-to-digital converters [1],[5], computational circuits [1], [3],[23], other kind of circuits [1],[8],[11]), all the previously reported designs were the analog circuits with maximum two outputs [1]. By contrast with the evolutionary design of digital circuits, where the scalability problem caused by numerous inputs and outputs is tackled ([29],[30],[31]), in the analog domain we could not find any similar example.
One reason is that the analog circuit with multiple outputs is supposed to perform a complicated signal processing providing the package of high-ordered output signals (in time) to the circuit’s outputs. The size of such kind of circuit may count hundreds of components that expand the solution space to search in drastically (about to b2k3l+ck+l, where
k
andl
are the numbers of 2-pin and 3-pin components in the circuit and b, c are some constants).In this paper we described the successful attempt to overcome this issue by applying ES to the design of 8- output Voltage Distributor. The conventional method of a circuit design could easily solve this task by utilizing the up-to-date digital signal processing circuits, such as controllers with built-in analog-digital-analogue conversion. However, purely analogue circuits, in comparison with digital ones, can provide considerably shorter delay in the circuit response and suggest the economy in components. The last argument becomes more vital if the difference in components between the competing circuits reaches hundreds of times.
The next section overviews the previous work in the area. Section 3 introduces the whole evolutionary technique. Section 4 describes the experiment. And, finally, the last section concludes the paper.
2. Previous work
The importance of analogue evolutionary circuit design is well described in [3] and [6]. In Table 1 we included the majority of the works in evolutionary
analogue circuit design. Most of the works start from evolving a passive low-pass filter which consist of R,C,L components. A low-pass filter is a convenient tool for the probation of evolutionary technique and tuning the EA parameters towards the more sophisticated designs [9].
The second stage of probation of the technique is usually undertaken over the circuits that have already been evolved previously by other researchers, however these are much more sophisticated and consisted of R,C,L and Q (npn/pnp) components. Obtained by authors the computational circuits [10] encouraged to approach more complex circuits targeting the analog circuits that never have been designed before due to their complexity.
The evolutionary design of complex circuits are numerously instantiated in digital domain, where according to [30] “designers have introduced various approaches, which can be divided into three classes:
functional level evolution, incremental evolution and development”. Among these methods only “divide-and- conquer” ([1],[12]) were distinctly utilized in analog domain, however, as it can be seen from Table 1, the
targeted circuits there were not complex enough to fully exploit the potential of the proposed techniques.
The experiment described in this paper utilized the incremental evolution, last one we see as a case of more general “divide-and-conquer” approach. Incremental evolution has widely been exploited in digital circuit synthesis (i.e. [28], [30]). The essence of incremental evolution lies in decomposing the target into subtargets that are supposed to be evolved more easily than initial target. In our case, the 8-output Voltage Distributor was decomposed into 8 separate subcircuits each of which was connected to the same one source and had its own output (Figure 1). The evolution started from the first device and upon the completion of the task moved to the next one, and continued until it finally designed the 8-th subcircuit. The experiment is accepted as finished if all 8 subcircuits evolved with satisfied fitness. Since the experiment ran non-stop throughout all eight substages, the dynamic fitness function was introduced similar to
“adaptive fitness schedule” from [7] that is, the fitness function was incremented “whenever the current fitness threshold was reached by at least one chromosome in a population”.
Table 1. Notable advances on the evolution of analog circuits. SA is Simulated Annealing, CS is Clonal Selection, D&C is Divide-and-Conquer, Dev is Development
Year Type of EA
Parameter optimization
Substruc-
ture reuse Method
Maximum inputs/outputs of
evolved circuits
Maximum circuit size evolved
Kruiscamp et al [27] 1995 GA No No No 1/1 22
Koza et al [1] 1997 GP No Yes D&C 3/3 64
Lohn et al [6] 2000 GA No No No 1/1 23
Goh et al [13] 2000 GA No No No 1/1 12
Zebulum et al [4] 1998 GP,GA No No No 2/2 19
Grimbleby [15] 1999 GA GA No No 1/1 10
Dastidar, et al [18] 2005 GA GA Yes No 2/1 18
Ando et al [14] 2003 GP,GA GP,GA No No 1/1 22
Sripramong et al [19] 2002 ES+SA hill-
climbing No No 1/1 41
Shibata et al [23] 2002 GA GA No No 1/1 66
Alpaydın et al [26] 2003 ES+SA No No No 1/1 33
Fan et al [16] 2002 GP No Yes Dev 1/1 19
Chang et al Su [21] 2006 GP No Yes No 1/1 17
Mattiussi et al [8] 2007 GA No Yes Dev 2/1 46
Xia et al [24] 2007 GA No No No 1/1 11
Gan et al [20] 2007 CS No No No 1/1 7
Das et al [22] 2007 GA GA No No 1/1 15
Wang et al [12] 2008 GP GA No D&C 1/1 13
Kim et al [25] 2009 ES GA No No 1/1 14
Sapargaliyev et al [9] 2006 ES No No No 1/1 27
Sapargaliyev et al
[10] 2009 ES No Yes No 1/1 44
In this paper 2009 ES No Yes Increm
ental 1/8 138
3. Evolutionary technique
3.1. Representation and embryo circuit
We suggest five types of components that the targeted circuit would consist of: NPN bipolar transistor (Qn), PNP bipolar transistor (Qp), resistor (R), inductor (L) and capacitor (C). The linear (direct) circuit representation is proposed for use, similar to one that exploited in [4], where is every component of a circuit is represented as a particular gene, and each gene consists of exactly 4 loci corresponding to component’s features:
component’s name, component’s nodes and component’s parameter (except Q). In such a way the whole circuit is represented by the column of genes that called
“chromosome” of that particular circuit. The chromosome looks exactly the same as the PSPICE netlist, so, there is no necessity to convert the genotype into the netlist.
Figure 1. Embryo circuit Figure 2. The N-output Voltage Distributor The embryo circuit is a group of components (including a source of input signal) that is predetermined for the particular circuit. Mostly, these components are located at the circuit’s inputs and outputs.
On Figure 1 there is the embryo for 8-out Voltage Distributor. It consists of source of input signals (V_IN), eight source resistors (Rs) and eight load resistors (Rl1…
Rl8). The embryo also have two sources of direct voltage suggesting the evolution to choose between (or use both) 15V and 1.5V.
3.3 Program structure and mutation types Figure 3
generally shows the algorithm of the experiment. It consists of 4 main blocks that
have been coded and united in one C++
program.
Figure 3. The flowchart of the experiment
The Start-block provides the population of embryo chromosomes in the form of PSPICE netlists to the ES block. At this stage the embryo is cloned to amount of the population number, and then every clone is grown up randomly with the help of 5 starting components described in section 3.1.
The ES block contains and applies the particular parameters of ES, such as: mutation rate, population size, selection criteria (fitness function) and termination terms. First of all, the ES block gets the whole population of size P with the fitness value assigned to each chromosome from the previous block. According to the prescribed selection value S% (usually from 1 chromosome to 50% of the total population), it chooses the best S% of the chromosomes as parents for the next generation. Then, the ES block clones each of the selected parent chromosome in amount of (P*S/100) per individual that makes the population complete again.
After that, the block applies the mutation procedure to each individual. There are totally 4 types of mutations, which are the Add_new_component_mutation (ANEM), the Delete_component_mutation (DEM), the Circuit_structure_mutation (CSM), last one includes 3 subtypes: component_name_mutation, component_pin_
mutation and component_parameter_mutation. We also regarded the Substructure_reuse_mutation (SRM), during which the group of genes are modified at one procedure, as another type of mutation, since it is just another way of chromosome modification. Each mutation modifies M% of the total amount of the chromosome’s loci, where M is the prescribed mutation rate value (usually varying from 0 to 10%). Since any gene (whole component) contents exactly of 4 loci, the ANEM and DEM modifies (adds/subtracts) the chromosome per fours loci at least, whereas CSM mutates per ones loci. So, to mutate 5% of the
chromosome with 20 genes (80 loci) means to modify only 4 loci, which is achievable by applying one ANEM or one DEM procedure or applying CSM four times.
In general, the behavior of the chromosome’s length (circuit size) during evolution corresponds to “oscillating length genotype strategy” proposed in [4], where the chromosome’s length can grow-up as well as short in size down.
Getting the cir-batch-file from Block 2 (ES block), the Block 3 starts PSPICE, simulate and saves the results in out-file. PSPICE is utilized in non-interactive batch simulation mode.
Block 4 contains the fitness function. It reads all chromosomes one by one from out-file, evaluates them assigning the fitness, selects the best S%, ranges them and sends the results to the Block 2.
3.4 Targeted circuit and the incremental evolution
The general view of the N-output Voltage Distributor is presented on Figure 2, where in our case N=8. As an input signal for targeted circuit we took the piecewise voltage form starting from 0V, going up to 5V for 3.5sec and down to 0V for last 1.5sec. (Figure 4.). The task for each output was working in filter-like mode that is to pass the input signal that located within particular voltage band, saving the form of the input signal. That is, the band-pass width for each of the output was the same and equaled to 0.625V: the 1-st output passed the only voltages from 0 to 0.625V), the 2-nd output passed the only voltages from (0.625-1.25V), the 3-rd band-pass was (1.25-1.875V) , the 4-th was (1.875-2.5V), the 5-th was (2.5-3.125V), the 6-th was (3.125-3.75V) , the 7-th was (3.75-4.375V) and finally the 8-th was (4.375-5V).
The summary of transient analysis at input and eight output pins of the targeted ideal 8-out Voltage Distributor is presented on Figure 4. As could be seen, the graph on Figure 4 must exactly repeat the form of the input piecewise signal.
As mentioned above, the incremental evolution was introduced for design of 8-output Voltage Distributor.
The fitness function were incremented each time whenever the current task was fulfilled. Totally 8 tasks corresponding to 8 subcircuits were set. Each subcircuit was responsible to get the incoming signal and to provide the outcoming signal to the corresponding output. If the first task was a design of the first subcircuit, the second task was the design of both the first and the second subsicruts, the third task was a design of the first, the second and the third subcircuits and so on. Finally, the 8-th task was a design of all 8 subcircuits that is the whole Voltage Distributor circuit.
For each task the new fitness function was introduced, that incrementally counted the fitness of all subcircuites evolved at the time.
Figure 4. The united transient analysis of potential at input and eight output pins of the targeted 8-out Voltage Distributor.
The main advantage of such the approach was the possibility to start the evolution of the next subcircuit (i.e. the 3-rd) based on the reuse of the previously evolved subcircuits (i.e. the 1-st and 2-nd). Due to the similarity of functions that subcircuits are going to perform, the evolution’s task (except the first subcircuit) was just to reprocess the previously evolved sibcircuits to the new subcircuit with a new pass band.
There are two types of substructure reuse that we implied in the frame of this work. The first one is one of the mutations (SRM) applied to chromosomes using as substructures the fragments of successful chromosomes.
Another kind of reuse was applied during incremental in between the transition from one subcircuit to another using as substructures the whole subcircuits evolved in previous substages. If the place for the first substructure inside the circuit is randomized, the place for the second one is definite: between source and load resistors on Figure 1.
3.5 Fitness function and experiment implementation
The dynamic fitness function scheduled to each incremental substage as a simple sum of the fitness values of all subcircuits evolved at the time. The final fitness function of the 8-output Voltage Distributor was
F=
8 1 i i
F
i,
whereF
i is a fitness value of the subcircuit i that calculated by the following way: we made the OrCAD PSPICE simulator to perform transient analysis at each output for 5 seconds at 81 equidistant time-points; a fitness value was set to the sum, over these 81 fitness cases of the absolute weighted deviation between the target value and the actual output value voltage produced by the circuit; the fitness penalized the output voltage by 10 if it was not within 50% of the target voltage value. The smaller the fitness value, thecloser the circuit to the target. The termination criteria for the whole circuit was the fitness value was not improve over 20 consecutive generations, or if the best subcircuit exceeded 100 components. The condition for stopping the evolution of current subcircuit and getting to another was whether fitness exceeds the fitness threshold (0.05) or the generation number exceeds 200.
The Evolutionary Strategy with linear representation and oscillating length genotype was utilized. 1%- selection scheme was applied that is S=1% of the best chromosomes were chosen for the next generation. Being chosen for the next generation each chromosome contributed 100 new chromosomes for the next population, thus, totally 1% of the selected chromosomes generated 100% population of the next generation. The evolutionary strategy is deserved the name of the simplest evolutionary algorithm, because it doesn’t content the crossover operation: all the offspring chromosomes are identical to a correspondent parent. A static mutation rate of 5% was allowed to apply to each chromosome by one of the mutation instruments described in subsection 3.3.
Population size of 30,000 chromosomes was set. We used 5 PCs with Intel Core 2 Duo/2GHz processor running at the same time independently from each other.
The results presented in the next section are the best out of the 5 runs for each case with different seeds for the random number generator.
4 Experimental Results
The average time of the evolution of the 8-out Voltage Distributor was 344 hours, which is about 43 hours per subcircuit. The best-of-run circuit (Figure 5) appeared at 629-th generation and had 138 components (embryo excl.), among which 38 resistors, 8 capacitors, 7 inductors, 46 NPN transistors and 39 PNP transistors, with the best overall fitness 1.757. Table 2 highlights the
detailed information per incremental substage: the best fitness, the component number of the evolved subcircuit and the successful generation number. The most ideal signal with fitness 0.028 was provided by out-pin No.2 that responsible for band 0.625V-1.25V; the worst reply with fitness 0.797 was at the out-pin No.7 in band 3.75V-4.375V. Figure 6A shows the transient reply of the circuit for the incoming piecewise signal.
Table 2. The summary of evolved 8-out Voltage Distributor and its composed subcircuits.
To verify that circuit we had got worked properly we applied the different arbitrary signals to it. Figure 6B shows the more complicated piecewise signal and the transient reply at outputs. Figure 6C shows the arbitrary sinusoidal signal applied and the transient reply of the circuit. As could be visually noticed each particular subcircuit gives accurate replies throughout the different examples, what enables us to assume that the relative fitness of each of the subcircuit as well as the whole circuit less of all depends on the characteristics of the incoming signal.
5 Conclusion
In this paper we described the application of the ES to the design of analog multi-output circuit, namely 8- output Voltage Distributor. To succeed with the target we utilized the linear representation, oscillating length genotype strategy, four types of mutation including the substructure reuse and the incremental evolution together with the dynamic fitness function that led us to the universal Voltage Distributor circuit with 8 outputs and with the largest component number for evolved analog circuits 138.
The technique described is plain with simple algorithm that could be easily reconstructed.
Fitness Componen t No
Generation succeed
Subcircuit 1 0.095 10 76
Subcircuit 2 0.028 22 132
Subcircuit 3 0.174 16 110
Subcircuit 4 0.323 23 37
Subcircuit 5 0.049 14 26
Subcircuit 6 0.200 23 107
Subcircuit 7 0.797 22 104
Subcircuit 8 0.089 8 37
Total 1.757 138 629
V_IN
V_OUT_3 V_OUT_2 V_OUT_1
V_OUT_8 V_OUT_7 V_OUT_6 V_OUT_5 V_OUT_4
R 5 3 . 9 E + 4
Q n 3 1
Qp11
R 2 7 1 . 2 K 1 . 5 V
Q n 1 8
R 2 5 6 8 1 . 5 V
R 3 7 1 E + 5
C 2 3 . 9 n
Qp19
Q n 1 9
1 5 V
R 7 1 5 0 K
Q n 4 1 Qp16
L 4 0 . 6 8
1 5 V
1 . 5 V
1 . 5 V
R 1 9 1 E + 5
Qp13
Q n 3 7
1 5 V 1 5 V
R 2 3 4 7 0
Qp7 R 0 2 7 0 K
1 5 V
Q n 1 3
Q n 2 0
L 6 6 8 M 1 . 5 V
1 5 V
Qp29 Qp14
Qp26
1 . 5 V Qp37
R 1 8 2 . 7 E + 7
1 5 V
Q n 3 8
Qp38 Qp10
Q n 4
Q n 5
R 8 3 9 0
1 . 5 V Q n 4 2
1 . 5 V
1 5 V
Qp12
Q n 2 9
R 2 6 1 8 0
R 3 2 4 . 7 K 1 5 V
R 3 1 . 8 k
Q n 4 4
R 9 4 7
R 2 8 1 8 0 K C 6
1 . 8 E - 4 1 5 V C 0 3 3 n
Q n 2 4
R 2 4 1 . 8 K
R 1 6 1 2 K
Q n 1 7
1 . 5 V
1 5 V R 1 2 3 . 3 K
Qp25
R 2 9 . 4 k
Qp21
1 5 V 1 5 V
1 . 5 V
Qp31 1 . 5 V
R 3 6 1 8
Q n 0
L 2 6 . 8 M
Q n 4 5 Qp5
Qp33 Qp6
Qp8 Qp2
R 1 0 1 . 2 E + 5 K
Qp23 R 2 2
1 . 2 K 1 5 V
R 1 7 8 2 K
C 5 8 2 n 1 . 5 V
Q n 4 3
Qp15 Qp9
1 5 V
Q n 2 7
1 5 V
R 3 3 2 . 2 K R s 4
3 0 R s 3 3 0 R s 2 3 0 R s 1 3 0
Q n 7
R s 5 3 0
R s 6 3 0
R s 7 3 0
R s 8 3 0
R l 5 1 0
R l 6
1 0
R l 7
1 0
R l 8
1 0 R l 4
1 0 R l 3
1 0 R l 2
1 0 R l 1
1 0
R 3 0 8 2 0 R 2 9 1 8 K
Q n 2 5
Qp22 R 2 1
1 . 8 K R 1
1 . 8 k
Qp36
C 4 2 . 7 E - 3
1 5 V Q n 3 3
1 . 5 V Q n 2
Q n 2 3 Q n 3
L 5 5 6 M
Q n 1 1 Q n 8
L 0 2 . 7 M R 1 3 1 2 K
Q n 6
Q n 2 2 Q n 9
R 1 4 1 E + 5
Q n 3 5
Qp0
Q n 3 4 Q n 1 0
Q n 2 1
Qp34 1 . 5 V
1 5 V
Q n 1 6
Q n 3 9 Q n 2 6
L1 2.7M
R 2 0 6 8 K
R 3 1 2 . 2 K
Q n 4 6 R 1 1
1 . 8 K
Q n 3 0
Qp30
1 . 5 V
Qp27 R 4 1 E + 3
1 5 V
1 . 5 V
R 3 4 1 . 5 K R 1 5 5 6 K
C 7 2 7 n
1 5 V
R 3 5 1 E + 9
Q n 4 0 1 5 V
1 5 V Qp17
Qp24
1 5 V
Qp3
Q n 1 5
1 . 5 V
Q n 1 2 Q n 1 4
Qp39 1 . 5 V
1 . 5 V
1 . 5 V Q n 2 8
1 . 5 V
Qp18
1 . 5 V
L3 0.33
C 1 2 . 7 E - 5
1 . 5 V
Qp32 1 . 5 V Qp1
Qp4
1 5 V Qp20
C 3 3 9 n
Q n 3 6 Qp35
Q n 4 7
Figure 5. The evolved 138-component 8-output Voltage Distributor
A B C
Figure 6. The summary of transient analysis at input and outputs of the 8-out Voltage Distributor. A-the input signal is a piecewise signal used in evolution, B-the input signal is an arbitrary piecewise signal applied for the circuit verification, C-the input signal is an arbitrary sinusoidal signal applied for the circuit verification
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