**2. Materials and methods**

#### **2.1 Metaheuristic structural rules for the algorithm building**

It is a rule of No Unreasonable Effectiveness of Mathematics in any Science [Wigner] [2], and therefore a notion that No Unreasonable Effectiveness of Axiomation in any Science, that 3 Rules of Information Physics [3IP] by Jonah Lissner exist:

*f x*ð Þ¼ sin *<sup>π</sup><sup>x</sup>*

*f x*ð Þ¼ *<sup>π</sup><sup>x</sup>* sin *<sup>π</sup><sup>x</sup>*

formula

over Y.

change).

tion Algorithm [GOA].

**4. Building the algorithm**

various scales and models.

**153**

the group's preference [4].

**SigtsetM v**ð Þ**xt** ¼ **1***=***l SigtsetG av**,**t xt**½ � *ibid :*

*DOI: http://dx.doi.org/10.5772/intechopen.96516*

2*λ*

*Atomistic Mathematical Theory for Metaheuristic Structures of Global Optimization…*

0, else (

2*λ*

Evolutionary Game Theory [EGT] challenges in optimization schedules are therein linked to Ant Colony Optimization [ACO], e.g. Eigenvector centrality

**Where for G** ≔ ð Þ **E**, **V with V vertices let A** ¼ ð Þ **av**,**t** , **e***:***g***:***av**,**t** ¼ **1 or av**,**t** ¼ **0***:***Therefore xv** ¼ **1***=***l**

It is a basis for optimization schedules that there is an asymmetrical velocity, mass and gravity of said scope of systems. At various times in the computational history, particle optimization on the manifolds evolve at a faster rate [or slower rate] than before. Hence the given incremental and discrete rate of increase, in valleys and peaks accelerates and stabilizes at a higher positive, null or negative value and result in extremal mechanics and nonlinear dynamics. An example can be demonstrated utilizing power faults and extremals on the electrical circuits [3].

These problems of prediction for probability of choice of one object or particle of

1. If every voter prefers alternative X over alternative Y, then the group prefers X

3.There is no "dictator": no single voter possesses the power to always determine

Important is Criteria 3, from whence adaptive and efficient algorithms have space to be constructed as particles on the run-time, for a given Global Optimiza-

In a praexological theory [5] this is proposed because of the inherent general inaccuracy of specific problems, learning rubrics, and Macrodynamic properties of a given performance landscape, and ultimately inefficient of any algorithmic system, given isomorphic [atomistic or non-atomistic] qualities of rulebase, algorithmic structure, weights, and variables [6]. These in turn can be represented as information sets, materiel, work, and symbolic representation and/or power in specific *qualia* of *Historical Rule of Perpetuation of Information Inequalities* set to

2. If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W

a set, for pariwise sets and in algorithms, have been demonstrated in Arrow's Impossibility Theorem and for Algorithmic Information Theory [AIT] whence we can replace *voter* for global optimization *particle* and replace *group* with *set*:

0, else (

� �, for 0 <sup>≤</sup>x≤*λ*;

� �, for 0<sup>≤</sup> <sup>x</sup><sup>≤</sup> *<sup>λ</sup>*;

(3)

(5)

*:* (4)

I.Problem of Demarcation.

II.Rule of Information Dichotomy [*Gestalt-Inverse Gestalt*], and thereby requiring a kind of.

III.Context-Restricted Deep Structure [CRDS] for the given topology.

Therefore hypothesized to be commutable terms within this 3IP rulebase, The Three Thermodynamic Rules of Macrodynamics by Jonah Lissner. The 3 General Rules of Macrodynamics [3GRM] which are established to define Global Optimization Algorithm [GOA] challenges:

