Improved Genetic Algorithm: Channel Allocation in Mobile Computing - D. P. Vidyarthi - Jawaharlal Nehru ...
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Improved Genetic Algorithm: Channel
Allocation in Mobile Computing
D. P. Vidyarthi
School of Computer & Systems Sciences
Jawaharlal Nehru University
New Delhi
2/6/2018 JNU, New DelhiSource Article
“Improved Genetic Algorithm for Channel
Allocation with Channel Borrowing in
Mobile Computing”, S. S. Mahapatra,
Kousik Roy, Sarthak Banerjee, Deo
Prakash Vidyarthi, IEEE Trans. on Mobile
Computing, Vol. 5, No. 7, July, 2006.
2/6/2018 JNU, New DelhiGAs: What Are They
• Large Class of problems having no fast
algorithms
• Any Problem solving can be perceived as a
search through a space of potential
solutions
• Objective is BEST solution
• Small Spaces- Exhaustive Methods
• Large Spaces- AI techniques
• GA is one such technique, Stochastic
Algorithms based on natural phenomena
Genetic Inheritance
Continued….
2/6/2018 JNU, New Delhi•Based on Darwin’s Theory “Survival of the fittest” •Example - Rabbits & Foxes •Darwin’s theory of natural selection, bending inheritance mixing like fluids •Mendel- hereditary factors of discrete nature •Morgan- Chromosomes are the carriers of hereditary information •Vocabulary borrowed from natural genetics individuals (genotypes, structures) in a population quite often called strings, chromosomes. 2/6/2018 JNU, New Delhi
•Every gene controls the inheritance of
characters.
•In contrast with the cell of organism which
carries a number of chromosomes (man has
46) chromosomes are made of genes
(features, characters, decoders)
•Search through population of chromosomes
•Objectives- Exploiting the Best solution &
Exploring the search space
•Each chromosomes represent a potential
solution
2/6/2018 JNU, New Delhi•Hill climbing- exploiting not exploring
•Random Search- exploring not exploiting
•GA- balance between exploitation & exploration
•It provides a multidirectional search by
maintaining a population of potential solutions.
•Successfully applied to various optimization
problems- Wire routing, Scheduling, Adaptive
control, Game playing, Cognitive modeling,
Transportation problems, TSP, optimal controls,
Mobile Communications etc.
2/6/2018 JNU, New DelhiEvolutionary Algorithms 2/6/2018 JNU, New Delhi
Simple Genetic Algorithm( )
{
Population Initialization;
Population Evaluation;
Until solution converges do
{
Perform Crossover & Mutation;
Evaluate Population;
Reproduction;
}
}
2/6/2018 JNU, New DelhiInitial Population • The chromosomes in GA population generally take the form of bit strings. – Bit strings (0101 ... 1100) – Real numbers (43.2 -33.1 ... 0.0 89.2) – Permutations of element (E11 E3 E7 ... E1 E15) – Lists of rules (R1 R2 R3 ... R22 R23) – Program elements (genetic programming) – ... any data structure ... 2/6/2018 JNU, New Delhi
GA Operations - Crossover • Choose randomly some crossover point • Copy everything before this point from the first parent • Then copy everything after the crossover point from the other parent. • Crossover probability is fixed. 11001011 + 11011101 = 11011111 2/6/2018 JNU, New Delhi
Crossover
Crossover site
1-point crossover
(used in SGA)
n-point crossover
Uniform crossover
2/6/2018 JNU, New DelhiMutation
A chromosome is altered a little bit
randomly(e.g. 0 to 1 or 1 to 0).
2/6/2018 JNU, New DelhiMutation
• Mutation means that the elements of DNA are a
bit changed.
• Mutation probability is fixed.
• Bit inversion - selected bits are inverted
11001001 => 10001001
2/6/2018 JNU, New DelhiFitness Function • The GA requires a fitness function that assigns a score to each chromosome in the population. • The fitness function in a GA is the objective function that is to be optimized. • It is used to evaluate search nodes, thus it controls the GA. 2/6/2018 JNU, New Delhi
Chromosome Selection Each individual chromosome (string) is assigned a fitness value by the fitness function. The chromosome is evaluated with this value for survival. The fitness function used to rank the quality of the chromosome. Chromosomes with higher value have a higher probability of contributing one or more offspring in the next generation. 2/6/2018 JNU, New Delhi
Chromosome Selection • Roulette Wheel Selection • Boltzman Selection • Tournament Selection • Rank Selection • Steady State Selection • ….. 2/6/2018 JNU, New Delhi
Selection-Roulette Wheel • Want to maintain an element of randomness but ‘fix’ the selection so that fitter individuals have better odds of being chosen • Assign areas on a number line relative to each individuals fitness • Generate a random number within the range of the number line • Determine which individual occupies that area of the number line • Choose that individual 2/6/2018 JNU, New Delhi
Selection-Roulette Wheel
This process can be described by the following algorithm.
[Sum] Calculate the sum of all chromosome fitnesses in population -
sum S.
[Select] Generate random number from the interval (0,S) - r.
[Loop] Go through the population and sum the fitnesses from 0 - sum
s. When the sum s is greater then r, stop and return the
chromosome where you are.
Of course, the step 1 is performed only once for each population.
2/6/2018 JNU, New DelhiSelection-Roulette Wheel 2/6/2018 JNU, New Delhi
An Example: TSP
• Must visit in his territory exactly once and
return to the starting point
• Given the cost of travel between all cities, how
should he plan for minimum total cost of his
entire tour
• Several BB, approximate, heuristic algorithms
are available for this
• Decide on chromosome: Integer or Binary
• If Binary, each cities should be coded as a
string of log n bits. A chromosome string of
2
nlog2n bits
2/6/2018 JNU, New DelhiTSP Continues…
• A mutation may result in a sequence of cities,
which is not a tour
• For 20 cities, 5 bits are needed and some
sequence may not correspond to a city
• Similar problems with Crossover
• Clearly we require some repair algorithm
• Integer representation is better
• Vector v=(i1i2..in) represents a tour
2/6/2018 JNU, New DelhiTSP Continues….
• For initialization: Heuristics (few outputs from
greedy algorithm) or random permutation
• Evaluation is straightforward.
• Crossover (e.g. OX operator)
• Populations are (1 2 3 4 5 6 7 8 9 10 11 12) &
(7 3 1 11 4 12 5 2 10 9 6 8) chosen part (4 5 6
7)
• Resulting offspring ( 1 11 12 4 5 6 7 2 10 9 8
3)
• The roles of the parents reversed for the next
offspring
2/6/2018 JNU, New DelhiHow GA Works: An Example
• Maximize the function for 4 decimal places
f(x1,x2)=21.5+x1*sin(4πx1)+x2*sin(20πx2)
Where –3.0• e.g.
(010001001011010000111110010100010)
• first 18 bits represent
x1 3.0 dec (010001001011010000)*12.1 (3.0)
218 1
x1=-3.0+4.052426=1.052426
• Similarly x2=5.755330
• So (010001001011010000111110010100010)
corresponds to (x1,x2)=(1.052426,5.755330)
• Fitness f(x1,x2)=20.252640
• For population size 20 random population is
2/6/2018 JNU, New Delhi• V1=(100110100000001111111010010100000) • V2=(111000100100110111001010100011010) • V3=(000010000011001000001010111011101) • V4=(100011000101101001111000001110010) • V5=(000111011001010011010111111000101) • V6=(000101000010010101001010111111011) • v7=(001000100000110101111011011111011) • V8=(100001100001110100010110101100111) • V9=(010000000101100010110000001111100) • V10=(000001111000110000011010000111011) 2/6/2018 JNU, New Delhi
• v11=(011001111110110101100001101111000) • v12=(110100010111101101000101010000000) • v13=(111011111010001000110000001000110) • v14=(010010011000001010100111100101001) • v15=(111011101101110000100011111011110) • v16=(110011110000011111100001101001011) • v17=(011010111111001111010001101111101) • v18=(011101000000001110100111110101101) • v19=(000101010011111111110000110001100) • v20=(101110010110011110011000101111110) 2/6/2018 JNU, New Delhi
• We evaluate each chromosome eval(vi) after
calculating the fitness from (x1,x2)
• eval(v1)=26.019600, eval(v2)=7.580015,
eval(v3)=19.526329, eval(v4)=17.406725,
eval(v5)=25.341160, eval(v6)=18.100417,
eval(v7)=16.020812, eval(v8)=17.959701,
eval(v9)=16.127799, eval(v10)=21.278435,
eval(v11)=23.410669, eval(v12)=15.011619,
eval(v13)=27.316702, eval(v14)=19.876294,
eval(v15)=30.060205, eval(v16)=23.867227,
eval(v17)=13.696165, eval(v18)=15.414128,
eval(v19)=20.095903, eval(v20)=13.666916
2/6/2018 JNU, New Delhi• Now the system constructs a roulette wheel for
selection.
• The total fitness F=Sum of vi=387.776822.
• Probability of selection pi for vi is eval(vi)/F
• Generate the cumulative probabilities of pi
• Generate 20 random numbers between 0 and
1.
• Select the population based on these numbers.
• Probability of crossover is 25% so 5 out of 20
will undergo crossover.
• Generate random number r [0..1] if r• Random integer pos is generated between 1
and 32 for the crossover site.
• New populations are generated after crossover.
• Probability of mutation is 0.01 so 1% of the bits
will undergo mutation. There are total 20*33 bits
• We expect 6.6% average mutations per
generation
• Again random number [0..1] is generated and if
rGA for Task Scheduling • GA is applied for Task Scheduling in DCS and Grid • Initial Population consists of allocation of modules to computing nodes in binary • Fitness: Turnaround Time, Reliability • Crossover, Mutation & Reproduction • Better Allocation with balanced load 2/6/2018 JNU, New Delhi
Channel Allocation
• Mobile Devices are increasing
• Radio frequency resources are limited
• Need for effective resource management
• Fixed Channel Allocation (FCA); No channel
Reuse
• Dynamic Channel Allocation (DCA); Channel
Reuse to balance the load
• Borrowing Channel Allocation (BCA); borrows
channel from the cells having light load
• Other Methods; Channel Sharing, Cell Splitting
2/6/2018 JNU, New DelhiImproved Genetic Algorithm for CA
• GA, with a variant, is used for the
Channel Allocation Problem
• Objective: To minimize Blocked Hosts
and to reduce channel borrowings
• A Host is blocked, if it enters into a cell
but didn’t get channel
• A new operator ‘Pluck’ is introduced
• Add some knowledge in Chromosome
selection for reproduction
2/6/2018 JNU, New DelhiEncoding
Borrowing information
Free channels
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Blocked hosts
Lending information
• A chromosome, for each cell, is an array of length 14
• A Superchromosome 7*14 formed with chromosome
of 6 neighbor cells
• One population is one Superchromosome
2/6/2018 JNU, New DelhiPluck Operation
• Incorporating problem specific
knowledge
• Idea is from Tealeaves plucking in Tea
garden
• It is applied when borrowing decision
are to be taken
• The information is extracted from the
cell itself (about free and blocked hosts)
• Pluck together with encoding
2/6/2018 JNU, New DelhiCrossover • The cut point is chosen randomly • Elements before cut-point are swapped • After cut-point, the commonality of the elements are checked • Uncommon elements are kept at the same position • For common elements, order is maintained from the other matrix • This is to preserve the information 2/6/2018 JNU, New Delhi
Crossover Cont..
1st matrix 2nd matrix
cut point cut point
1 2 3 4 5 6 7 4 5 6 5 7 4 6
2 3 4 3 4 8 7 4 3 5 8 7 9 4
5 6 7 5 6 4 3 1 2 2 6 6 3 4
offspring 1 offspring 2
4 5 6 5 7 4 6 1 2 3 4 5 6 7
4 3 5 3 8 7 4 2 3 4 4 8 9 7
1 2 2 5 6 3 4 5 6 7 6 6 4 3
2/6/2018 JNU, New DelhiMutation • Mutation is not effectuated • Weakness is giving borrowing decision ahead of time • It may result in non-optimality • Simple reason: Their effect is not measured in fitness function 2/6/2018 JNU, New Delhi
Fitness
Fitness = αc* current_blocked + αn*next_blocked +
β*next_free + µ*hotcell + *transaction
αc, αn, β, µ, are constant values to suit the environment
• Next_blocked and next_free are calculated by
the behavior variable of the cell and the host
• Hotcell is taken into account when cell has no
free channel
• Transaction is the number of blocked or free
hosts of the cell
• Fittest is one with lowest fitness value
2/6/2018 JNU, New DelhiRepair • It is possible that during crossover some information becomes irrelevant • If Host number > Available Free channels then free channel number is updated to 0 • Also the lending part will be updated to 0, as the cell with no free channel can not spare an extra channel to any cell • Similarly, when host number < available free channels it need not to borrow and its borrowing part becomes 0 2/6/2018 JNU, New Delhi
Experiments Input: • Total number of cells: 19 • Channel per cell: 10 • Crossover probability: 1 • Number of hosts in the network: 50, 75,100. • Number of time units in seconds: 10, 20, 50, 100, 150 2/6/2018 JNU, New Delhi
FCA Vs. IGA
FCA w ith 50
hosts
Average Blocked
80 FCA w ith 75
70
60 hosts
Hosts
50 FCA w ith 100
40
30 hosts
20 IGA w ith 50
10
0 hosts
10 20 50 100 150 IGA w ith 75
hosts
2/6/2018 Time JNU, New Delhi
IGA w ith 100Modified Mutation GA Vs. IGA
120
Number of Blocked Hosts
100
80
60
40
20
0
10 20 50 100
Time
FCA Modi Mutation GA IGA
2/6/2018 JNU, New DelhiOther Applications • GA has been applied for Resource Management in Cellular IP networks • Resources considered are Bandwidth, Buffer and Router CPU cycle • Better results are achieved • A variant, MGA was also proposed that uses elitist selection method • For Multi Objective Optimization problems NSGA-II was also applied 2/6/2018 JNU, New Delhi
Conclusion • GA suited for any optimization problem where search space is large • Much better than exhaustive search • Provides good result • Incorporating problem specific knowledge converges the solution quickly • Is applicable for variety of problems 2/6/2018 JNU, New Delhi
2/6/2018 JNU, New Delhi
You can also read
