Swarm Intelligence, Fuzzy Logic1...11/5/2018 1 INF3490 -Biologically inspired computing Swarm...

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INF3490 - Biologically inspired computingSwarm Intelligence, Fuzzy Logic

Weria KhaksarNovember, 06, 2018

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Swarm Intelligence: Concept

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Collective behavior emerged from social insectsworking under very few rules.

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Swarm Intelligence: Concept

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Fish, birds, ants, termites, lions, …

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Swarm Intelligence: Key Features

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Simple local rules Local interaction Decentralized control Complex global behavior

• Difficult to predict from observing the local rules

• Emergent behavior

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Swarm Intelligence: General Principles

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Proximity principleThe basic units of a swarm should be capable of simplecomputation related to its surrounding environment.

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Quality principleApart from basic computation ability, a swarm should be able toresponse to quality factors, such as food and safety.

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Principle of diverse responseResources should not be concentrated in narrow region. Thedistribution should be designed so that each agent will be maximallyprotected facing environmental fluctuations.

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Principle of diverse responseResources should not be concentrated in narrow region. Thedistribution should be designed so that each agent will be maximallyprotected facing environmental fluctuations.

Principle of stability and adaptabilitySwarms are expected to adapt environmental fluctuations withoutrapidly changing modes since mode changing costs energy.

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Swarm Intelligence: Particle Swarm Optimization (PSO)

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Mimicking physical quantities such as velocity and positionin bird flocking, artificial particles are constructed to “fly”inside the search space of optimization problems.

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Initially, a population of particles is distributed uniformlyin the search space of the objective function of theoptimization problem.

Two quantities are associated with particles, a positionvector 𝑥 and a velocity 𝑣 .

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At each time step, the velocities of particles will beupdated according to the following formula:

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Swarm Intelligence: Particle Swarm Optimization (PSO) Example

06.11.2018PSO algorithm maximizing f(x, y) = -|x**2 - y| (finding squares).

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Swarm Intelligence: Ant Colony Optimization (ACO)

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The most recognized example of swarm intelligence in realworld is the ants. To search for food, ants will start out fromtheir colony and move randomly in all directions.

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Once an ant finds food, it returns to colony and leave a trailof chemical substances called pheromone along the path.Other ants can then detect pheromone and follow the samepath.

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The interesting point is that how often is the path visit byants is determined by the concentration of pheromonealong the path. Since pheromone will naturally evaporateover time, the length of the path is also a factor. Therefore,under all these considerations, a shorter path will befavored because ants following that path keep addingpheromone which makes the concentration strong enoughto against evaporation. As a result, the shortest path fromcolony to foods emerges.

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06.11.2018 Ant Colony Optimization on Traveling Salesman Problem

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Swarm Intelligence: Bee Colony Optimization (BCO)

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Just like ants, bees have similar food collecting behaviors.Instead of pheromones, bees colony optimization algorithmrelies on the foraging behavior of honey bees. At the firststage, some bees are sent out to look for promising foodsources.

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After a good food source is located, bees return back tocolony and perform a waggle dance to spread outinformation about the source. Three pieces of informationare included: (1) distance, (2) direction, (3) quality of foodsource. The better the quality of food source, the morebees will be attracted. Therefore, the best food sourceemerges.

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06.11.2018Using the Bee colony Algorithm to solve the Knight's Tour Problem

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Swarm Intelligence: Cuckoo Search

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This algorithm is inspired by the brood parasitism behaviorof some species of cuckoo. They will lay their eggs in otherbird's nest. If the host bird find out about this, it will eitherthrow away the intruding egg or simply abandon the wholenest and start a new one. However, some species ofcuckoo are very good at making their eggs the same as thehost's egg, and therefore greatly increase the survivalprobability of their eggs.

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Basic rules of cuckoo search: Each cuckoo lays one egg at a time and dumps it in a

randomly chosen nest. The best nests with high quality of eggs will be brought to the

next generation. The number of host nests is fixed. A host bird will discover the

egg is laid by cuckoo by a probability 𝑃 ∈ 0,1 . The host birdcan get rid of the egg or build a new nest.

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Swarm Intelligence: Cuckoo SearchExample: Finding the maximum of 2D Michalewicz' function

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From left to right: Initial and final positions of the nests marked using dots.

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Swarm Intelligence: Other Algorithms

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Artificial Immune Systems

Bacterial Foraging

The Shuffled Frog Leaping

The Cat Swarm

Invasive weed optimization

Monkey Search

Water flow-like algorithm

Biogeography-based optimization

The Fish School Search

Bat-inspired Algorithm

Lion Optimization

Firefly algorithm

Dolphin Partner Optimization

Dolphin echolocation algorithm

Flower pollination algorithm

Krill herd

Wolf search

Grey Wolf Optimizer

Water cycle algorithm

The Social spider optimization

Forest Optimization algorithm

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References:

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1. Keerthi, S., Ashwini, K., & Vijaykumar, M. V. (2015). Survey Paper on Swarm Intelligence. International Journal of Computer Applications, 115(5).

2. Keerthi, S., Ashwini, K., & Vijaykumar, M. V. (2015). Survey Paper on Swarm Intelligence. International Journal of Computer Applications, 115(5).

3. Cui, X. Swarm Intelligence.

4. Hu, Y. Swarm intelligence.

5. Bonabeau, E., & Meyer, C. (2001). Swarm intelligence: A whole new way to think about business. Harvard business review, 79(5), 106-115.

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Fuzzy Logic: What is fuzzy thinking?

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Fuzzy logic is determined as a set of mathematicalprinciples for knowledge representation based on degreesof membership rather than on crisp membership of classicalbinary logic.

Range of logical values in Boolean and fuzzy logic: (a) Boolean logic; (b) multivalued logic.

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Traditional Control Systems: Need to know detailed physical properties of the system. Most systems are too complex and have to be idealized to

develop a traditional controller. The condition when traditional controllers will work is usually

fairly limited.

Fuzzy logic Control Systems: Do not need much detailed knowledge of the system. If optimization tools are used like GA, can get away with not

knowing much of anything. The condition when fuzzy logic controller will work are much

more robust because they can account for more variability inthe inputs.

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Unlike two-valued Boolean logic, fuzzy logic is multi-valued. It deals with degrees of membership and degreesof truth.

Fuzzy logic uses the continuum of logical values between0 (completely false) and 1 (completely true).

Instead of just black and white, it employs the spectrumof colors, accepting that things can be partly true andpartly false at the same time.

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Let 𝑋 be a classical (crisp) set and 𝑥 an element. Thenthe element 𝑥 either belongs to 𝑋 𝑥 ∈ 𝑋 or does notbelong to 𝑋 𝑥 ∉ 𝑋 .

Classical set theory imposes a sharp boundary on thisset and gives each member of the set the value of 1, andall members that are not within the set a value of 0.

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Who is tall?

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Fuzzy membership function

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Let 𝑋 be the universe of discourse and its elements be denoted as 𝑥. Inclassical set theory, crisp set 𝐴 of 𝑋 is defined as function 𝑓 𝑥 calledthe Characteristic Function of 𝐴.

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Let 𝑋 be the universe of discourse and its elements be denoted as 𝑥. Inclassical set theory, crisp set 𝐴 of 𝑋 is defined as function 𝑓 𝑥 calledthe Characteristic Function of 𝐴. Membership Function

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Representation of crisp and fuzzy sets.

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Linguistic variables and hedges

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Fuzzy Rules

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How to reason with fuzzy rules?

Evaluating the rule antecedent Implication the results to the consequent

Monotonic Selection

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Fuzzy Logic: Fuzzy Inference

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Fuzzy Inference Style

Mamdani Inference Style

Sugeno Inference Style

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Let’s take a look at an example:

Project Funding (adequate, marginal, inadequate) Project Staffing (small, large)

Project Risk (low, normal, high)

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The basic structure of Mamdani-style fuzzy inference

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Step 1: FuzzificationThe first step is to take the crisp inputs, x1 and y1 (project funding andproject staffing), and determine the degree to which these inputs belongto each of the appropriate fuzzy sets.

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Step 2: Rule EvaluationThe second step is to take the fuzzified inputs, 𝜇 0.5, 𝜇 0.2, and𝜇 0.1, and apply them to the antecedents of the fuzzy rules. If a givenfuzzy rule has multiple antecedents, the fuzzy operator (AND or OR) is used toobtain a single number that represents the result of the antecedent evaluation.

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Step 3: Aggregation of the rule outputsAggregation is the process of unification of the outputs of all rules. In otherwords, we take the membership functions of all rule consequents previouslyclipped or scaled and combine them into a single fuzzy set. Thus, the input ofthe aggregation process is the list of clipped or scaled consequent membershipfunctions, and the output is one fuzzy set for each output variable.

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Step 4: DefuzzificationThe last step in the fuzzy inference process is defuzzification. Fuzziness helpsus to evaluate the rules, but the final output of a fuzzy system has to be a crispnumber. The input for the defuzzification process is the aggregate output fuzzyset and the output is a single number.

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Step 4: Defuzzification

How do we defuzzify the aggregate fuzzy set?

There are several defuzzification methods, but probably the most popular one isthe centroid technique. It finds the point where a vertical line would slice theaggregate set into two equal masses. Mathematically this center of gravity(COG) can be expressed as:

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A centroid defuzzification method finds a point representing the center of gravityof the fuzzy set, 𝐴, on the interval, 𝑎𝑏. In theory, the COG is calculated over acontinuum of points in the aggregate output membership function, but inpractice, a reasonable estimate can be obtained by calculating it over a sampleof points. In this case, the following formula is applied:

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Fuzzy Logic: Some real applications:

06.11.2018Fuzzy Logic Application - Automatic Speed Controller by Unity C#

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Fuzzy Logic: Some real applications:

06.11.2018NASA | Fuzzy Logic Models for Real-Time Simulations

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Fuzzy Logic: Prof. Lotfi Zadeh, father of fuzzy logic

06.11.2018Lotfi zadeh, father of mathematical 'fuzzy logic,' died at 96

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References:

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1. Lee, C. C. (1990). Fuzzy logic in control systems: fuzzy logic controller. I. IEEE Transactions on systems, man, and cybernetics, 20(2), 404-418.

2. Negnevitsky, M. (2005). Artificial intelligence: a guide to intelligent systems. Pearson Education.

3. Klir, G., & Yuan, B. (1995). Fuzzy sets and fuzzy logic (Vol. 4). New Jersey: Prentice hall.

4. Lochan, K., & Roy, B. K. (2015). Control of two-link 2-DOF robot manipulator using fuzzy logic techniques: A review. In Proceedings of Fourth International Conference on Soft Computing for Problem Solving (pp. 499-511). Springer, New Delhi.

5. Petrosino, A., Loia, V., & Pedrycz, W. (Eds.). (2017). Fuzzy Logic and Soft Computing Applications: 11th International Workshop, WILF 2016, Naples, Italy, December 19–21, 2016, Revised Selected Papers (Vol. 10147). Springer.

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Swarm Intelligence, Fuzzy Logic1...11/5/2018 1 INF3490 -Biologically inspired computing Swarm...

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