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Artificial IntelligenceArtificial Intelligence

Daniel Tauritz, Ph.D.Daniel Tauritz, Ph.D.Associate Professor of Computer ScienceAssociate Professor of Computer Science

Director, Natural Computation LaboratoryDirector, Natural Computation Laboratory

Missouri S&TMissouri S&T

Intro to AI

• Thinking Humanly (Cognitive Modeling)

• Acting Humanly (Turing Test)• Thinking Rationally (Logic)• Acting Rationally (Optimizing

Utility Function)

Algorithm

An algorithm is a sequence of well-defined instructions that can be executed in a finite amount of time in order to solve some problem.

Optimization Algorithm

An optimization algorithm is an algorithm which takes as input a solution space, an objective function which maps each point in the solution space to a linearly ordered set, and a desired goal element in the set.

Stochastic Algorithm

A stochastic algorithm is an algorithm which when executed multiple times with the same input, produces different outputs drawn from some underlying probability distribution.

Evolutionary Algorithm

A stochastic optimization algorithm inspired by genetics and natural evolution theory.

Population Initialization

Problem Description

Reproduction

Fitness Evaluation

Termination Criteria Met?

Solution

Competition

Strategy Parameters

Fitness Evaluation

Problem Specific Black Box

Evolutionary Problem Solving

yes

no

Evolutionary Cycle

Deriving Gas-Phase Exposure History through Computationally Evolved Inverse Diffusion Analysis

• Joshua M. Eads• Undergraduate in Computer Science

• Daniel Tauritz• Associate Professor of Computer Science

• Glenn Morrison• Associate Professor of Environmental Engineering

• Ekaterina Smorodkina• Former Ph.D. Student in Computer Science

Introduction

UnexplainedSickness

Examine IndoorExposure History

Find Contaminantsand Fix Issues

Background

• Indoor air pollution top five environmental health risks

•$160 billion could be saved every year by improving indoor air quality

•Current exposure history is inadequate

•A reliable method is needed to determine past contamination levels and times

Problem Statement

•A forward diffusion differential equation predicts concentration in materials after exposure

•An inverse diffusion equation finds the timing and intensity of previous gas contamination

•Knowledge of early exposures would greatly strengthen epidemiological conclusions

Gas-phase concentration history material phase concentration profile

Elapsed time

Con

cen

trati

on

in

gas

Con

cen

trati

on

in

solid

x or distance into solid (m)

0 0

Gas-phase concentration history and material absorption

Proposed Solution

x^2 + sin(x)sin(x+y) + e^(x^2)

5x^2 + 12x - 4

x^5 + x^4 - tan(y) / pisin(cos(x+y)^2)

x^2 - sin(x)X +

/

Sin

??

•Use Genetic Programming (GP) as a directed search for inverse equation

•Fitness based on forward equation

Related Research

• It has been proven that the inverse equation exists

•Symbolic regression with GP has successfully found both differential equations and inverse functions

•Similar inverse problems in thermodynamics and geothermal research have been solved

Candidate

Solutions

Population

Fitness

Interdisciplinary Work

•Collaboration between Environmental Engineering, Computer Science, and Math

Parent Parent SelectionSelection

Parent Parent SelectionSelection

ReproductioReproductionn

ReproductioReproductionn

CompetitioCompetitionn

CompetitioCompetitionn

Genetic Programming Algorithm

Forward Forward Diffusion Diffusion EquationEquation

Forward Forward Diffusion Diffusion EquationEquation

Genetic Programming Background

++

**

XX

SiSinn

**XX

XX PiPi

Y = X^2 + Sin( X * Pi )

Summary

•Ability to characterize exposure history will enhance ability to assess health risks of chemical exposure

A Coevolutionary Arms-Race Methodology for Improving

Electric Power Transmission System Reliability

Delivery Problems

• Transmission Grid Expansion Hampered– Social, environmental, and

economic constraints

• Transmission Grid Already “Stressed”– Already carrying more than intended– Dramatic increase in incidence reports

The Grid

The Grid: Failure

The Grid: Redistribution

The Grid: A Cascade

The Grid: Redistribution

The Grid: Unsatisfiable

The Grid: Unsatisfiable

Failure Summary

• Failure spreads relatively quickly– Too quickly for conventional control

• Cascade may be avoidable– Utilize unused capacities

(Flow compensation)

• Unsatisfiable condition may be avoidable– Better power flow control to reduce severity

Measuring hardening performance

• In practice: evaluate over a representative sampling of scenarios

• Sampling approaches– Pruned Exhaustive (e.g., n-1 security index in

power systems)– Monte Carlo– Intelligent adversary

Intelligent Adversary

• Game Theoretic: Two-player game of defenders & attackers

• Dependent search spaces: grid hardening space (defenders) & scenario space (attackers)

• Computational methods for dependent search:– Iterative approach– Competitive Coevolution approach– Generalized Co-Optimization approach

Competitive Coevolution

• Type of Evolutionary Algorithm where solution quality is dependent on other solutions

• For two-player games an arms-race is created by having two opposing populations of solutions where solution quality is inversely dependent on solutions in the opposing population

Co-Optimization• Generalization of Coevolution

• Evolutionary principles are replaced by arbitrary black-box optimization techniques

• Allows matching of interactive problem domains to optimization techniques

Summary of methodology

• Improve grid robustness by creating an arms-race between hardenings (defenders) and fault scenarios (attackers) through the use of Co-Optimization

• Hardenings are evolved to minimize economic loss

• Fault scenarios are evolved to maximize economic loss

• Stair stepping of ability

Advanced Power Transmission System with Distributed Power Electronics Devices - Case Study

• Hardenings: Unified Power Flow Controller (UPFC) placements

– Control power flow through transmission lines

– UPFCs are a powerful type of Flexible AC Transmission System (FACTS) device

• Fault scenarios: line outages

FACTS Interaction Laboratory

HIL Line

UPFC

Simulation

Engine

Social & Ethical Implications

• Grid really improved?– Margins versus profits– New weaknesses introduced

• Who decides delivery priorities?

• Can this research be misused?

Coevolutionary Automated Software Correction (CASC)

ISC Sponsored Project

Ph.D. student: Josh Wilkerson

Objective: Find a way to automate the process of software testing and correction.

Approach: Create Coevolutionary Automated Software Correction (CASC) system which will take a software artifact as input and produce a corrected version of the software artifact as output.

Coevolutionary Cycle

Population Initialization

Population Initialization

Population Initialization

Population Initialization

Initial Evaluation

Initial Evaluation

Reproduction Phase

Reproduction Phase

Reproduction Phase

Evaluation Phase

Evaluation Phase

Competition Phase

Competition Phase

Termination

Termination