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

1. R.E.A.C.H.ing Optimum Designs through Processes Inspired by Principles of Evolution

2. The Next Half-Hour Evolution Genetic Algorithm Some Applications of Genetic Algorithm

3. 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

4. Evolution 101 (II) For evolution to occur Heredity Information needs to be passed on from one generation to the next Genetic Variation There has to be differences in the characteristics of individuals in order for change to occur Differential Reproduction Some individuals need to (get to) reproduce more than others thereby increasing the frequency of their genes in the next generation

5. Evolution 101 (III) Heredity Heredity is the transfer of characteristics (or traits) from parent to offspring through genes

6. 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: Gene Flow Sexual Reproduction Mutations

7. 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

8. 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

9. Evolution 101 (VII) Sexual Reproduction This type of producing young can introduce new gene combinations through genetic shuffling

10. 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

11. Evolution 101 (IX) Heredity Variation Differential Reproduction Overview

12. From Organisms to Abstract Beings (I) The fight to survive (selection operation) 110011 101010 000010 110010 010010 111001 000000

13. 111 010 0 110 00 111 0 010 From Organisms to Abstract Beings (II) The Survivors and Mating Offsprings 110010 101010 111001 010010 110011

14. 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

15. Population of individuals or alternative (feasible) solutions Next generation of individuals Evaluate individuals on their fitness Arbitrarily change some characteristic Select individuals based on fitness for subsequent mating Select individuals & exchange charac- teristics to create new individuals Mating pool of “fitter” individuals Genetic Algorithms (II) Differential Reproduction Genetic Variation Heredity

16. z x,y,z 1001,0000,1101 24,2,11 y x i i h h (a,b)(b,c)(c,d)…(h,i) a,b,c,d,…i g g e d d f f e c a a b c b Genetic Algorithms (III) What is an individual?

17. Genetic Algorithms (IV) Basic Tasks Generation of initial population Evaluation Selection (Reproduction operation) Exchange characteristics to develop new individuals (Crossover operation) Arbitrarily modify characteristics in new individuals (Mutation operation)

18. 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 Choose n individuals randomly Pick the one with highest fitness Place n copies of this individual in the mating pool Choose n different individuals and repeat the process till all in the original population have been chosen Assign p as the prob. of choosing an individual for the mating pool p is proportional to the fitness Choose an individual with prob. p and place it in the mating pool Continue till the mating pool size is the same as the initial population’s

19. 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 Genetic Algorithms (VI) Crossover operator

20. 1 0 0 1 1 0 1 1 0 0 0 1 0 1 Genetic Algorithms (VII) Mutation

21. Genetic Algorithms (VIIIa) Results from a small example: Minimize Initial Population Generation 10

22. Genetic Algorithms (VIIIb) Generation 20 Generation 30 Generation 50 Generation 40

23. Generation of initial population Evaluation Reproduction operation Crossover and Mutation operations and feasibility issues Genetic Algorithms (IX) Issues Representation

24. 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

25. Optimizing with Genetic Algorithms Some Examples

26. Some Applications Decision making / decision support systems Engineering component / equipment design Engineering process optimization Portfolio optimization Route optimization; optimal layout; optimal packing Schedule optimization Protein structure analysis

27. Transit Routing: Description

28. 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.

29. Transit Routing: Characterization (II) A solution is a “route set;” each route within a route set is a meaningful juxtaposition of links. 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.

30. 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.

31. Transit Routing: Formulation (II) Representation……….

32. Parents Children Transit Routing: Formulation (III) Crossover (inter-string)……….

33. Transit Routing: Formulation (IV) Crossover (intra-string)……….

34. Transit Routing: Formulation (V) Mutation……….

35. 0 2 5 3 4 9 7 6 1 8 14 11 10 13 12 Transit Routing: Results Mandl’s Swiss network --- a benchmark problem

36. Single Vehicle Routing: Description (I)

37. Single Vehicle Routing: Description (II) Nodes can be visited in any order and at any time Travelling Salesman Problem Some nodes cannot be visited before others; no restrictions on visit time Pick-up and Delivery Problem Some nodes cannot be visited before others; restrictions on visit time Dial-a-ride Problem

38. Single Vehicle Routing: Description (II) J J I I A A H H K B K B G C G C D D F F E E A-B-C-H-G-D-E-F-I-J-K-A A-B-C-D-E-F-H-G-I-J-K-A A-B-C-D-E-F-H-G-K-J-I-A A-B-C-D-E-F-G-K-J-H-I-A

39. Single Vehicle Routing: Formulation A general formulation for all types of SVRP: A mutation-only GA approach

40. Single Vehicle Routing: Results (I) TSP; 202 node problem; geospherical distances, (GR202 --- a benchmark problem) Near-optimal (obtained here) Optimal (reported in liter.)

41. Single Vehicle Routing: Results (II) PDP; 70 node problem; Euclidean distances, (ST70PD --- a modified benchmark problem) Optimum

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

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

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

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

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

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

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

49. Transit Scheduling: Description (I) Stops Transfer stops

50. Transit Scheduling: Description (II) From a scheduling standpoint determining the schedule of bus arrivals and departures at a transfer stop is important as these stops typically represent major stops and also because at these stops passengers can transfer from one route to the 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.