“Forget it”: Generic concept and application in engineering optimal design – A Review

8/8/2019 “Forget it”: Generic concept and application in engineering optimal design – A Review

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“Forget it”: Generic Concept and Application in Engineering

Optimal Design – A Review

Adeola A Adedeji

Department of Civil Engineering, University of Ilorin, PMB 1515, Ilorin, [email protected];[email protected]

Abstract

Many efforts have been made to use genetic algorithms to solve symbolic regression problems by generating symbolic

functions to model data. One of the problems that plagues most of the efforts is finding a way to efficiently mutate and cross-breed symbolic expressions so that the resulting expressions have a valid mathematical syntax. The problem with this

approach is that if limited mutations are used, the evolution process is hindered, and it may take a large number of generations to find a solution, or it may be completely unable to find the optimal solution. This work has suggested thatduring mutation either all functions and terminals are removed beneath an arbitrarily determined node and a new branch is

randomly created, or a single node is swapped for another, by the application of “Forget it” and key in permanently for thematerial to forget all that it has learnt to that time, so that it can be reactivated any time the analytical bank is stimulated. By

mimicking the forgetter mechanism, in a moment of intense pain (force), the action of the analytical mind (approach) issuspended and the mental image (virtual) pictures of the experience (engram) are then recorded in the reactive mind(reaction). When the painful incident (collapse/failure) is over, the analytical mind resumes recording. The reactive mind

however begins recording again if the person (mater) undergoes another painful experience (failure) and so it goes. Reactive

mind is never selective, It “faithfully’ records everything during a moment of pain and it could be regarded as a survivormechanism by restimulating the engram . The results of this work showed that despite the large design space of permissiblesolutions, the procedure converged rapidly towards the best possible solution.

Keywords: mutation, accelerated aging forgetter mechanism, engram

1. Introduction and Concept

Forgetfulness (retention loss), and not thoughtlessness, refers to apparent loss of information already encoded

and stored in an individual's long term memory. It is a spontaneous or gradual process in which old memories

are unable to be recalled from memory storage. It is subject to delicately balanced optimization that ensures thatrelevant memories are recalled. Forgetting can be reduced by repetition and/or more elaborate cognitive

processing of information. Reviewing information in ways that involve active retrieval seems to slow the rate of

forgetting.Forgetting functions (amount remembered as a function of time since an event was first experienced) have

been extensively analyzed. The most recent evidence suggests that a power function provides the closestmathematical fit to the forgetting function. German psychologist Hermann Ebbinghaus (en.wikipedia.org), who

once studied the mechanisms of forgetting, used himself as the sole subject in his experiment; he memorizedtwo consonants and one vowel in the middle. He then measured his own capacity to re-learn a given list of

words after a variety of given time period. He found that forgetting occurs in a systematic manner, beginning

rapidly and then leveling off just as in the experience curve effect that can on occasion come to an abrupt stop.

From this simple study, basic premises have held true today and have been reaffirmed by moremethodologically sound methods. The unusual practice, for the recovery of a patient which depends on the life

units freed from his/her reactive bank (the sum total of pictures that contain charge, harmful energy or force), is

to ‘forget’ such things, i.e. to forget as soon as possible to have a complete healing. For instance when somefiles or documents are deleted (to be forgotten) in a computer, they are located in the recycle (regenerate or

reuse) bin and from where the files are again deleted, but to where? What have been deleted from the recycle bin

would not go into the ‘swine’ but will be sitting down in the computer “engram”

\In order to use genetic algorithms to solve symbolic regression problems – that is, to generate symbolic

functions to model data, one approach is to perform a mutation, check the result and then try a different randommutation until a syntactically valid expression is generated. Obviously, this can be a time consuming process for

complex expressions. A second approach is to limit what type of mutations can be performed – for example,only exchanging complete sub-expressions. During mutation either all functions and terminals are removed

beneath an arbitrarily determined node and a new branch is randomly created, or a single node is swapped for

another, it is then necessary to apply “Forget it” and key in permanently for the material to forget all that it haslearnt to that time, so that it can be reactivated any time it is stimulated to remember what happened at the last

time.



2. Theories of Forgetfulness

The five main theories of forgetting apparent in the study of psychology as follows (Wikipedia 2009,

Underwood 1957, Wixted 2004): Cue-dependent forgetting or retrieval failure is the failure to recall a memorydue to missing stimuli or cues that were present at the time the memory was encoded. It states that a memory is

sometimes temporarily forgotten purely because it cannot be retrieved, but the proper cue can bring it to mind.

A good example for this is searching for a book in a library without the reference number, title, author or even

subject. The information still exists, but without these cues retrieval is unlikely. Furthermore, a good retrievalcue must be consistent with the original encoding of the information. It is also appropriate to have anotherdirection of cue for a similar topical book, by checking directly at the library shelf, by going through the stacked

books. Along the line the same book may be obtained, by chance, from the shelf or a similar book can also be

obtained; Trace decay is when the memory is physically no longer present. Forgetting that occurs throughphysiological damage or dilapidation to the brain is referred to as organic causes of forgetting. These theories

encompass the loss of information already retained in long term memory or the inability to encode new

information again. Examples include Alzheimer's, Amnesia, Dementia, consolidation theory and the gradual

slowing down of the central nervous system due to presumed aging; Interference theory is the idea thatforgetting occurs because the recall of certain items interferes with the recall of other items. In nature, the

interfering items are said to originate from an over stimulating environment. Interference theory exists in twobranches, Retroactive (when new information/memories interfere with older information) and Proactive (whenold information interferes with the retrieval of new information) inhibition each referring in contrast to the

other; Decay theory states that when something new is learned, a neuro-chemical, physical "memory trace" isformed in the brain and over time this trace tends to disintegrate, unless it is occasionally used, State-dependent

cues are governed by the state of mind and being at the time of encoding. The emotional or mental state of theperson, such as being inebriated, drugged, upset, anxious, happy, or in love, are the key cues. State-dependent

learning or a state dependent memory is an idea of learning and recalling that is based upon the physiological

and mental state of the organism. Factors affecting state-dependent learning may include: environment,intoxication, emotional state, and sensory modality. In neuro-psycho-pharmacology, state-dependent learning

denotes the fact that information that has been learned while the animal is under the influence of a certain stateof drug, which can only be recalled and used to solve a task when the animal is in the same state in which theinformation was learned, but not in a different state; and Context-dependent cues are dependent and based on the

environment and situation. Memory retrieval can be facilitated or triggered by replication of the context inwhich the memory was encoded. Such conditions include weather, company, location, smelling of a particular

odour, hearing a certain song, even taste can sometimes act as a cue. For example, students sometimes fail torecall diligently studied material when an examination room's environmental differs significantly from the room

or place where learning took place. To improve learning and recall, it is recommended that students shouldstudy under conditions that closely resemble an examination. A recently identified type of context-dependent

learning is the effect of language. The linguistic context of a memory may be encoded during learning.

Psychologists that have researched context dependent recall include Abernathy (1940), as well as Godden &

Baddeley (1975).

3. "Cosmic Forgetfulness" in Relation with the Experience curve Effects

Many think of the Big Bang as the "fireball" that triggered the immensely hot, dense state roughly 14 billionyears ago to expand into the vast cosmos we see today. The loss of the singularity, however, opens up the

possibility that the Universe could have had a state that extended back in time before the Big Bang. This wouldmean that the Big Bang did not mark the beginning of the universe, but was rather a transition – or a "bounce" –

of the universe from a prior collapsing state to our familiar expanding one. But the indication is thatforgetfulness is an attribute to human and as such it is worthwhile to note its importance in life and mimic the

same attribute in optimisation design.

3.1 Experience curve effects Models of the learning curve effect and the closely related experience curve effect express the relationship

between equations for experience and efficiency or between efficiency gains and investment in the effort. The

experience of "learning curves" was first observed by the 19th Century German psychologist Hermann

Ebbinghaus according to the difficulty of memorizing varying numbers of verbal stimuli.

The rule used for representing the learning curve effect states that the more times a task has been performed,the less time will be required on each subsequent iteration. This relationship was probably first quantified in

1936 at Wright-Patterson Air Force Base in the United States, where it was determined that every time totalaircraft production doubled, the required labour time decreased by 10 to 30 percent, but in most cases the



percentage is constant: It did not vary at different scales of operation. Learning curve theory states that as the

quantity of items produced doubles, costs decrease at a predictable rate. This predictable rate is described byEquations 1. This equation describes the basis for the cumulative average or cum average curve. In this

equation, Y represents the average cost of different quantities (X) of units. The significance of the "cum" in cumaverage is that the average costs are computed for X cumulative units. Therefore, the total cost for X units is the

product of X times the cum average cost. For example, to compute the total costs of units 1 to 200, an analyst

could compute the cumulative average cost of unit 200 and multiply this value by 200.

(1)

In general, the experience curve effect states that the more often a task is performed; the lower will be the cost

of doing it. In Figure 1 shows competitive cost dynamics: the experience curve (Hax and Majluf 1982).

Figure 1. Experience curve (Wikipedia, 2009)

The curve is plotted with cumulative units produced on the horizontal axis and unit cost on the vertical axis. Acurve that depicts a 15% cost reduction for every doubling of output is an “85% experience curve”, indicating

that unit costs drop to 85% of their original level. Mathematically the experience curve is described by a powerlaw function sometimes referred to as Henderson's Law:

(2)

Where, C1 is the cost of the first unit of production, Cn is the cost of the nth unit of production, is the

cumulative volume of production and a is the elasticity of cost with regard to output The equations for theseeffects come from the usefulness of mathematical models for certain somewhat predictable aspects of those

generally non-deterministic processes. They include: Labour efficiency; standardization, specialization, andmethods improvements; technology-driven learning; better use of equipment; changes in the resource mix;product redesign; network-building and use-cost reductions; shared experience.

3.2 Experience curve discontinuities

It is worthwhile to note that the experience curve effect can on occasion come to an abrupt stop. Graphically, thecurve is truncated. Existing processes become obsolete and the firm must upgrade to remain competitive. The

upgrade will mean the old experience curve will be replaced by a new one.

Bojowald (2008) has explored whether we might be able to glimpse such a pre-Big Bang universe. He beganwith a model based on loop quantum gravity (LQG), which assumes that time proceeds in finite quantum

"jumps", that the universe's state is defined by a few parameters, including how it is currently expanding, the

amount of matter present and the strength of gravity. He was able to find equations of the state of the universethat were exactly solvable at the time of the Big Bang.

Living in the post-Big Bang era, we enjoy a fairly smooth space-time. But before the Big Bang, if such atime existed, there is the possibility that the universe was in a highly-fluctuating quantum state in which even

the usual concept of time might have little meaning. Bojowald has found that the sheer size of our presentuniverse gives rise to a fundamental uncertainty in his equations that prevents us from ever learning how big

quantum fluctuations before the Big Bang were.

This means that we may not, for example, perform backwards calculations to trace back all aspects of the

universe prior to the Big Bang – what he calls "cosmic forgetfulness". The fact that some properties cannot bepredicted completely was very unexpected, he confirmed. Nevertheless, Bojowald added that aspects associated

with classical behaviour, such as the universe's size and contraction rate, could in principle be determined



because they existed before the so-called Big-bang. The fact remains that the said attributes are there in an

engram, though forgotten.Applying this to forgetting design and using the car driver’s theory, the initial learning state, which may not

be known or remembered, was a state of high-fluctutating quatum state and as an optimum design time of astructure and as the time “we enjoy a fairly smooth space-time of the structure”. The structure remains in that

state as long as its service lasts or the time of its “big-bang” – total transformation (recycled).

As reported by Cartwright (2007), John Barrett, a quantum-gravity theorist from the University of

Nottingham in the UK, warns that LQG is not widely-adopted among theorists, which could put Bojowald'sconclusions on shaky ground. "LQG is a partially-baked cake," he said. "There are some aspects one would needto make a complete quantum theory of gravity that just aren't there yet."

4. Forgetter Mechanism

“Forget it” is one of a class of phrases of the forgetter mechanism which is most sever in its abberative effect,

whereby denying the data entirely to the analyser. The unusual practice, for the recovery of a patient which

depends on the life units freed from his/her reactive bank, is to ‘forget’ such things, i.e. to forget as soon aspossible to have a complete healing. This, according to Dianetics (the modern science of mental health), does

not work at all. Dianetics claim that anything forgotten is a festering sore even when it has despair connectedwith it. According to Hubbard (1992), an auditor (the listener) will find that every time he locates that arch-denier or ‘forget it’, which has been suppressed, will be sitting down as a somatic or a ‘forget it’ in the contents

of the engram (a mental image picture which is a recording of an experience containing pains, uncousciousnessand a real or fancied threat to survival and it is found in the reactive mind, defined as portion of person’s mind

working on stimulus-response basis under a volitional control – ie sum total of pictures containing charge, forceor energy). For instance when some files or documents are deleted (to be forgotten) in a computer, they are

located in the recycle (regenerate or reuse) bin and from where the files are again deleted, but to where? What

have been deleted from the recycle bin would not go into the ‘swine’ but will be sitting down in the computer“engram”. ‘Forget it’ indicates that when a thing has been ‘put out of mind’ it has been put straight into the

reactive mind.It is appropriate to note that when an analytical mind (analyzer), which thinks, observes data, remember it

and resolves problems, is shot down or suspended, the reactive mind starts to record. These actions are not

memories as such but engrams. During a moment of intense pain, the action of the analytical mind is suspendedand the mental image pictures of the experience are then recorded in the reactive mind (bank). When the painful

incident is over, the analytical mind resumes recording. The reactive mind however begins recording again if theperson undergoes another painful experience and so it goes. Reactive mind is never selective, It “faithfully’

records everything during a moment of pain and it could be regarded as a survivor mechanism by restimulatingthe engram. All it takes to restimulate an engram during moments of pain or fatigue is something in the current

environmemnt that appropriates the perceptions stored in the engram – words, sounds etc.

In such situations, the engram has the power of command over the individual actions, body and purposes,

where a person acts in a certain manner and not knowing what he is doing. Dianetics discovered the source of

man’s irrationalities, neuroses, pains etc and through auditing these engrams could be found and eliminate (tocompletely forget) their effects by erasing the charge connected to them. The experience can be refilled in astandard memory bank of the analytical mind.

In the case of man, Thetan or Higher Being (Hubbard, 2008), senior to both body and mind is supposed toerase engrams charge.

5. Forgetting Theory and Engineering Design

In the design of an engineering element, there is the need to adapt a material to its environment against all odds.

In the application of GAs, for instance, in an instance of the optimal design, the pseudocode (canonical GA) willinvolve: A choice of initial population; evaluating individual’s fitness by selecting individuals to reproduce,

mate pairs (parents) at random, apply crossover operator, apply mutation operator and evaluate individual’sfitness until the termination of the condition. Because a child (offspring), who thinks others are bad to him, wastold by his mother that those guys didn’t really mean to be bad to him, “They have good heart really”, she

assured her child. Because the child wanted to be alright, he has to believe his mother saying that: “I love you

very much and don’t worry honey, forget it now”. The phrases contain in his engram, a sympathy engram.

When this is encountered, it is discovered to have been buried either in alignment with a purpose or i t has the so

called forgetter mechanism on it. The former indicates a self-protection of the mind to give up the engram onlywhen enough tension is taken off the case so the mind gets along with the engram or by the latter, a repeater

technique will begin to release the phrase from various engrams and begin to show up incidents. Hence, this



remains utterly out of sight (remember the files deleted to recycle bin is only out of use, but it is there active)

until the case was almost finished and as soon as it is contacted, the disintensified reactive bank is collapsed.In the second analysis, the GA pseudocode, for instance, did not consider an offspring, a child who could get

an uncommon sympathy engram as an incident that occurred when the child had been badly hurt in an accidentand remained in coma for several days. He has never learnt that such an accident could happen to him. In a

forgetting theory, a state-dependent learning or a state dependent memory is an idea of learning and recalling

that which is based upon the physiological and mental state of the organism. Factors affecting state-dependent

learning may include: environment, intoxication, emotional state, and sensory modality. Applying this tomaterial involves no deterministic process. A process where debatable yet popular concept is "trace decay" canoccur in both short and long-term memory. This theory, applicable mostly to short-term memory, is supposedly

contradicted by the fact that one is able to ride a bike or drive a car even after not having done so for decades.

The fact is that, the bike rider or a car driver has learnt riding or driving in a very short-term that keeps himriding or driving, though the learning ended (forgotten) at a time he could ride or drive alone without an aid. As

in neuro-psycho-pharmacology, a state-dependent learning denotes the fact that information that has been

learned while the animal is under the influence of a certain drug (“state”) can only be recalled and used to solve

a task when the animal is in the same state in which the information was learned, but not in a different state. Inother words, material design will be in the same state through out its life time and beyond from the short term

memory at the state when the material “forgets to remember” any form of failure. This will be made easy whenapplying the Simplified Protocol for Accelerated Aging in data cellection.

6. Data Collection

6.1 Simplified protocol for accelerated aging of engineering materials

Researchers had located the genes for telomerase, a protein that might help cells live longer. Now, related

research from the University of Texas and the Geron Corporation had confirmed that the presence of telomeraseactually does make ordinary cells live longer. The telomerase is a cap of repeating genes at the tip of the

chromosome. Every time the cell divides, the chromosome is duplicated – and its telomerase get shorter.Logically, telomerase gets shorter perhaps it has forgotten its original size and when it has reached null (unlessthere is the limit to shortening of the size), the cell may not be able to divide further and the cell remains for as

long as it reaches state of physical demolition (Mahomed et al. 2009).Dyskeratosis congenita (DC) is characterized by multiple features including mucocutaneous abnormalities,

bone marrow failure and an increased predisposition to cancer. It exhibits marked clinical and geneticheterogeneity. DKC1 encoding dyskerin, a component of H/ACA small nucleolar ribonucleoprotein (snoRNP)

particles is mutated in X-linked recessive DC. Telomerase RNA component (TERC), the RNA component andTERT the enzymatic component of telomerase, are mutated in autosomal dominant DC, suggesting that DC is

primarily a disease of defective telomere maintenance. The gene(s) involved in autosomal recessive DC remains

elusive.

Walne et al (2007) showed that NOP10, a component of H/ACA snoRNP complexes including telomerase is

mutated in a large consanguineous family with classical DC. Affected homozygous individuals have significanttelomere shortening and reduced TERC levels. While a reduction of TERC levels is not a universal feature of DC, it can be brought about through a reduction of NOP10 transcripts, as demonstrated by siRNA interference

studies. A similar reduction in TERC levels is also seen when the mutant NOP10 is expressed in HeLa cells.These findings identify the genetic basis of one subtype of AR-DC being due to the first documented mutations

in NOP10. This further strengthens the model that defective telomere maintenance is the primary pathology inDC and substantiates the evidence in humans for the involvement of NOP10 in the telomerase complex and

telomere maintenance (Vulliamy et al, 2001) Increasing the Life Expectancy of Human Cells by AlteringDNA.

Scientists in the United States have been able to make human cells live longer by altering their geneticmaterial. The research may offer renewed hope for age-related illnesses and the fight against cancer.

According to the results, when chromosomes divide they go through a process called DNA replication. Thedouble helix separates and unwinds. When the double helix has completely separated new nucleotides completethe base pairings. Then the new phosphate backbones are made. In the end the two double helixes are identical

to the original. This happens every time that a cell divides. Most cells in the body grow and divide to form

organs and tissues but cells can divide only a limited number of times before they stop. Now scientists have

found out it has to do with their chromosomes, the long threads of DNA at the centre of each cell. The ends of

each chromosomes are capped to protect them by structures called telomeres. Each time the cell divides thetelomeres gets shorter until the cell can divide no more. Scientists at the University of Texas have discovered

that making the telomeres bigger again encourages cells to divide and grow once more. The American teamstresses that it has not discovered the key to everlasting life but says the discovery may help in combating



certain diseases such as cancer where cells divide uncontrollably. British experts said the discovery is important

but add a note of caution.(123HelpMe, 2010).The introduction of new or modified engineering material products requires the assurance that their life span

can be an extended period without any decrease in performance that may affect safety and efficacy under liveand dead loads. Because full-period, ambient-aged samples usually do not exist for such products, it is generally

necessary to, aside the conduction of accelerated-aging tests, analyse the effect of aging to support a

performance until the full-period life span is obtained. The ability of product designers to accurately predict

changes in properties of engineering is of critical importance to the construction industry. Modeling the kineticsof such materials deterioration is difficult and complex, and the difficulty is compounded by the fact that asingle-rate expression of degradation or a change developed over the short term may not be valid over the long-

term service life of the product or material being studied. In order to design a test plan that accurately models

the time-correlated degradation of the materials, it is necessary to possess an in-depth knowledge of the materialcomposition and structure, end-product use, assembly and sterilization process effects, failure-mode

mechanisms, and unused-state conditions.

A given engineering material may have many functional chemical groups organized in diverse ways

(crystalline, glass, amorphous, etc.), along with additives such as antioxidants, inorganic fillers, plasticizers,coloration/painting, and production aids. It is the sum of these variations—combined with variations in product

use and storage environment — that determines the degradation chemistry. Fortunately, the majority of thesematerials are constructed from a limited number of materials that have been well-characterized over extended-use periods. A procedure known as the Simplified Protocol for Accelerated Aging or a "10-degree rule" was

developed around the collision theory–based Arrhenius model. When applied to well-characterized engineeringsystems over moderate temperature ranges, the test results obtained can be within the required degree of

accuracy.The aging of materials refers to the variation of their properties over time, the properties of interest being

those related to safety and efficacy. Accelerated aging can be defined as a procedure that seeks to determine the

response of a device or material under normal service conditions over a relatively long time, by subjecting theproduct for a much shorter time to stresses that are more severe or more frequently applied than normal

environmental or operational stresses. Many accelerated-aging techniques used for the qualification testing of materials are based on the assumption of zero-, first-, and pseudo-first-order chemical reactions following theArrhenius reaction rate function. This function states that an increase or decrease in the reaction rate at which a

chemical reaction proceeds changes according to the following equation:

(/ kT Aedt

dqr 3)

where r = the rate at which the reaction proceeds; A = the constant for the material (frequency factor); =apparent activation energy (eV); k = Boltzmann's constant (0.8617 x 10

–4 eV/K); and T = absolute temperature.

With appropriate substitutions, the simplified expression for the 10-degree rule can be derived:

(210/ ]12[ T T C

dt

dqr 4)

Where C2 indicates the effect of the rule. It should be noted that the 10-degree rule provides a conservative

acceleration factor at room temperature for activation energies less than 0.7 eV. The 10-degree rule will likelybe conservative in the prediction of service life. However, the technique depends on numerous assumptions that

must be verified by real-time validation testing conducted at room temperature for the targeted service life. A

well-designed product test program will involve the use of continued more than "room-temperature" aging that

is always greater in age than the age of any material product under service load. This is especially important

when using these techniques for the qualification of critical (life-saving) components or elements. The approachdoes involve some limited risk of potential recall, in the event that room-temperature-aged testing shows a

significant deficiency following real-time-aged testing of the product. Applying accelerated-aging testtechniques in conjunction with a comprehensive knowledge of the materials involved is a prudent method of

doing business and with the benefits of early product introduction thus outweighing the minimal risk of premature material failure.

6.2 The “10-Degree Rule" Application in Engineering

For any engineering material products, a simplified approach for accelerated aging should be based onconducting testing at a single accelerated temperature and then employing the rule stating that the rate of a





symbols. Symbols in the tail can be replaced only by terminals. Using the same example K-expression shown

above, assume mutation replaces the ‘/’ symbol with d. Then the K-expression is: +-d,abcd. And the expressiontree in Figure 3. becomes

Figure 3 Result of the expression tree Note that this expression tree has fewer nodes than the previous one. This illustrates an important point: by

allowing mutation to replace functions with terminals and terminals with functions, the size of the expression

can change was well as its content. As a further example, assume the next mutation changes the first symbol in

the K-expression from ‘+’ to c. The K-expression becomes: c-d,abcd. The expression tree for this is: © The

“tree” consists of a single node which is the variable c. Note

8. Natural Selection and Fitness

The principle of natural selection is that healthy, fit individuals should breed and produce offspring at a fasterrate than sick, unfit individuals. Through this selection process, each generation becomes healthier and more fit.

In order for this to take place, there must be some characteristics of individuals that determine fitness for theenvironment, and there must be a selection mechanism that favours the breeding of individuals with greater

fitness. In gene expression programming, fitness is based on how well an individual models the data. If thetarget variable has continuous values, the fitness can be based on the difference between predicted values and

actual values. For classification problems with a categorical target variable, fitness can be measured by the

number of correct predictions. DTREG (Koza 2009, Vereira 2006) on Gene Expression Programming andSymbolic Regression, provides a variety of fitness functions that you can choose from for an analysis.

Evolution stops when the fitness of the best individual in the population reaches some limit that is specified forthe analysis or when a specified number of generations have been created or a maximum execution time limit is

reached.All of the fitness functions produce fitness scores in the range 0.0 to 1.0 with 1.0 being ideal fitness – that is,

the individual exactly fits the data. If a function is unviable – for example it takes the square root of a negative

number or divides by zero – then its fitness score is 0.0. Once the fitness has been calculated for the individualsin the population, roulette-wheel sampling is used to select which individuals move on to the next generation.

Each individual is assigned a slot of a roulette wheel, and the size of the slot is proportional to the fitness of theindividual. Unviable individuals whose fitness is 0.0 have slots that can never be selected, so they are not

propagated to the next generation. Roulette-wheel sampling causes individuals to be selected with a probabilityproportional to their fitness, and it eliminates unviable individuals. Since individuals are not removed from thepopulation once they are selected, individuals may be selected more than once for the next generation.

8. Application of GA-FT

The application of the GA-FT using the forgetfulness theory involves the use of the simplified protocol foraccelerated aging of engineering materials – collection of data, and the use of cues theory as well as the

procedures GA-SR pseodocode (the pseudocode does not consider an offspring (“child”) who could get anuncommon sympathy engram. During mutation in a genetic programming (GP) (Koza,1992), there is random

changes in an individual before it is introduced into the subsequent population. Unlike crossover, mutation is

asexual and thus only operates on one individual. During mutation either all functions and terminals are

removed beneath an arbitrarily determined node and a new branch is randomly created, or a single node isswapped for another), it is then necessary to apply “Forget it” and key in permanently for the material to forget

all that it has learnt to that time, so that it can be reactivated any time it is stimulated to the analytical process. A child is born into the world. He forgets (even his mother) his experience gained at the exact time (t bb) of hisbirth - his “big-bang”, and unless he is informed about it he would never remember. But the essence of his birthremains the same till his last time in this world. It is that essence (i.e. “Forget it” ) used as simplified protocol

for accelerated aging and experience curve analysis, that must be keyed-in during mutation to experience or gain

its new environment at which the body will live. Figure 4 represents a simple concept of the analysis



9. GA-FT Numerical Example and Comparison

The discrete weight optimization of a 10-bar plane truss shown in Figure5 which has been solved (Adedeji,

2007 using a floating point GA and solved (Shaw, 2004) GP based work to the results generated by a previous

GA and GP based systems where the solution is reported by splitting it into three sections of the Model, View

and Controller This example will solve this problem using GA-FT. In this example, given the initial structure,the goal was to minimise the structure’s weight by varying its’ shape and topology.. Forty two shapes taken

from BS5950 manual are available and are given in SI units in Table 3. The assumed data are modulus of

elasticity, E=68.9 x 103 MPa, density of the material, =2770 kg/m3, allowable stress = ±172 MPa and

allowable displacement = ± 50.8mm.

6.1 Modelling and Problem formulation

The Model represents the underlying data of the object, in this instance the structural analysis andevolutionary parts of the overall system. The fitness function rewards a lightweight truss but penalises any

structure that violates a specified constraint e.g. maximum allowable member stress. A penalty based approachwas employed, rather than outright rejection because the good solutions will typically be located on the

boundary between the Figure 2: 10 member planar truss. The mathematical model of minimum weight designusing available member sizes can be expressed as in the following:

)7(42,...2,1)(.1

)(

m

i

ijjnijALC W Min

Subject to:

5 3 1

1 2

7 9

5 6 9 m

8 10

6 4 2 3 4

445 kN 445 kN

9 m 9 m

Figure 5 Plane truss system with 10 steel-bars

Fitness StatesA B C= A B

100 C = 100 to 10% drop

and reactivate

to “Forget it”Units 10Cost(Fitness)

00 10 100

0 10 100

0 10 100Units Product Generation

Figure 4. Product (Element) optimum values



(a) Compressive and tensile stresses

i - all 0, i = 1, 2, . . .10

Where i due to load in compression and tension

(b) Thermal stresses

as in Equation (3), where i due to Arrhenius reaction rate function and a modified Arrhenius equation,

that makes explicit the temperature dependence of the pre-exponential factor. If one allows arbitrarytemperature dependence of the prefactor, the Arrhenius description becomes overcomplete, and the inverseproblem (i.e. determining the prefactor and activation energy from experimental data) becomes singular.

The modified equation is usually of the form

(9)

where T 0 is a reference temperature and allows n to be a unit-less power. Clearly the original Arrheniusexpression above corresponds to n = 0. Fitted rate constants typically lie in the range -1<n<1. Theoretical

analyses yield various predictions for n. It has been pointed out that "it is not feasible to establish, on thebasis of temperature studies of the rate constant, whether the predicted T

½dependence of the pre-

exponential factor is observed experimentally. However, if additional evidence is available, from theoryand/or from experiment (such as density dependence), there is no obstacle to incisive tests of the Arrheniuslaw. Another common modification is the stretched exponential form:

(10)

where β is a unitless number of order 1. Taking the natural logarithm of the Arrhenius equation yields:

(11)

So, when a reaction has a rate constant which obeys the Arrhenius equation, a plot of ln( k ) versus T −1

gives a straight line, whose slope and intercept can be used to determine E a and A. This procedure has

become so common in experimental chemical kinetics that practitioners have taken to using it to define theactivation energy for a reaction. That is the activation energy is defined to be (-R) times the slope of a plot

of ln(k ) vs. (1/ T ):

(12)

The constraint equation becomes,

)13(0 T lA

E

ee

a

where Ae, le = cross sectional area, length of the element, = coefficient of linear expansion, T=changein temperature

( c) Deflection

k - all 0, k = 1, 2, …12

where A is a cross sectional area pointed by the 10-element design vector j(i). For example, A8(3) is the

shape 8 from Table 3, pointed for member 3 (A8(3)) =1858 mm2

). And and Li are, density and length forthat member respectively. The design vector j (i) is treated as a floating point number, and its integer part is

used as a pointer. Since there are 10 design variables and 42 available shapes, the intrinsic size of the searchspace is 42

10(10

16).



Table 3 – Properties of Steel ShapesShape Area

(mm2)Shape Area

(mm2)Shape Area

(mm2

1 1045 15 2342 29 7419

2 1161 16 2477 30 8710

3 1284 17 2497 31 8968

4 1374 18 2503 32 9161

5 1535 19 2697 33 10000

6 1690 20 2723 34 10323

7 1697 21 2897 35 10903

8 1858 22 2961 36 12129

9 1890 23 3097 37 12839

10 1993 24 3206 38 14193

11 2019 25 3303 39 14774

12 2181 26 3703 40 17097

13 2239 27 4658 41 1935514 2290 28 5142 42 21613

As the present problem is a constrained optimization one, it is necessary to transform it into an unconstrained

problem. Many alternatives are possible. In this study, a transitional exterior penalty approach is used. Thetransformed model is expressed as follows:

m

i

i

i

i

i

k

k

i

iiijnijeeePLAC W Min

1

1010

1

12

1

)( )15(42,...2,1)())1()1()1((.

in which = 1 for = 0 or = 0 and P is a penalty coefficient.

In order to compare the results properly with those from the literature, all the computations are done in theoriginal units used by the other researchers, and then converted to SI units. The use of PseudoCode program

with the relevant parameters is given in the executional steps on GA.

6.2 Genetic operators

In this work, the following GA operators are used: Tournament selection, Whole linear crossover: From two

parents P1 and P2, three offsprings are generated, namely 0.5P1+0.5P2, 1.5P1-0.5P2, and -0.5P1+1.5P2. Thebest two of the three offsprings are then selected.

mutation: Though It allows new genetic patterns to be formed, thus improving the search method but

ccasionally, it protects some useful genetic material loss. During the process, a rate of mutation determines thepossibility of mutating one of the design variables. If a variable (V) is chosen to be mutated, its value ismodified as follows:

V = V + (t, bU,L

– V) (16)

where t is the actual generation used as infinite value, bU

and bL

the upper and lower bounds for the variable,

and (t, y) is given as (Turkkan,,2003),

(t, y) = y (1 – r(1 – c/T)2)

where r is a uniform random number between 0 and 1, T, in a fogetter mechanism is the maximum generationbetween 0 and 1, and c is a parameter determining the degree of dependency on the generation number ≥ 1

(t, y) = y (1 – r2)

Elitist strategy: In standard GA the best possible solution is not preserved, thereby increasing the chance of

loosing the obtainable best possible solution. Elitist strategy overcomes this problem by copying the bestmember of each generation into the next one.

6.3 Comparison of results

The result produced in this example is compared with the bit string coded GA solutions obtained by severalresearchers as shown in Table 4. It is believed that the minimum weight obtained by Cal and Thierauf (1993)



and the present work is the global minimum, therefore the best possible solution. The solutions obtained by

Galante (1996) and Ghasemi et al. (1999) are not acceptable solutions in a mathematical sense, as they violateslightly the displacement constraint. It is observed that the vertical displacement of node 2 is the binding

constraint and a maximum stress of 99 MPa, well below 172MPa, is reached in member 5. State of stress anddisplacement of the structure is shown in Fig. .

Because of its simplicity and ease of coding the floating point GA procedure described here can be applied to

a wide variety of optimization problems. It has been shown here that it can be also used successfully in the

discrete weight optimization of structures. Despite the large design space of permissible solutions, the procedureconverged rapidly towards the best possible solution.

Table 4. Comparison of the optimum solution for the truss system

Note: I: Rajeev and Krishnamoorty (1992), II: Cai and Thierauf (1993), III: Coello (1994), IV: Galante (1996)V: Ghasemi et al. (1999) with population = 100, VI: GA (floating point) Adedeji (2007), VII: Present work

all = 50.8 mm, all = 172 MPa, and max = 99 MPa (number 5, ), all = 15 Mpa (due to thermal effect)

7. Conclusion

Applying accelerated-aging test techniques in conjunction with a comprehensive knowledge of the materialsinvolved is a prudent method with the benefits of early product introduction thus outweighing the minimal risk

of premature material failure.

The result produced in this example is compared with the bit string coded GA solutions obtained by severalresearchers. It is believed that the minimum weight obtained by Cal and Thierauf (1993) and the present work is

the global minimum, therefore the best possible solution. The solutions obtained by Galante (1996) andGhasemi et al. (1999) are not acceptable solutions in a mathematical sense, as they violate slightly the

displacement constraint. Contrary to the floating point GA procedure used in the previous woks relating to

simple GA-SR and GP, GA-FT can be applied to a wide variety of optimization problems. It has been shownhere that it can be also used successfully in the discrete weight optimization of structures. Despite the large

design space of permissible solutions, the procedure converged rapidly towards the best possible solution.

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Method Weight(kg)

2y

(mm)

Shape of members

1 2 3 4 5 6 7 8 9 10

I

IIIIIIV

VVI

VII

2545.4

2490.62534.12475.9

2471.02490.5

2475.0

-50.5

-50.5-50.5-51.1

-51.2-50.5

-48.8

42

424142

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1

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1

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393938

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33

323032

3132

33

1

111

11

1

111

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32

263128

2828

35

37

383838

3938

38

37

383838

3938

42

6

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