Download A Niched Cartesian Genetic Programming for Evolvable Hardware

Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 3, 37 - 43, 2016
doi:10.21311/001.39.3.6
A Niched Cartesian Genetic Programming for Evolvable Hardware
Fuchuan Ni1, 2*, Yuanxiang Li1 , Xiaoyan Yang1, Jinhai Xiang2
State Key Lab of Software Engineering, Wuhan 430072, Hubei, China
2
College of Informatics, Huazhong Agricultural University, Wuhan 430070, Hubei,China
*Corresponding author(E-mail: [email protected])
1
Abstract
Evolvable hardware (EHW) adapts its structure and functionality at run time, by evolutionary algorithms, in a
dynamic and uncertain environment. Because of man-for-one genotype-phenotype map in EHW, the problems
of evolving digital circuit are multi-modal optimizations. As an important algorithm for EHW, Cartesian
Genetic Programming suffers from a premature convergence caused by the genetic drift. The genetic diversity in
a population decreases quickly and it loses an exploration capability. To maintain the diversity of the population
and search for all the global solutions, niched techniques are tailored into traditional Cartesian Genetic
Programming (NCGP). The results of the compared experiments on benchmark circuits demonstrate that the
niched Cartesian Genetic Programming can maintain the diversity of the evolving population, avoiding
premature and is more likelyto find all the global solutions.
Key words: Evolvable Hardware, Cartesian Genetic Programming, Multi-modal Optimization, Niched
Technique.
1. INTRODUCTION
Evolvable hardware (EHW), is an adaptive hardware system (AHS) to dynamically alter the hardware
functionality and structure of its circuits using technics inspired by natural evolution (X. Yao and T. Higuchi,
1999). The circuit structure and parameters are reconfigurable by the control of evolutionary algorithms (EAs)
on the flexible hardware substrate. These techniques began to be treated with increasing interest in the mid1990s when Garis introduced the concept of EHW (Garis, 1997). Eiben A E and Jim Smith deem that
evolutionary algorithms pave the way: from software to hardware, going from digital evolutionary systems to
physical ones (Eiben and Jim2015).
In the beginning, the binary bitstreams, is the simplest form of evolvable hardware. But scalability is the
issue when large designs are considered. To search efficiently and effectively, many representations for EAs
were researched, such as genetic programming (GP) (Koza,1992), evolution strategy (ES) (Bäck and
Hoffmeister, 1991), grammatical evolution (GE) (Ryan and Collins,1998), evolutionary programming (EP)
(Fogel and Owens, 1996), Cartesian Genetic Programming (CGP) (Miller and Thomson,1999), adaptive GA
(AGA) (Ko and Kang, 1997), parallel GA (PGA) (Alba and Tomassini,2002), compact GA (Harik and
Lobo,1999), traceless genetic programming (Oltean,2004), multi expression programming (Oltean,2004), gene
expression programming (Yan and Wei, 2006), and so on . Genetic programming (GP), gene expression
programming (GEP) and multi expression programming (MEP) are tree-representations algorithms; Cartesian
Genetic Programming uses directed acyclic graphs to represent the digital circuits and programs.
Among these algorithms, CGP is the most popular, important algorithm for evolvable digital circuits.
Cartesian Genetic Programming (CGP), uses evolution strategy (ES), operating with the population of (μ+λ)
individuals by point mutation. Like other forms of evolutionary algorithms, CGP is easily to fall into local
optimal point, and is difficult to find all the global optimal solution for multi-modal problems.
Niching methods are effective to maintain the population diversity and reduce the losses that result from
genetic drift. (Goldberg and Richardson, 1987) proposed Genetic algorithms with sharing for multimodal
function optimization. (Manner and Mahfoud, 1994)utilized crowding to preserve multimodal diversity. (Hwang
and Cho, 2009) uses the speciation technique to enable diverse circuits to evolve efficiently by the process of
one-step evolution. However, the speciation techniques in (Hwang and Cho, 2009) woks on bitstreams
representation based on the simplified GAL chips with only one OLMC. The techniques can not apply in EHW
based on FPGA directly.
This paper proposes a concise niched technique for Cartesian Genetic Programming algorithm to evolve
the digital circuits. The proposed techniques are useful for fault tolerant application, evolvable robotics.
This paper is organized as follows. Section 2 considers the principle of EHW, Cartesian genetic
programming and the many-for-one mapping problems in EHW. Section 3 proposes a sharing niched technique
and tailors the technique into CGP to maintain the diversity and the ability of searing all the global solutions for
evolving combinational circuit. Sections 4 present the simulation results with the 3-bit adder circuit. The
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Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 3, 37 - 43, 2016
experiments are conducted by comparing the conventional CGP and the Niched CGP. Finally, section 5 presents
the main conclusions.
2. CARTESIAN GENETIC PROGRAMMING
Based on Programmable Logic Devices (PLDs) or reconfigurable devices, the configure strings, are
evolved, selected and evaluated in an adapt process controlled by EAs. The principle schema of an EHW is
illustrated in Figure 1.
Inititial Chromosome
New Chromosome
0111000101001110101
Evolve
1011010101001110101
Select
I0
I1
Reconfigurable device
Evolve
1011010101001110101
Select
I0
I1
Evaluate
I2
Evolved Chromosome
...
...
I2
EA Process
I0
I1
Evaluate
I2
EA Process
Reconfigurable device
Reconfigurable device
Figure 1. Principal schema of an EHW.
2.1.The Cartesian genetic programming
Cartesian genetic programming (CGP), as a linear genetic programming, was proposed by J.F. Miller et al in
1997. CGP uses directed acyclic graphs to represent programs, rather than the more familiar representation of
programs as trees. This is loosely inspired by the architecture of digital circuits called FPGAs (field
programmable gate arrays). The original CGP was represented by a two-dimension matrix of nodes. There are
functional nodes and output nodes in CGP. Each functional node consists of connecting genes and functional
gene and the output nodes is composed of connecting gene. In a feed-forward manner, nodes take their inputs
from either a program input or output of the previous nodes in the matrix. Nodes in the same columns cannot be
connected to each other. The chromosome is linearly sequenced. The genotype of CGP has a fixed length. CGP
has an important trait of non-boat. CGP does not suffer from genotype growth and phenotypic growth (Miller
and Smith, 2006).The genotype is a list of integers that represent the program primitives and genetic encoding is
compact, simple and easy to implement. CGP can handle multiple outputs easily (Miller and Thomson,2000).
To detail CGP, the one-bit adder is exemplified, as it is shown in Fig. 2 and Fig. 3. Fig 2 is the genotype
representation of the one-bit adder and Fig. 3 is the one-bit adder circuit decoded from the genotype. The
chromosome is arranged as : 2 0 1, 0 1 3,1 0 3 ,4 2 1,0 1 1,2 4 3,2 8 1,6 7 2,3 1 0 ,10,8 .The Length of the
genotype is 3 ×3 ×3 ＋2＝29.
B
0
1
3
0
A
3
4
1
C
2
5
4
1
6
9
10 Cout
2
0
1
7
6
2
10
3
8
S
8
7
1
2
11
4
Figure 2. the genotype representation in CGP
A
B
Cout
C
S
Figure 3.one-bit adder circuit decoded
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The genotype-decoded process begins form the output nodes by checking which nodes is connected to the
output nodes. Then these nodes are examined to find out which nodes required recursively. Refer to Fig.2, the
output node Cout is addressed by 10; then move to 10. Node 10 connects to node 6 ,7 and move to node 6 and
node 7. Node 7 connects to the program input 0 and 1; Node 6 connects to node 4 and the program input 2. Then
move to node 4 which connects to the program input 0 and 1. Therefor output node Cout is decoded. The output
node S is decoded in the same manner. The nodes decoded are active nodes. According to the function look-up
table, the final circuit is decoded as Fig. 3.
When the genotype is decoded, some nodes may be not used in the calculation of output data. These nodes
are non-coding nodes. In Fig.2 nodes 3, 5, 9, 11 are not decoded and they are inactive. These inactive genes
have a neutral effect on genotype fitness. This phenomenon is “neutrality”. (Miller and Smith, 2006) argued that
the influence of neutrality beneficial to the efficiency of the evolutionary process on a range of benchmarks.
The genotype-evaluated process compares the output to the desired program outputs, and calculates the
fitness of the genotype fi for a single input data item. In digital-circuit evolution the usual number of fitness
cases is no2ni (here no is number of output, n i is number of input).
CGP evolutionary algorithm is a form of evolutionary strategy using small populations and elitism. A simple
(μ+λ) evolutionary algorithm is widely used for CGP. The traditional Cartesian Genetic Programming is shown
in the following procedure (Miller,2011).
The (μ+λ) Cartesian Genetic Programming (μ=1,λ= 4)
for all i such that 0 ≤ i < 5 do
Randomly generate individual i
end for
Select the fittest individual, which is chosen as the parent
while a solution is not found or the generation limit is not reached do
for all i such that 0 ≤ i < 4 do
Mutate the parent to generate new individual
end for
Select the fittest individual according to the following rules:
If the new individual is no worse than the parent then
the new individual is promoted as the fittnest
else
The parent chromosome remains the fittest
end if
end while
The Mutation operator in traditional CGP is point mutation, which works by randomly choosing a valid
allele at a randomly chosen gene location. When offspring genotypes in the population have the same fitness as
the parent and there is no offspring better than the parent, an offspring is chosen as the fittnest. (Yu and Miller
2001; 2002) argued that both the simple operator and the simple evolutionary strategy are so effective is related
to the presence of non-coding genes. Also the CGP algorithm navigates the search space using neutral drift.
There is a different opinion. (Hu and Joshua, 2012) demonstrated that the benefits of neutrality are
problem-dependent and that the relationships between robustness, evolvability, and accessibility vary amongst
the genotypic, phenotypic, and fitness spaces of linear GP.
2.2 The genotype-phenotype Map
The genotype-phenotype Map in EHW is a Many-for-one Map. It lies in three ways. First of all, a logic
circuit could be described with many logic expressions. Even the simple logic expression, could be represented
as "multiply of sum” or "sum of multiply". There is many-for-one map between physical logic circuits and the
formal description. Secondly, there is a Map between genotype and phenotype in CGP chromosome
representations. Many chromosomes would map into only one circuit that has the same functionality, i.e. the
same physical logic circuit has many encoding representations. CGP does not guarantee similarity of hardware
structures resulting in similarity of fitness. Finally, as mentioned above, because neutral drift results that the
mutational offspring are not necessarily phenotypically different from parents, fitness evaluations may be
wasteful.
(Hwang and Cho, 2009)studied the landscape of the half-adder contained in the EHW. They calculated the
ruggedness of the fitness landscape by using the auto-correlation function and found complicated spaces contain
many peaks that can lead to deceptions when using the evolving process. This means it is very difficult to search
for the optimal points.
In CGP, the individuals that have the greater fitness have greater possibilities to reproduce. Thus, in the
later stage in evolving process, the difference between the individuals becomes little and “stalling effect"
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appears. CGP, as other evolutionary algorithms, also suffers from a premature convergence problem caused by
the genetic drift. The genetic diversity in a population decreases quickly and it loses an exploration capability.
Due to the Many-for-one Map, CGP has many local optimal solutions and the problems solved by EHW
have the limitations in scalability (Vassilev and Miller, 2000; Gordon and Bentley,2005; Haddow and
Tyrrell,2011). (Ni and Li, 2014) proposed an orthogonal genetic operator to improve the CGP. More scalable
ways to search the solution space for more complex EHW applications must be explored. Niched techniques
increase the increase the diversity of population in evolutionary algorithms and maintain diverse solutions in a
multimodal optimization problem with high dimension.
3.THE NICHED CARTESIAN GENETIC PROGRAMMING
Because the solution space grows exponentially with the increasing number of inputs and the outputs
(assuming that an output decided by all possible input combinations) and many for one genotypes- phenotype
map, The problem of EHW is a multimodal optimization .The simple evolutionary strategy (ES) often traps into
local optima ,or Stalling. It is difficult to find the global optimal solution, not to mention all local optimal
extreme value points. To improve the efficiency of CGP for the multi-modal problems in EHW, niched
techniques are tailored to be a niched Cartesian Genetic Programming. They maintain diverse solutions by
punishing overpopulated solutions or discarding similar one. The distance measuring is an essential part of the
algorithms because they use the closeness of solutions to decide to whether give a penalty or discard one.
3.1 The fitness sharing niched elimination strategy
To maintain the diversity of the population, a fitness sharing niched method is adopted to eliminate the
similar chromosomes. Similarity is Hamming distance on genotype or Euclidean distance on phonotype. In this
paper, hamming distance di on genotype is utilized to measure the Similarity between the ith chromosome and
the parent chromosome, here i, 0<i<Max_Popsize i≠parent.
If di < Min_Len, let Fitness[i] =PENALTY, here Fitness[i] is the fitness of the ith chromosome, PENALTY is
a litter constant number, Min_Len is a parameter predefined.
The Niched elimination
for all i such that 0 ≤ i < 5 do
if( i == the parent) continue;
d= 0;
for all gene j that 0 ≤ j < geneNumber do
d = d + distance( the jth gene of individual , the jth gene of the parent);
end for
if d < Min_Len then
Fitness[i] =PENALTY;
end for
3.2 The Niched Cartesian Genetic Programming (NCGP)
A simple evolutionary algorithm known as a 1+λ evolutionary algorithm is widely used for CGP. The
niched Cartesian Genetic Programming is shown in the following procedure. The new population is formed
from μ best parents and population_size -μ offspring. The μ parents are copied across unchanged, i.e. elitism
strategy. In this paper, let μ = 1, λ = 4. The Mutation operator is random point mutation. The best solutions are
circuits that match the truth table with the minimal logical gates.
The (1+4) Niched Cartesian Genetic Programming
for all i such that 0 ≤ i < 5 do
Randomly generate individual i
end for
Select the fittest individual, which is chosen as the parent
while a solution is not found or the generation limit is not reached do
for all i such that 0 ≤ i < 4 do
Mutate the parent to generate new individual
end for
Niche elimination;
Select the fittest individual according to the following rules:
If the new individual is no worse than the parent then
the new individual is promoted as the fittnest
else
The parent chromosome remains the fittest
end if
end while
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4.RESULTS OF EXPERIMENTS
This section shows the implementation of the experiment: Traditional CGP and the Proposed NCGP are
compared with 3-bit adder circuit has 6 inputs and 7 outputs. Both algorithms use the (1+λ) evolutionary
strategy, which new population is generated from 1 best parent and λ offspring. The parent is copied across
unchanged, i.e. elitism strategy. The goal is to find the digital circuits that match the truth table and have the
minimal logic gates. This means that the global optimal solutions are the matched digital circuits with the
minimal gates, other circuits matched are the local optimal and there are many global optimal solutions.
The parameters are set as: evolving generation: 5000000, population: 10, mutation probability: 5%.
Table 1.The node operating function types
Operation type
data[in1]
~data[in1]
data[in1] & data[in2]
data[in1] | data[in2]
data[in1] ^ data[in2]
~(data[in1] & data[in2])
~(data[in1] | data[in2])
~(data[in1] ^ data[in2])
Function code
0
1
2
3
4
5
6
7
The digital circuit is showed as : (7)2 5 5, (8)1 4 7,(10)2 5 5,(13)7 1 7, (31)5 7 4,(39)4 0 7,(48)13 8
6,(55)48 39 4,(60)0 55 2,(75)3 55 7,(79)75 55 3,(80)60 79 7,80 75 31 10.Numbers in comma is the identifier of
the node. The first two numbers are connective genes and the last number is the function code listed in Table
1.The two algorithms rum 20 times and the solutions are shows in Table 2. In traditional CGP, only 2 times the
global optimal solution are found while 15 times are gotten in NCGP.
Table 2. The solutions,20 times runs
CGP
①
14
②
16
③
16
④
13
⑤
12
⑥
16
⑦
21
⑧
14
⑨
14
⑩
17
⑪
15
⑫
14
⑬
16
⑭
15
⑮
14
⑯
13
⑰
15
⑱
12
⑲
17
⑳
14
NCGP
13
12
12
12
12
12
12
13
13
12
12
12
12
12
12
13
12
13
12
12
Figure4 (a), (b) show the evolving process of the NCGP and CGP. The vertical coordinate is the fitness and
horizontal coordinate is sequence number of the evolving generations. The red curve (annotated with +)，is the
best fitness in current generation; The green curve (annotated with ×),is the average fitness in current generation.
From the curves, the average fitness curve rises and falls sharply in CGP and the average fitness curve in NCGP
is non-decreasing.
Figure 4 (a ). the convergence curve in NCGP
Figure4 (b). the convergence curve in
CGP
Figure5 (a), (b) show the First Hit Generation when NCGP and CGP finds the first local solutions which
match the truth table. The vertical coordinate is the First Hit Generation and horizontal coordinate is sequence
number of the run times. CGP convergence faster than NCGP in most runs. But CGP is easy to stalling in the
later evolving procedure and cannot always get the global optimal solutions, which match the truth table with 12
logical gates.
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Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 3, 37 - 43, 2016
Figure 8 (a ).the First Hit Generation in NCGP
CGP
.5. CONCLUSIONS
Figure 8 (b).the First Hit Generation in
Due to the Many-for-one genotype-phenotype Map, the problems of evolving digital circuits in EHW are
multimodal optimization. The classical CGP often falls into local optimal point and fail to find all the global
optimal solutions. The proposed NCGP could find all the global optimal solution with the niched technique. The
result of the compared experiment on benchmark circuits demonstrates that the niched technique can maintain
the diversity of the evolving population, avoiding premature. But how to select the niched radius relies on
practical experiences and NCGP convergences slower than CGP for extra distance computing. In the future, a
self-adaption niched CGP will be developed.
Acknowledgements
This work was supported by Project 2662015PY147supported by the Fundamental Research Funds for the
Central Universities of China and Natural Science Foundation of China (NO.60442001).
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