Gray code

Q: How deeply does Optimization Algorithms: AI techniques for design, planning, and control problems cover gray code?

Explains adjacency, Hamming cliffs, four-bit examples, and XOR conversion, but does not detail a full genetic-algorithm implementation.

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A binary numeral system in which adjacent numerical values have representations differing in exactly one bit.

Gray code, also called reflected binary code, represents adjacent numerical values with exactly one differing bit. This locality reduces the Hamming-cliff effect in binary-coded genetic algorithms, where flipping a significant bit can abruptly change the decoded solution and fitness. section 8.1

A four-bit sequence

The table maps decimal values to binary and Gray representations: 0 is 0000, 1 is 0001, 2 is 0011, and 3 is 0010. Each successive Gray representation changes one bit, unlike ordinary binary around transitions such as 3 to 4. section 8.1

Table 8.1 Decimal, binary, and Gray coding (view table figure)

Decimal number	Binary code	Gray code
0	0000	0000
1	0001	0001
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111
6	0110	0101
7	0111	0100
8	1000	1100
9	1001	1101
10	1010	1111
11	1011	1110
12	1100	1010
13	1101	1011
14	1110	1001
15	1111	1000

Compare decimal values with their four-bit binary and Gray-code representations from 0 through 15. section 8.1

Gray coding is useful when representation changes should produce gentler solution changes:

Use it in binary-coded genetic algorithms to smooth the genotype-to-phenotype mapping and reduce disruptive crossover or mutation effects. section 8.1
Convert four-bit binary values with XOR gates; XOR returns 1 for different inputs and 0 for matching inputs. section 8.1
Apply the representation in rotary encoders and digital-to-analog converters, where minimizing conversion errors matters. section 8.1
Treat Gray code as an alternative to binary or real-valued encoding when binary representation creates poor convergence or inefficient exploration and exploitation. section 8.9

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

Cover of Optimization Algorithms: AI techniques for design, planning, and control problems

liveBook manning.com

Read Optimization Algorithms: AI techniques for design, planning, and control problems on liveBook Get the book at manning.com

Related concepts

gray-coded genetic algorithmused by · A genetic algorithm that represents candidate solutions with Gray-coded strings so adjacent numeric values differ in a single bit.
logical XORproduced by · Logical XOR is a binary operation that produces true when exactly one operand is true and false when both operands have the same truth value.
hamming cliffaddresses · A representation discontinuity in which a small encoded change, such as flipping one bit, causes a large change in the decoded solution value or fitness.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.