# Documentation

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## I Ching Algorithm: Outstanding advantages of Hexagram Model compared to Diagram Theory

The Genetic Algorithm used to be a pretty good algorithm because it maintained a population of solutions. Therefore, it significantly overcomes the local minima in the optimization problem compared to other methods, typically the hill climbing method. But that advantage of Genetic Algorithm can only be used for simple problems.
Today's life is as complicated as the COVID-19 pandemic shows. Now, looking at it from a broader perspective, Genetic Algorithms have one drawback, which is a big one.
The crucial disadvantage of Genetic Algorithm is that it derives from a purely technical solution. That is, its operating principle is Diagram Theory. Technical problems can never touch real life. Although a diagram covers a fairly large space of solutions and is much more powerful than the point-by-point search of the hill-climbing method, in turn, it becomes the local diagram for complex problems and Genetic algorithms cannot converge to global optimality.
I Ching Algorithm does not limit the problem to any technical areas, its principle is to find the Tao or path to the optimal solution. This is the basic thing. As we see in The hexagram space theorem, all data is compressed into hexagram data. In the opposite direction, the hexagram data is decoded back to the problem data whose union covers the entire space.

I/ DIAGRAM THEORY
A diagram of length m is a sequence representing m-bit binary sequences whose bits are the same as the fixed bits of the diagram. The other bits whose positions correspond to the * character in the diagram can be any bit 0 or bit 1.
Example diagram with length m = 10 below
`10010110*0`
will match 2 sequences
1001011000 and 1001011010
If each binary sequence is considered a valid solution in the problem space, then a diagram is a set of solutions. The idea is that the less cardinality the diagram has, the more compact the space is.
1) Degree of the diagram
The degree of the diagram S, denoted o(S), is the number of fixed bits in the diagram. For example
`S1 = *****1*1*0`
`S2 = 1**0*1*01*`
`S3 = 001001*1*0`
We have
o(S1) = 3
o(S2) = 5
o(S3) = 8
Thus, diagram S3 has the highest degree, its space is considered the most compact.
Unfortunately, the higher the degree of the diagram, the more vulnerable it is to mutations. When a fixed bit is mutated, the diagram is no longer what it is, it is broken.
2) Specified length of the diagram
The specified length of a diagram S, denoted δ(S), is the distance between two fixed positions at the beginning and at the end. We have
(S1) = 10 – 6 = 4
(S2) = 9 – 1 = 8
(S3) = 10 – 1 = 9
The larger a diagram of a specified length, the easier it is to be cut out, i.e. broken by hybridization.
3) Diagram theorem
Short, low-degree, above-average diagrams receive a exponentially increasing number of sequences in successive generations of the genetic algorithm.
This is only possible at an early stage in evolution, when the diagrams are beginning to form and the average fitness of the population is low. When approaching the optimal point, long, high-degree diagrams are very vulnerable. Furthermore, the diagram is unlikely to have above-average fitness because it has become "conservative" while novel elements are often more adaptive.
Above all, the foregoing is not yet the biggest weakness of Diagram Theory.

II/ CRITICAL DISADVANTAGE OF DIAGRAM THEORY AND WHY HEXAGRAM MODEL?
To illustrate, we use the simplest possible problem: Find the maximum of the function y with x in the interval [0, 4194303] as shown in the graph below

## I Ching Algorithm: Further review of hybridization

In the article Hybridization, we have given two individuals to crossbreed to reproduce, but have not assessed the quality of the offspring. Now let's see which of the 64 hexagrams the child is born corresponds to.

To make it easier to remember, we copy the 64 hexagrams in order with their summary meanings below

Thuần càn, Thuần khôn, Thủy lôi truân, Sơn thủy mông, Thủy thiên nhu, Thiên thủy tụng, Địa thủy sư, Thủy địa tỉ, Phong thiên tiểu súc, Thiên trạch lý, Địa thiên thái, Thiên địa bĩ, Thiên hỏa đồng nhân, Hỏa thiên đại hữu, Địa sơn khiêm, Lôi địa dự, Trạch lôi tùy, Sơn phong cổ, Địa trạch lâm, Phong địa quan, Hỏa lôi phệ hạp, Sơn hỏa bí, Sơn địa bác, Địa lôi phục, Thiên lôi vô vọng, Sơn thiên đại súc, Sơn lôi di, Trạch phong đại quá, Thuần khảm, Thuần ly; Trạch sơn hàm, Lôi phong hằng, Thiên sơn độn, Lôi thiên đại tráng, Hỏa địa tấn, Địa hỏa minh di, Phong hỏa gia nhân, Hỏa trạch khuê, Thủy sơn kiển, Lôi thủy giải, Sơn trạch tổn, Phong lôi ích, Trạch thiên quải, Thiên phong cấu, Trạch địa tụy, Địa phong thăng, Trạch thủy khốn, Thủy phong tỉnh, Trạch hỏa cách, Hỏa phong đỉnh, Thuần chấn, Thuần cấn, Phong sơn tiệm, Lôi trạch quy muội, Lôi hỏa phong, Hỏa sơn lữ, Thuần tốn, Thuần đoài, Phong thủy hoán, Thủy trạch tiết, Phong trạch trung phu, Lôi sơn tiểu quá, Thủy hỏa kí tế, Hỏa thủy vị tế.

The arrangement of 64 hexagrams starts from the two hexagrams  Càn and Khôn. Càn is heaven, Khôn is earth, there is heaven and earth before there are all things. The book "Hexagram words story" divides 64 hexagrams into "Upper sutra" and "Lower sutra". The Upper sutra consists of the first 30 hexagrams meaning the Tao of heaven. The Lower sutra includes the last 34 hexagrams that talk about human relationships in the lower world:

## I Ching Algorithm: More about the I Ching transformation phase

We know that I Ching transformation is movement in heaven and earth. The transformation hexagram is formed from the dynamic dime, but the dynamic dime is found from natural signals or cues. If the quantitative value of the signal is 1, then dime 1 occurs, if it is 2, then it is dime 2, if it is 3, then it is dime 3, if it is 4, then it is dime 4, if it is 5, then it is dime 5 and if it is 6 then dime 6 occurs in end of the growing cycle. Going to 7 is a new cycle, 7 divided by 6 leaves remainder 1, dynamic dime is again dime 1. Dime 1 is also known as initial dime, is the initial stage of things. Just like that, the cycle changes through the phases, from phase 1 to phase 6. For example, the sun rotates cyclically from east to west, from day to night it rotates non-stop.
I Ching Algorithm is an evolutionary algorithm that considers the laws of the universe, a primordial, preamble algorithm. The names attached to the algorithm all show that they are in phase 1 not random.
We repeat the number of strokes in the algorithm name and the author's name, then add other relevant names and events.

1) Algorithm name: I Ching Algorithm
I CHING ALGORITHM
2 + 1+3+2+3+3 + 3+2+3+1+3+2+2+3+4 =
`2 + 12 + 23 = 37`
37 divided by 6 leaves remainder 1. Name of the algorithm owns phase 1.

2) Author's name: Phạm Thành Tuyên
PHẠM THÀNH TUYÊN
2+3+3+4+1 + 2+3+3+3+3+1 + 2+2+2+6+3 =
`13 + 15 + 15 = 43`
43 divided by 6 leaves remainder 1. Author's name is in the same phase 1.

I Ching Algorithm is the original evolutionary solution, its author is Vietnamese, it must be towards the origin of the Vietnamese nation. The ancestor of the Vietnamese nation is Vua Hùng (Hung King)
3) Ancestor's name: Vua Hùng
VUA HÙNG
2+2+3 + 3+2+3+3+1 =
`7 + 12 = 19`
19 divided by 6 leaves remainder 1. The ancestor's name is the initial phase, phase 1 of course.

Everyone is born from their father, the author's father is Phạm Nguyên Lâm
4) Father's name: Phạm Nguyên Lâm
PHẠM NGUYÊN LÂM
2+3+3+4+1 + 3+3+2+2+6+3 + 2+5+4 =
`13 + 19 + 11 = 43`
The number of strokes of the father's name is the same as the son's name, certainly phase 1.

It is revealed that the author's father died on the day of the death anniversary of Vua Hùng on the 10th day of the third lunar month.
5) Hung King's death anniversary
10/3
`10 + 3 = 13`
13 divided by 6 leaves remainder 1. Ancestor's death anniversary is also phase 1, which is the first milestone completing the mission of being a human that all Vietnamese people must know.

Above are 5 events about the initial phase of the Creator, the numbers are clear, very serious but also very interesting!

## I Ching Algorithm: Hybridization

Given two chromosomes
`1101111001001010101111`
`1001001001010110110110`
The chromosomes perform conditional hybridization. The paternal and maternal chromosomes are considered as to whether their reproductive combination is good or evil. Breeding is carried out only when the offspring is good to ensure that the population evolves at the same pace as I Ching transformation following the expected natural laws without degradation or stomping in place.
Applying The hexagram space theorem, compress the 22-bit binary sequence into 3-bit binary sequence to be the size of a single hexagram
len_in = 22; len_out = 3
len_w = 8; stride = 7
The first chromosome is the paternal chromosome, corresponding to the upper hexagram
`1101111001001010101111`
`‘11011111’0,010010’1,0101111`
`11011110 00100101 10101111`
`[6/8, 3/8, 6/8]`
`101`
Father's hexagram number is 5, so the upper hexagram is the TỐN.
The second chromosome is the maternal chromosome, corresponding to the lower hexagram
`1001001001010110110110`
`'1001001'0,010101'1,0110110`
`10010010 00101011 10110110`
`[3/8, 4/8, 5/8]`
`011`
Mother's hexagram number is 3, so the lower hexagram is LY.
We have a double hexagram PHONG HỎA GIAI NHÂN

## I Ching Algorithm: mutation

Review binary sequence
`1010101000000111100100`
Applying The hexagram space theorem, we use convolution with the following parameters:
Len_in = 22; Len_Out = 6
len_w = 7; stride = 3
Filter = [1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7]
`‘101’010’1,00’0,00’0,11’1,100,100`
The six binary segments in the extracted window are
`1010101 0101000 1000000 0000111 0111100 1100100`
Output is a 6-element vector [4/7,  2/7,  1/7,  3/7,  4/7,  3/7]
Applying The theorem of problem space representation We get a 6-bit binary sequence
`100010`
We have two 3-bit subsequence
`100 010`
Upper hexagram is CHẤN, lower hexagram is ĐOÀI, the double hexagram is LÔI TRẠCH QUY MUỘI

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