Voicu Groza, 2008 SITE, 2008 - HARDWARE/SOFTWARE CODESIGN OF EMBEDDED SYSTEMS 1 Hardware/Software Codesign of Embedded Systems OPTIMIZATION Voicu Groza.

Voicu Groza, 2008

SITE, 2008 - HARDWARE/SOFTWARE CODESIGN OF EMBEDDED SYSTEMS

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Hardware/Software Codesign of

Embedded Systems

OPTIMIZATION Voicu Groza SITE Hall, Room 5017

562 5800 ext. [email protected]

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Dominance, Pareto Points

• A (design) point Jk is dominated by Ji, if Ji is– better or equal than Jk in all criteria and– better in at least one criterion.

• A point is Pareto-optimal or a Pareto-point, if it is not dominated.

• The domination relation imposes a partial order on all design points– We are faced with a set of optimal solutions.– Divergence of solutions vs. convergence.

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Multiobjective Optimization • Maximize (y1, y2, …, yk) = ƒ(x1, x2, …, xn)

•Pareto set = set of all Pareto-optimal solutions

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Multi-objective Optimization

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Design Space, Pareto Points• The task graph shows a system specification with four tasks, T1 ...T4.

The tasks can be executed on different components.

• The following table displays the execution times for the tasks on the different components as well as the component cost.

For example, the MIPS processor costs 200 units and can run tasks T1 in 5 ms and task T4 in 2 ms.

The table shows also the number of components available for each component type (MIPS, DSP, FPGA and ASIC).

• All components execute tasks sequentially – at any given time a component executes at most one task. Task execution is non-preemptive – once a task is started, it runs to completion.

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A design point consists of an allocation (selection of components), a binding (assignment of tasks to selected components) and a schedule (execution order for the tasks). Determine the total cost and execution time for each design point.

Pareto Points(a) Construct the design space by

listing all possible design points.

(b) Draw the design points in a cost-time diagram. Which design points are Pareto points?

T1

T2

T3

T4

Costtexec

cost

texec (ms)

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Pareto Points(c) Consider an allocation without resource constraints. That means

we are given an arbitrarily high number of components of each type (MIPS, DSP, FPGA and ASIC). Are there new design points?

Does the set of Pareto points change?

T1

T2

T3

T4

Costtexec

cost

texec

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Genetic Algorithms• Directed search algorithms based on the mechanics

of biological evolution• Developed by John Holland, University of Michigan

(1970’s)– To understand the adaptive processes of natural systems– To design artificial systems software that retains the

robustness of natural systems• Provide efficient, effective techniques for

optimization and machine learning applications• Widely-used today in business, scientific and

engineering circles

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Classes of Search Techniques

F inonacc i N ew ton

D irect m ethods Indirec t m ethods

C alcu lus-based techn iques

E volu tionary s trategies

C entra l ized D is tr ibuted

Para l le l

S teady-s ta te G enera tiona l

S equentia l

G enetic a lgori thm s

E volutionary a lgori thm s S im u lated annealing

G uided random search techniques

D ynam ic program m ing

E num erative techn iques

S earch techniques

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Components of a GA

A problem to solve, and ...• Encoding technique (gene, chromosome)

• Initialization procedure (creation)

• Evaluation function (environment)

• Selection of parents (reproduction)

• Genetic operators (mutation, recombination)

• Parameter settings (practice and art)

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GA Algorithmic Phases

Initialize the populationInitialize the population

Select individuals for the mating poolSelect individuals for the mating pool

Perform crossoverPerform crossover

Insert offspring into the populationInsert offspring into the population

The EndThe End

Perform mutationPerform mutation

yesyes

nonoStop?Stop?

ChromosomeChromosome

GeneGene

LocusLocus

PopulationPopulation

PhenotypePhenotype

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Simple Genetic Algorithm{

initialize population;

evaluate population;

while TerminationCriteriaNotSatisfied{

select parents for reproduction;

perform recombination and mutation;

evaluate population;}

}

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The GA Cycle of Reproduction

reproduction

population evaluation

modification

discard

deleted members

parents

children

modifiedchildren

evaluated children

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Population

Chromosomes could be:– 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 ...

population

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Reproductionreproduction

population

parents

children

Parents are selected at random with selection chances biased in relation to chromosome evaluations.

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Chromosome Modification

modificationchildren

• Modifications are stochastically triggered• Operator types are:

– Mutation– Crossover (recombination)

modified children

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Mutation: Local Modification

Before: (1 0 1 1 0 1 1 0)

After: (0 1 1 0 0 1 1 0)

Before: (1.38 -69.4 326.44 0.1)

After: (1.38 -67.5 326.44 0.1)

• Causes movement in the search space (local or global)• Restores lost information to the population• The Mutation Rate is the chance that a bit within a chromosome will be

flipped. This is usually a very low value for binary encoded genes, say 0.001

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One point crossover is performed by selecting a random gene along the length of the chromosomes and swapping all the genes after that point

10001001110010010 01010001001000011

Crossover is a critical feature of genetic algorithms:– It greatly accelerates search early in evolution of a population– It leads to effective combination of schemata (subsolutions on

different chromosomes)

The Crossover Rate is the chance that two chromosomes will swap their bits. A good value for this is around 0.7.

Crossover: Recombination

* 10001001101000011

01010001010010010

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Two point crossoverTwo point crossover calls for two points to be selected on the parent chromosome strings. Everything between the two points is swapped between the parent organisms, rendering two child organisms:

"Cut and splice"Another crossover variant, the "cut and splice" approach, results in a change in length of the children strings. The reason for this difference is that each parent string has a separate choice of crossover point.

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Evaluation

• The evaluator decodes a chromosome and assigns it a fitness measure

• The evaluator is the only link between a classical GA and the problem it is solving

evaluation

evaluatedchildren

modifiedchildren

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Fitness Function• Quantifies the optimality of a solution (a chromosome) such that

particular chromosome may be ranked against all the other chromosomes. Optimal chromosomes, are allowed to breed and mix their datasets producing a new generation that will (hopefully) be even better.

• An ideal fitness function correlates closely with the algorithm's goal, and may be computed quickly. Speed of execution is very important, as a typical genetic algorithm must be iterated many, many times in order to produce a usable result for a non-trivial problem.

• Definition of the fitness function is not straightforward in many cases and often is performed iteratively if the fittest solutions produced by GA are not what is desired.

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Deletion

• Generational GA:entire populations replaced with each iteration

• Steady-state GA:a few members replaced each generation

population

discard

discarded members

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Stopping Criteria

• Final problem is to decide when to stop execution of algorithm.

• There are two possible solutions to this problem: – First approach:

• Stop after production of definite number of generations

– Second approach: • Stop when the improvement in average fitness

over two generations is below a threshold

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An Abstract Example

Distribution of Individuals in Generation 0

Distribution of Individuals in Generation N

Rennard Genetic Algorithm Viewer 1.0 • http://www.rennard.org/alife/english/gavgb.html

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A Simple Example

The Traveling Salesman Problem:

Find a tour of a given set of cities so that – each city is visited only once– the total distance traveled is minimized

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Representation

Representation is an ordered list of city

numbers known as an order-based GA.

1) London 3) Dunedin 5) Beijing 7) Tokyo

2) Venice 4) Singapore 6) Phoenix 8) Victoria

CityList1 (3 5 7 2 1 6 4 8)

CityList2 (2 5 7 6 8 1 3 4)

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Crossover

• Crossover might combine inversion & recombination; • e.g. given two chromosomes

* *

Parent1 (3 5 7 2 1 6 4 8)

Parent2 (2 5 7 6 8 1 3 4)

Child (8 5 7 2 1 6 3 4)

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Mutation involves reordering of the list: * *

Before: (5 8 7 2 1 6 3 4)

After: (5 8 6 2 1 7 3 4)

• the Crossover Rate is the chance that two chromosomes will swap their bits. A good value for this is around 0.7

Mutation

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TSP Example: 30 Cities

0

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100

120

0 10 20 30 40 50 60 70 80 90 100

x

y

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Solution i (Distance = 941)TSP30 (Performance = 941)

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100

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0 10 20 30 40 50 60 70 80 90 100

x

y

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Solution j(Distance = 800)44626967786462544250404038213567606040425099

TSP30 (Performance = 800)

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0 10 20 30 40 50 60 70 80 90 100

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Solution k(Distance = 652)TSP30 (Performance = 652)

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Best Solution (Distance = 420)423835262135327

3846445860697678716967628494

TSP30 Solution (Performance = 420)

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Overview of PerformanceTSP30 - Overview of Performance

0

200

400

600

800

1000

1200

1400

1600

1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

Generations (1000)

Dis

tan

ce

Best

Worst

Average

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GA For Optimal Implementation of Logic Functions in FPGAs

1. Attempting to evolve the minimized logic solution of a logic function

2. The evolution is done through a hardware implementation of a genetic algorithm (GA), while the minimization is one of FPGA look-up tables (LUTs) and logic levels

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System Architecture• Optimizer = ECP Controller

(ECPC)• Host = ECP• Both optimizer and host are PLDs• Optimizer is where function is

evolved• Host is where circuit is tested• Optimizer/Host = Server/Client• Multiple hosts can connect to one

optimizer• Multiple functions can be evolved

on one optimizer

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Optimizer Module1. HIGA (HW implemented GA)

• Much faster because done mostly in H/W

• Adds caveats on the std. GA

2. ECLBs

Evolvable Configuration Logic Blocks

• Where the chromosomes are evaluated for fitness assignment

1. hcache

• Common DB for future use

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Optimizer Architecture

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System Operation

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Figure 5

System Operation

(2)

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FPGA

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Figure 7

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Figure 8

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Issues for GA Practitioners• Choosing basic implementation issues:

– representation– population size, mutation rate, ...– selection, deletion policies– crossover, mutation operators

• Termination Criteria• Performance, scalability• Solution is only as good as the evaluation

function (often hardest part)

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Benefits of Genetic Algorithms

• Concept is easy to understand

• Modular, separate from application

• Supports multi-objective optimization

• Good for “noisy” environments

• Always an answer; answer gets better with time

• Inherently parallel; easily distributed

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Benefits of Genetic Algorithms (cont.)

• Many ways to speed up and improve a GA-based application as knowledge about problem domain is gained

• Easy to exploit previous or alternate solutions

• Flexible building blocks for hybrid applications

• Substantial history and range of use

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When to Use a GA• Alternate solutions are too slow or overly

complicated

• Need an exploratory tool to examine new approaches

• Problem is similar to one that has already been successfully solved by using a GA

• Want to hybridize with an existing solution

• Benefits of the GA technology meet key problem requirements

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Some GA Application TypesDomain Application Types

Control gas pipeline, pole balancing, missile evasion, pursuit

Design semiconductor layout, aircraft design, keyboardconfiguration, communication networks

Scheduling manufacturing, facility scheduling, resource allocation

Robotics trajectory planning

Machine Learning designing neural networks, improving classificationalgorithms, classifier systems

Signal Processing filter design

Game Playing poker, checkers, prisoner’s dilemma

CombinatorialOptimization

set covering, travelling salesman, routing, bin packing,graph colouring and partitioning

Voicu Groza, 2008 SITE, 2008 - HARDWARE/SOFTWARE CODESIGN OF EMBEDDED SYSTEMS 1 Hardware/Software Codesign of Embedded Systems OPTIMIZATION Voicu Groza.

Documents

set of pareto points

cost t exec cost t exec

possible design points

new design points

pareto points c

design point j

design space

paretooptimal solutions