Spring 2011 Artificial Intelligence COSC 40503

1. Antonio Sanchez Texas Christian University References www.cs.vu.nl/~gusz/ecbook/slides/Genetic_Algorithms.ppt web.umr.edu/~ercal/387/slides/GATutorial.ppt igda-phx.org/resources/20031121_ga.ppt parasol.tamu.edu/~amato/Courses/ 689-608/presentations/jkp2866/gep-jack.ppt www.niss.org/affiliates/proteomics200303/ presentations20030306/04%20Jennifer.ppt http://www.eece.unm.edu/~akbazar/ Spring 2011Artificial Intelligence COSC 40503

2. Softcomputing Softcomputing refers to a set of problem solving methods used when the required solution • Permits some degree of imprecision • It is subject to uncertainty • Deals with knowledge(beliefs, choices) rather than information(truth) • A quasi optimized solution is acceptable • Allows ample time to come with the solution In this case soft computing such as GA’s and Learning offers solutions with • Robust results • Low cost • Easy tractability

3. Who benefits from Applying GA’s • The search space is large, complex or poorly understood. • Domain knowledge is scarce or expert knowledge is difficult to encode to narrow the search space. • No mathematical analysis is available. • Traditional search methods fail.. Source: http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/tcw2/report.html

4. Who benefits from Applying GA’s • Optimization: • Automatic Programming: • Machine and robot learning: • Economic models: • Immune system models: • Ecological models: • Models of social systems: Source: http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/tcw2/report.html

5. Real valued optimization Many problems occur as real valued problems, e.g. continuous parameter optimization f : n  Illustration: Ackley’s function

6. Application: Protein Signature Selection in Mass Spectrometry relative intensity http://www.uni-mainz.de/~frosc000/fbg_po3.html molecular weight

7. JSSP: job shop scheduling problem Precedence constrained job shop scheduling problem • J is a set of jobs. • O is a set of operations • M is a set of machines • Able O  M defines which machines can perform which operations • Pre O  O defines which operation should precede which • Dur :  O  M  IR defines the duration of o  O on m  M The goal is now to find a schedule that is: • Complete: all jobs are scheduled • Correct: all conditions defined by Able and Pre are satisfied • Optimal: the total duration of the schedule is minimal

8. Real World Applications • Lockheed Martin Missiles and Space Co. - Near-Minimum-Time Spacecraft Maneuvers [Howley, 96] • GP applied to the problem of rest-to-rest reorientation maneuvers for satellites • Optimal time solution is a vector of nonlinear differential equations, which are difficult to solve • An approximate solution is necessary for a real-time controller • Results: Rest-to-Rest Maneuver Times (8 test cases) • Optimal Solution: 287.93 seconds • Expert Solution: 300.3 seconds • GP Solution: 292.8 seconds

9. 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 Source: Wendy Williams,web.umr.edu/~ercal/387/slides/GATutorial.ppt

10. Representation Representation is an ordered list of city numbers known as an order-based GA. No encoding, this is EA (Evolutive Algorithm) 1) Forth Worth 3) Austin 5) Houston 7) El Paso 2) Dallas 4) Waco 6) San Antonio 8) Lubbock 9) Temple CityList1(3 5 7 2 1 6 4 8 9) CityList2(2 5 7 6 8 1 3 4 9) Source: http://cs.felk.cvut.cz/~xobitko/ga/

11. Crossover Single point crossover Two point crossover Uniform crossover Bit inversion Logical crossover 11001011 + 11011111 = 11001001 (AND) Source: http://cs.felk.cvut.cz/~xobitko/ga/

12. Permutations • Single point crossover - one crossover point is selected, the permutation is copied from the first parent till the crossover point, then the other parent is scanned and if the number is not yet in the offspring, it is added ` (1 2 3 4 5 6 7 8 9) + (4 5 3 6 8 9 7 2 1) = (1 2 3 4 5 6 8 9 7) • Order changingMutation- two numbers are selected and exchanged (1 2 3 4 5 6 8 9 7) => (1 8 3 4 5 6 2 9 7) Source: http://cs.felk.cvut.cz/~xobitko/ga/