The Evolvable Motherboard

We now introduce a research tool designed to allow exploration of design space further than is possible with commercial FPGAs. The tool (henceforth referred to as the Evolvable Motherboard (EM)) allows a large variety of electronic components to be used as the basic active elements, and has an interconnection architecture such that any component pin can be independently connected to any other. Interconnections are directly accessible to test equipment, facilitating analysis of circuits configured on the EM. Fig. 27 is a simplified diagram of one corner of the EM and the plug-in daughter-boards containing the basic elements. The diagonal lines represent digitally-controlled analogue switches which allow row/column interconnection. The minimum number $s$ of switches required to ensure all possible combinations of interconnections between basic elements is equal to the number of different pairs of the total of their pins:

$$s = \frac{n(n-1)}{2}$$ (3)

where $n$ is equal to the total number of basic element pins.

Figure 27: Simplified schematic of part of the EM.

Eqn. 3 can be realised using a triangular matrix of $n$ rows $\times$ $n$ columns, approximated on the EM using commercial analogue crosspoint switch arrays. Each daughterboard takes up to eight lines on the switch matrix, plus a further eight connections to allow for power lines and I/O, which may be required by components such as operational amplifiers or digital potentiometers. EMs have been constructed using $n$ = 48 (Fig. 28), admitting up to 6 daughter-boards. Expansion ports are provided so that several EMs can be daisy-chained together.

Figure 28: An Evolvable Motherboard, with daughter-boards of two transistors each attached.

Connections made using the analogue switches have resistance and capacitance, hence forming an integral part of any circuit configured. In total, approximately 1500 switches are used, giving a search space of $10^{420}$ possible circuits. The `on' resistance of the analogue switches prevents configurations that short the power rails from damaging the EM provided the power supply is less than 3Vdc. Using an ISA interface (not shown), the switches can be programmed by direct writes to a PC's internal I/O ports, allowing circuits to be instantiated in hardware in a very short time ($<$ 1ms).

The Evolvable Motherboard was conceived to help provide insights into choosing the basic element type and interconnection architecture of an FPGA ideally suited to circuit design using artificial evolution, and to aid analysis of bizarre evolved circuits whose operation could not be explained by function-level models. Research is currently in progress using transistors, multiplexers, and operational amplifiers as basic elements, but results presented in this paper are restricted to the use of bipolar transistors. By catering for all possible interconnections, a variety of more restrictive architectures can be evaluated for a given EA by the appropriate choice of genotype-phenotype mapping. While simple circuits have been successfully evolved using the full complement of switches (by directly mapping each genotype bit to a different switch), this is not generally appropriate since candidate solutions tend to short out the basic elements [69]. The following example illustrates the use of an interconnection architecture chosen to reflect the connectivity found in conventional circuits.

The task was to evolve a circuit to minimise the ac error between the output and amplified input voltages, using the fitness measure:

$$f = -\frac{1}{500}\sum_{i=1}^{500} \left\vert a \left( V_{in... ...in} \right) - \left( V_{out_{i}} - O_{out} \right) \right\vert$$ (4)

where a is the desired amplification factor, $V_{in_{i}}$ and $V_{out_{i}}$ are the $i^{th}$ input and output voltage measurements respectively, and $O_{in}$ and $O_{out}$ are the dc offsets of input and output respectively. Amplification $a$ was set to -10. The fitness measure equates to a simple inverting amplifier, however it is not intended to be a practical amplifier since the fitness measure makes no provision for phase shift, and only a single frequency was applied at the input during evaluation: a 1kHz sine-wave of 2mV peak-to-peak amplitude, offset at +1.4Vdc. A rank based, generational genetic algorithm with elitism was used for all the runs, with population size 50. Genetic operators were mutation and single-point crossover, with mutation probability set at 0.01 per bit. The genotype is mapped to the motherboard switches so as to limit the quantity of switches on per row, so that the pins of active components are not too highly interconnected. This is consistent with many conventional circuits where each component pin is only connected to two or three other pins. In the encoding, each column is assigned a corresponding row. The genotype represents the switches a row at a time. For each row, one bit specifies whether the corresponding column is connected, followed by column address and connection bits for up to $n$ additional switches. $n$ was set to 3, and 48 rows/columns were used giving a genotype length of 1056 bits. The task was made non-trivial by denying evolution the use of components that would be considered essential for conventional design, in this case resistors and capacitors. This constraint is potentially useful for VLSI.

Fig. 29 is a circuit diagram typical of those obtained for the task during 20 runs of 8000 generations each. The circuits cannot be analysed in the traditional manner, since the current gain of bipolar transistors ($\beta$) varies widely for different specimens of a given type. Conventional circuits are designed to rely only on this property being above some minimum value [27], whereas unconstrained evolution will exploit the actual value for this and other properties. It is therefore difficult to be certain from the diagram alone which transistors have an active role, and which are `junk'. Using the EM, analysis is far simpler: unplugging each transistor and re-evaluating shows that only Q8 and Q10 are essential to the circuit's operation (Fig. 30). Measuring the voltage directly at the transistors' terminals reveals both are operating as emitter-followers. This simple example demonstrates the EM's potential for evolving and analysing small circuits with arbitrary architectures and active elements, which are elaborate enough to be used as building blocks in analogue design. Currently, the EM's flexibility and observability is being used to study the topologies, dynamics, and failure modes, of unconventional evolved circuits.

Figure 29: A typical evolved amplifier. The small squares represent analogue switches turned on.

Figure 30: A pruned circuit diagram of the amplifier.