R.E.A.C.H.ing Optimum Designs through Processes Inspired by

Principles of Evolution

Partha ChakrobortyProfessor

Department of Civil EngineeringIIT, Kanpur

The Next Half-Hour

Evolution

Genetic Algorithm

Some Applications of Genetic Algorithm

Evolution 101 (I)

Evolution

Evolution is the process by which modern organisms have descended from ancient ones

Microevolution

Microevolution is evolution within a single population; (a population is a group of organisms that share the same gene pool). Often this kind of evolution is looked upon as change in gene frequency within a population

Evolution 101 (II)

For evolution to occur

HeredityInformation needs to be passed on from one generation to the next

Genetic VariationThere has to be differences in the characteristics of individuals in order for change to occur

Differential ReproductionSome individuals need to (get to) reproduce more than others thereby increasing the frequency of their genes in the next generation

Evolution 101 (III)

Heredity

Heredity is the transfer of characteristics (or traits) from parent to offspring through genes

Evolution 101 (IV)

Genetic Variation

Is about variety in the population and hence presence of genetic variation improves chances of coming up with “something new”The primary mechanisms of achieving genetic variation are:

Mutations

Gene Flow

Sexual Reproduction

Evolution 101 (V)

Mutation

It is a random change in DNA

It can be beneficial, neutral or harmful to the organism

Not all mutations matter to evolution

Evolution 101 (VI)

Gene Flow

Migration of genes from one population to another

If the migrating genes did not exist previously in the incident population then such a migration adds to the gene pool

Evolution 101 (VII)

Sexual Reproduction

This type of producing young can introduce new gene combinations through genetic shuffling

Evolution 101 (VIII)

Differential Reproduction

As the genes show up as traits (phenotype) the individuals get affected by what is around; some die young while others live

Those who live compete for mates; only the winners pass on their gene to the next generation

In some sense the fitter (with respect to the current environment) gets to leave more of his/her genes in the next population; often the term fitness is used to describe the relative ability of individuals to pass on their genes

Evolution 101 (IX) Overview

Differential Reproduction

Variation

Heredity

From Organisms to Abstract Beings (I)

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111001

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The fight to survive (selection operation)

From Organisms to Abstract Beings (II)

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The Survivors and Mating Offsprings

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Genetic Algorithms (I)

Basic Questions

How does one decide who survives

How does one decide how successfully each survivor produces offsprings

How are the offsprings related to the parents

How does one ensure that genetic variation is maintained even though with every generation individuals are supposed to become fitter

Genetic Algorithms (II)

Population of individuals or alternative

(feasible) solutions

Next generationof

individuals

Mating pool of“fitter”

individuals

Evaluate individualson their fitness

Select individuals based on fitness

for subsequent mating

Select individuals& exchange charac-

teristics to createnew individuals

Arbitrarily change some characteristic

Differ

entia

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Repro

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HeredityGenetic

Variatio

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Genetic Algorithms (III)

What is an individual?

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Genetic Algorithms (IV)

Generation of initial population

Basic Tasks

Evaluation

Selection (Reproduction operation)

Exchange characteristics to develop newindividuals (Crossover operation)

Arbitrarily modify characteristics in newindividuals (Mutation operation)

Genetic Algorithms (V)

Reproduction / Selection Operator

The purpose is to bias the mating pool (those who can pass on their traits to the next generation) with fitter individuals

Assign p as the prob. of choosingan individual for the mating pool

p is proportional to the fitness

Choose an individual with prob. pand place it in the mating pool

Continue till the mating pool sizeis the same as the initial population’s

Choose n individuals randomly

Pick the one with highest fitness

Place n copies of this individual inthe mating pool

Choose n different individuals andrepeat the process till all in the original population have been chosen

Genetic Algorithms (VI)

Crossover operator

1 0 0 1 1 0 1

1 1 0 0 1 1 1

1 0 0 1 1 1 11 1 0 0 1 0 1

Genetic Algorithms (VII)

Mutation

1 0 0 1 1 0 1

1 0 0 0 1 0 1

Genetic Algorithms (VIIIa)

Results from a small example:

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Initial Population Generation 10

Genetic Algorithms (VIIIb)

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Genetic Algorithms (IX)

Issues

Generation of initial population

Evaluation

Reproduction operation

Crossover and Mutation operations andfeasibility issues

Representation

Genetic Algorithms

Benefits to engineers as an optimization tool

Problem formulation is easier

Allows external procedure based declarations

Can work naturally in a discrete environment

Optimizing with Genetic Algorithms

Some Examples

Some Applications

Engineering component / equipment design

Engineering process optimization

Portfolio optimization

Route optimization; optimal layout; optimal packing

Schedule optimization

Protein structure analysis

Decision making / decision support systems

Transit Routing: Description

Transit Routing: Characterization (I)

The purpose is to determine a set of routes which serve many people quickly and without using too many transfers.

The number of passengers using a particular route depends on the layout of the route as well as the layout of the other routes.

Evaluation of a route set (note, it is not very meaningful to evaluate a route in isolation) is not easy. Obtaining an objective “function” is not possible.

A solution is a “route set;” each route within a route set is a meaningful juxtaposition of links.

Transit Routing: Characterization (II)

Defining “meaningful juxtaposition” (a feasible route) through algebraic relations is difficult.

Traditional MP formulation is at best extremely difficult and most probably impossible.

Procedure based determination of the “goodness” and “feasibility” are more practical.

Transit Routing: Formulation (I)

The problem is formulated for a GA based solution.

The initial population of route sets are created using problem specific information.

Tournament selection is chosen.

Problem specific crossover and mutation operators are devised.

Transit Routing: Formulation (II)

Representation……….

Transit Routing: Formulation (III) Crossover (inter-string)

……….

Parents

Children

Transit Routing: Formulation (IV) Crossover (intra-string)

……….

Transit Routing: Formulation (V) Mutation……

….

Transit Routing: Results

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11 Mandl’s Swiss network --- a benchmark problem

Single Vehicle Routing: Description (I)

Single Vehicle Routing: Description (II)

Nodes can be visited in any order and at any time

Some nodes cannot be visited before others; no restrictions on visit time

Travelling Salesman Problem

Pick-up and Delivery Problem

Some nodes cannot be visited before others; restrictions on visit time

Dial-a-ride Problem

Single Vehicle Routing: Description (II)

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Single Vehicle Routing: Formulation

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Single Vehicle Routing: Results (I)

TSP; 202 node problem; geospherical distances, (GR202 --- a benchmark problem)

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Single Vehicle Routing: Results (II)PDP; 70 node problem; Euclidean

distances, (ST70PD --- a modified benchmark problem)

Opti

mu

m

Single Vehicle Routing: Results (IIIa)GA evolving a good TSP route, Eil51,

Initial Best

Single Vehicle Routing: Results (IIIb)GA evolving a good TSP route, Eil51,

Intermediate

Single Vehicle Routing: Results (IIIc)GA evolving a good TSP route, Eil51,

Intermediate

Single Vehicle Routing: Results (IIId)GA evolving a good TSP route, Eil51,

Intermediate

Single Vehicle Routing: Results (IIIe)GA evolving a good TSP route, Eil51,

Intermediate

Single Vehicle Routing: Results (IIIf)GA evolving a good TSP route, Eil51, Final

Best

Single Vehicle Routing: Results (IIIg)GA evolving a good TSP route, Eil51, Initial

Best

Transit Scheduling: Description (I)

Stops

Transfer stops

Transit Scheduling: Description (II)

From a scheduling standpoint determining theschedule of bus arrivals and departures at a transfer stop is important as these stops typicallyrepresent major stops and also because at thesestops passengers can transfer from one route tothe other.

Given the fleet size, the idea is to determine the schedule such that the total time spent waiting (for a bus) by transferring and non-transferring passengers is minimized.

Transit Scheduling: Characterization (I)

Let’s look at one transfer station with 3 routes ……

time

Transit Scheduling: Characterization (II)

Waiting time for non-transferring passengers ……

Arrival rate

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Transit Scheduling: Characterization (III) Waiting time for transferring passengers ……

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Transit Scheduling: Formulation (I)

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Transit Scheduling: Formulation (II)

The MP formulation is an NLMIP problem. Efficient solution techniques do not exist.

A GA formulation was attempted to solve this and similar problems. The general characteristics of the formulation are:

(a)Headway and stopping times used as variables

(b)Variables d are computed through external procedures

(c)Binary coding, single point crossover, and bitwise mutation used

(d)One set of constraints remained; these were handled using penalty functions

Transit Scheduling: Results (I)

3 routes, 8-10-12 buses, only IWT

3 routes, 8-10-12 buses, TT+IWT

Transit Scheduling: Results (II)

3 transfer stations, 6 routes, 10-12-8-12-8-10 buses, TT+IWT

R1

R5

R4

R3

R2

R6

S3

S2

S1

Transit Scheduling: Results (III) 3 routes, fleet distribution unknown, only IWT

3 routes, fleet distribution unknown, TT+IWT

That’s it !!!!!

Thank you