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9/9/19 GAs: What are they used for? Genetic Algorithms Problems - PDF document

Dec 11, 2023 •396 likes •489 views

9/9/19 GAs: What are they used for? Genetic Algorithms Problems can be classified in different ways: Black box model Search problems CS 419/519 Optimization vs constraint satisfaction NP problems / 20 Black box model

  1. 9/9/19 GAs: What are they used for? Genetic Algorithms Problems can be classified in different ways: • Black box model • Search problems CS 419/519 • Optimization vs constraint satisfaction • NP problems / 20 “Black box” model “Black box” model Model: an input (solution) evaluator • “Black box” model consists of 3 components Input: a proposed solution Output: result of the computation • Two components are known, one is unknown (May be broad description rather • Each unknown results in a different problem type than specific value.) / 20 / 20 1

  2. 9/9/19 Important distinction: Examples problem instance vs. input • Traveling salesperson problem: • Problem instance: what we often think of as an “input” to • Input: a sequence of destinations our algorithms. • Model: function to sum distances between adjacent destinations • Input (for the purposes of this discussion): a candidate • Output: total distance traveled solution to the problem. • University classroom scheduler: • Input: a schedule assigning classes to classrooms • Example: TSP • Model: function to determine time conflicts, seat shortages, etc • Problem instance: a set of destinations • Output: values for number of conflicts, seat delta, etc • Input: a sequence of the destinations • Eight-queens problem: • Example: Classroom scheduling • Input: arrangement of eight queens on chessboard • Problem instance: sets of classes and classrooms • Model: checker for conflicts • Input: a schedule that may or may not satisfy all constraints • Output: indication of conflict or not / 20 / 20 “Black box” model: Input unknown “Black box” model: Optimization Optimisation example 1: university timetabling • Model and desired output are known. We seek inputs Task: find a timetable that maximize or minimize the desired variable(s) • Enormously big search space • Timetables must be good • “Good” is defined by a number of competing criteria – Courses well distributed – Not too many late in the day • Timetables must be feasible – Satisfies constraints • Examples: • Enough seats Time tables for university, call center, or hospital • • No time conflicts Design specifications (circuit, probe placement) • • Vast majority of search space is Traveling salesperson problem (TSP) • infeasible Eight-queens problem • / 20 / 20 2

  3. 9/9/19 “Black box” model: Optimization example 2: satellite structure Task: find a design • Optimized satellite designs for NASA to maximize vibration isolation • Evolving: design structures • Fitness: vibration resistance • Evolutionary “creativity” / 20 / 20 “Black box” model: “Black box” model: Model unknown Optimization example 3: 8 queens problem Modelling • We have corresponding sets of inputs & outputs. We Task: find an arrangement seek a model that delivers correct output for every • Given an 8-by-8 chessboard known input and 8 queens • Place the 8 queens on the chessboard without any conflict • Two queens conflict if they share same row, column or • Examples: diagonal Stock market prediction • • Can be extended to an n Loan applicant evaluation • queens problem (n>8) Facial recognition • Autonomous driving • / 20 / 20 3

  4. 9/9/19 “Black box” model: Model unknown “Black box” model: Modelling Modeling example: loan applicant evaluation • Note: modelling problems can be transformed into • British bank evolved optimisation problems creditability model to • Error rate (or success rate) of the model is quantity to be predict loan paying minimized (or maximized) behavior of new applicants • Examples • Evolving: prediction • Evolutionary machine learning models • Evolve a neural network that maximizes hit rate of identifications • Predicting stock exchange • Fitness: model accuracy • Minimize difference between predicted value and actual value on historical data • Voice control system for smart homes • Minimize error in commands performed / 20 / 20 “Black box” model: “Black box” model: Output unknown Modeling example: stock market prediction Simulation • We have a given model. We seek the outputs that arise Two methods under different input conditions • Build a time machine • DeLoreans are hard to find • Evolve a predictive model • Fitness: difference between Often used to answer “what-if” questions in evolving • actual value of DJIA and dynamic environments predicted value Examples • What are the inputs? • Evolutionary economics, Artificial Life • Weather forecast system • Impact analysis of new tax systems • / 20 / 20 4

  5. 9/9/19 “Black box” model: “Black box” model: Simulation example: evolving artificial societies Simulation example 2: cosmology Simulate the physics • Simulating trade, economic competition, etc. to calibrate beginning at some point in models time to test our understanding of the • Use models to optimize universe strategies and policies Large number of variables • Evolutionary economy and values requires substantial computational • Survival of the fittest is resources universal (big/small fish) / 20 / 20 Search problems Problems vs. problem solvers • Simulation is different from optimization/modelling Important distinction: • Optimization/modeling problems search through huge space of possibilities • search problems: define search spaces • Search space: collection of all objects of interest • problem-solvers: describe how to move through search including the desired solution(s) spaces • Question: how large is the search space for different tours through n destinations? / 20 / 20 5

  6. 9/9/19 Optimization vs. constraint satisfaction Optimization vs. constraint satisfaction • Objective function: a way of assigning a value to a Goal: possible solution that reflects its quality – Number of un-checked queens (maximize) A solution that: – Length of a tour visiting given set of destinations (minimize) • “performs well” according to the objective • Constraint: binary evaluation telling whether a given function requirement holds or not • satisfies all constraints – Find a configuration of eight queens on a chessboard such that no two queens check each other – Find a tour with minimal length where city X is visited after city Y / 20 / 20 Optimization vs. constraint satisfaction Optimization vs. constraint satisfaction • When combining the two: Objective function Constraints Yes No Yes Constrained Constraint Objective function optimization satisfaction problem problem Constraints Yes No Yes Constrained Constraint No Free No problem optimization satisfaction optimization problem problem problem No Free No problem Problem: maximize number of unchecked queens on a optimization chess board problem Which category? Free optimization problem (FOP) / 20 / 20 6

  7. 9/9/19 Optimization vs. constraint satisfaction Optimization vs. constraint satisfaction Objective function Objective function Constraints Yes No Constraints Yes No Yes Constrained Constraint Yes Constrained Constraint optimization satisfaction optimization satisfaction problem problem problem problem No Free No problem No Free No problem optimization optimization problem problem Problem: find a configuration of eight queens on a chess Problem: minimize length of tour visiting every destination, board such that no two queens check each other in a set of n destinations, exactly once (TSP) Which category? Which category? Constraint satisfaction problem (CSP) Free optimization problem (FOP) / 20 / 20 Optimization vs. constraint satisfaction Another classification scheme: P and NP • So far, we have only looked at classifying problems; we Objective function have not discussed problem solvers Constraints Yes No Yes Constrained Constraint optimization satisfaction • For this new classification scheme, we need the problem problem properties of the problem solver – we will classify No Free No problem problems by how easy or hard they are to solve optimization problem Problem: find a TSP tour with minimal length such that city • Applies to combinatorial optimization problems – these X is visited after city Y are problems for which the variables are discrete rather than continuous Which category? Constrained optimization problem (COP) / 20 / 20 7

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