Some issues of design philosophy… Basic Concepts Some issues of design philosophy…

Memory-Processor Link and the von Neumann Bottleneck Processor = CPU Memory = hierarchy of caches, main memory, and bulk storage Connection = address, control, data busses Source of contention = bus traffic during the FETCH/EXECUTE cycle 8/23/2019 Copyright G.A. Tagliarini, PhD

Memory-Processor Link Biological systems Memory unit = processor Large numbers of independent but interacting processors (circa 1010 neurons) Small computational complexity Massive connectivity (circa 1012 synapses) Connections and state represent solutions 8/23/2019 Copyright G.A. Tagliarini, PhD

Common Characteristics of BIP Parallel distributed processing Rummelhart, McClelland and Hinton Stigmergy Feedback Negative Positive 8/23/2019 Copyright G.A. Tagliarini, PhD

Copyright G.A. Tagliarini, PhD Emergent Behavior Adaptation Learning Supervised – a teacher instructs using a set of examples and the student generalizes to produce a representation Unsupervised – examples are presented and a rule for forming group representations may be given Evolution Fitness/selective pressure Crossover/recombination Mutation 8/23/2019 Copyright G.A. Tagliarini, PhD

Emergent Behavior (continued) Self-organization Cooperation Coordination Order arises without external intervention Contrast with Templates Supervisors Instructions/blueprints Key question: How to formulate behaviors that give rise to self-organization? 8/23/2019 Copyright G.A. Tagliarini, PhD

Example: How to Get Ants to Cooperate when Foraging Suppose ants have been endowed with search behaviors and individual carrying capacity? Allow the reward structure to be changeable What behaviors or conditions would elicit cooperation? 8/23/2019 Copyright G.A. Tagliarini, PhD

A Search Problem: Satisfiability Given A set of m logic variables {p1, p2, …, pm} A collection of n disjunctive clauses, e.g., ci = (p1 + p2’ + p5) Place the clauses in conjunctive normal form (CNF) to create c = c1 c2 …ci …cn Question Is there an assignment of truth values that satisfies c? “…satisfies c…” means “…for which c is true…” See further: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem 8/23/2019 Copyright G.A. Tagliarini, PhD

An Optimization Problem: Maximum Satisfiability Given A set of m logic variables {p1, p2, …, pm} A collection of n disjunctive clauses, e.g., ci = (p1 + p2’ + p5) Place the clauses in conjunctive normal form (CNF) to create c = c1 c2 …ci …cn Question What is the assignment of truth values that maximizes the number of clauses satisfied? 8/23/2019 Copyright G.A. Tagliarini, PhD

An Optimization Problem: Weighted Maximum Satisfiability Given A set of m logic variables {p1, p2, …, pm} A collection of n disjunctive clauses, e.g., ci = (p1 + p2’ + p5) Each clause ci has a corresponding nonnegative weight wi Question What assignment of truth values maximizes the sum of the weights of the satisfied of clauses? See further: http://web.udl.es/usuaris/m4372594/MAX-SATweb.html 8/23/2019 Copyright G.A. Tagliarini, PhD

General Problem Solving Concerns Goal Representation Constraints (How do I know I have a solution?) “No free lunch theorem” (Wolpert and Macready, 1997) 8/23/2019 Copyright G.A. Tagliarini, PhD

Copyright G.A. Tagliarini, PhD Goal Search Find any solution; time to verify a solution bounded by some polynomial E.g., queen placement, knight’s tour, map coloring, SAT Leads to a Boolean assessment function Optimize Find solutions of a given “quality” (Maximize/Minimize) E.g., TSP, weighted MAX-SAT, WTA, QAP, network flow 8/23/2019 Copyright G.A. Tagliarini, PhD

Copyright G.A. Tagliarini, PhD Representation Choosing a feature space Telling time: rectangular versus polar coordinates Speech recognition: time domain versus frequency domain Face recognition: templates, eigenfaces 8/23/2019 Copyright G.A. Tagliarini, PhD

Copyright G.A. Tagliarini, PhD Constraints How do I know I have a solution? Linear Nonlinear Inequality Integer Zero/One 8/23/2019 Copyright G.A. Tagliarini, PhD

Why Can’t I Just Learn One Problem Solving Method? “No free lunch theorem” (Wolpert and Macready, 1997) No single optimization method will perform best on all instances of all problems. 8/23/2019 Copyright G.A. Tagliarini, PhD

Two Conventional Benchmark Techniques Hill Climbing Simulated Annealing 8/23/2019 Copyright G.A. Tagliarini, PhD

Hill Climbing (Minimization) Assume: Candidate solutions → s0 and s1 in a space S Goal → g Fitness function f such that f:S →R+ Repetition limit → L Algorithm Initialize s0 = s1, f0 = f(s0), f1 = f(s1), Counter While (counter<L, f0>g) s1 = mutate(s0), f1 = f(s1) If f1 < f0 (Note: Improvements are always kept) s0 = s1 f0 = f(s0) Increment counter 8/23/2019 Copyright G.A. Tagliarini, PhD

Stochastic Hill Climbing (Minimization) Assume: Candidate solutions, goal, fitness function, solution space, and iteration limit as in basic hill climbing A scaling parameter T Algorithm Initialize While (counter<L, f0>g) s1 = mutate(s0), f1 = f(s1) Df = (f0 – f1) If rand >1/ (1+exp(Df/T) (Note: Improvements are often kept) s0 = s1 f0 = f(s0) Increment counter 8/23/2019 Copyright G.A. Tagliarini, PhD

Copyright G.A. Tagliarini, PhD Simulated Annealing http://people.uncw.edu/tagliarinig/Courses/340/Lectures/Simulated%20Annealing.ppt#1 8/23/2019 Copyright G.A. Tagliarini, PhD

Evolutionary Algorithms Based on analogy to evolution in biological systems Key process elements Fitness function “Artificial selection” Crossover and recombination Mutation 8/23/2019 Copyright G.A. Tagliarini, PhD