This document provides an introduction to several metaheuristic optimization algorithms including genetic algorithms, ant colony optimization, simulated annealing, and particle swarm optimization. It describes the basics of each algorithm, including how they were inspired by natural processes and how they can be applied to optimization problems. As an example, it discusses how genetic algorithms and ant colony optimization have been used to optimize municipal waste collection vehicle routing.

1. ECVET Training for Operatorsof IoT-enabledSmart Buildings (VET4SBO)
2018-1-RS01-KA202-000411
Level: 2
Module: 2 - Optimization strategies to meet quality
of service criteria
Unit 2.2 - Introduction to some optimization
algorithms

2. Introduction to some optimization algorithms
• UNIT CONTENTS
– Metaheuristic optimization and its possibilities for
application in contemporary buildings.
– Nature-inspired metaheuristicoptimization and
examples of variety of methods.
– Basics of genetic algorithms.
– Basics of ant colony optimization.
– Basics of simulated annealing.
– Basics of particle swarm optimization.
https://pixabay.com/illustrations/business-
search-seo-engine-2082639/

3. Metaheuristic optimization methods:
• Most famous metaheuristics [5]:
– Genetic Algorithms,
– Simulated Annealing,
– Ant Colony Optimization,
– Bee Algorithms,
– Particle Swarm Optimization,
– Tabu Search,
– Harmony Search,
[5] Sörensen, Kenneth; Sevaux, Marc; Glover, Fred (2017). "A History of Metaheuristics" (PDF). In Martí, Rafael; Panos, Pardalos; Resende, Mauricio
(eds.). Handbook of Heuristics. Springer. ISBN 978-3-319-07123-7.

4. Metaheuristic optimization methods:
• Most famous metaheuristics [5]:
– Firefly Algorithm,
– Cuckoo Search,
– Grey Wolf Optimizer,
– Bat Algorithm,
– Memetic Algorithm,
– Artificial Immune Systems,
– Cross-entropy Method,
– Bacterial Foraging Optimization,
etc.
[5] Sörensen, Kenneth; Sevaux, Marc; Glover, Fred (2017). "A History of Metaheuristics" (PDF). In Martí, Rafael; Panos, Pardalos; Resende, Mauricio
(eds.). Handbook of Heuristics. Springer. ISBN 978-3-319-07123-7.

5. Classification of
metahuristic
optimization
methods
Johann "nojhan" Dréo, Caner Candan - Metaheuristics classification (french version),
https://commons.wikimedia.org/w/index.php?curid=16252087

6. Genetic Algorithms
• Genetic algorithms (GAs) are probably
the most popularevolutionary
algorithms with a diverse range of
applications.
• Genetic algorithms, developed by John
Holland in the 1960s and 1970s, are a
model or abstractionof biological
evolution based on Charles Darwin's
theory of natural selection.
https://pixabay.com/illustrations/dna-microscopic-cell-
gene-helix-1903318/

7. Genetic Algorithms
• In computer science and operations
research, a genetic algorithm (GA) is a
metaheuristic inspired by the process
of natural selection that belongs to
the larger class of evolutionary
algorithms (EA). https://pixabay.com/vectors/evolution-evolving-
mankind-men-ape-1295256/

8. Genetic Algorithms
• Genetic algorithms are commonly used to generate
high-quality solutions to optimization and search
problems by relying on bio-inspired operators such
as mutation, crossover and selection.
• John Holland introduced genetic algorithms in 1960
based on the concept of Darwin’s theory of
evolution; afterwards, his student David E. Goldberg
extended GA in 1989 [2].
» [2] Goldberg, David (1989). Genetic Algorithms in Search,
Optimization and Machine Learning. Reading, MA: Addison-
Wesley Professional. ISBN 978-0201157673.
https://pixabay.com/photos/charles-
robert-darwin-scientists-62911/

9. Genetic Algorithms
• Holland was the first to use crossover, recombination,
mutation and selection in the study of adaptive and artificial
systems.
• These genetic operators are the essential componentsof
genetic algorithms as a problem-solving strategy.
• Since then, many variants of genetic algorithms have been
developed and applied to a wide range of optimization
problems.

10. Genetic Algorithms
• GA involves the encoding of solutions as
arrays of bits or character strings
(chromosomes), the manipulationof these
strings by genetic operators and a selection
based on their fitness to find a solution to a
given problem.
https://pixabay.com/illustrations/cyborg-
board-dna-conductors-4094940/

11. Genetic Algorithms
• This is often done through the following procedure:
– 1) definition of an encoding scheme;
– 2) definition of a fitness function or selection criterion;
– 3) creation of a population of chromosomes (generation);
– 4) evaluation of the fitness of every chromosome in the population;
– 5) creation of a new population by performing fitness-proportionate
selection, crossover and mutation;
– 6) replacement of the old population by the new one.
• Steps 4), 5) and 6) are then repeated for a number of generations.
At the end, the best chromosome is decoded to obtain a solution
to the problem.

12. Genetic Algorithms
• A two-population
EA search of a
bounded optima
of Simionescu's
function.
By Pasimi - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=37611580

13. Ant Colony Optimization
• Ant colony optimization [1] was pioneered by
Marco Dorigo in 1992 [2] and is based on the
foraging behaviour of social ants.
• Many insects such as ants use pheromone as a
chemical messenger.
• Ants are social insects and live together in
organized colonies.
» [1] Ant colony optimization algorithms,
https://en.wikipedia.org/wiki/Ant_colony_optimization_
algorithms
» [2] M. Dorigo, Optimization,Learning and Natural
Algorithms, PhD thesis, Politecnico di Milano, Italy, 1992.
https://pixabay.com/photos/peony-bud-
ants-rain-drip-raindrop-1414875/

14. Ant Colony
Optimization
https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms#/media/File:Artificial_ants.jpg
Jean-Baptiste Waldner - Source : "Nanocomputers and Swarm Intelligence", Jean-Baptiste
Waldner, John Wiley & Sons, 2008.

15. Ant Colony Optimization
• When foraging, a swarm of ants or mobile
agents interact or communicatein their
local environment.
• Each ant lays scent chemicals or pheromone
to communicate with others. https://pixabay.com/photos/ants-red-ant-
climb-the-tree-branch-1370824/

16. Ant Colony Optimization
• Each ant is also able to follow the route
marked with pheromone laid by other ants.
• When an ant finds a food source, it will
mark it with pheromone and also mark the
trail to and from it.
• In the figure, the ants prefer the smaller
drop of honey over the more abundant,
but less nutritious, sugar.
CC BY-SA 2.5,
https://commons.wikimedia.org/w/index.php?curid=1122164

17. Ant Colony Optimization
• From the initial random foraging route, the pheromone
concentrationvaries and the ants follow the route with
higher pheromone concentration.
• In turn, the pheromone is enhanced by the increasing
number of ants.
• As more and more ants follow the same route, it becomes
the favored path.

18. Ant Colony Optimization
• Thus, some favorite routes emerge, often the
shortest or more efficient ones.
• This is actually a positive feedback mechanism.
• As the system evolves, it converges to a self-
organized state, which is the essence of any ant
algorithm.
By Mehmet Karatay - Own work, CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.php?
curid=2179109

19. Ant Colony Optimization
• The ant colony optimization of the travelling salesman problem: 1) an ant choose a path among
other, and lay a pheromonal trail on it. 2) all the ants are travelling some paths, laying a trail
proportionnal to the quality of the solution. 3) each edge of the best path is more reinforced
than others. 4) the evaporation makes disapear the bad solutions.
By Nojhan - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=820846

20. Simulated Annealing
• Simulated annealing [1] is based on the
metal annealing processing [2].
• Unlike the gradient-based methods and
other deterministic methods, advantage
of simulated annealing is its ability to
avoid being trapped in local optima.
» [1] Simulated annealing,
https://en.wikipedia.org/wiki/Simulated_anneal
ing
» [2] Kirkpatrick, S.; Gelatt Jr, C. D.; Vecchi, M. P.
(1983). "Optimization by Simulated Annealing".
Science. 220 (4598): 671–680.
https://pixabay.com/photos/pour-iron-foundry-
heat-fire-hot-4455451/

21. Simulated Annealing
• Simulated Annealing can be
used to solve combinatorial
problems.
• Here it is applied to
the travelling salesman
problem to minimize the
length of a route that
connects all 125 points.
By Geodac - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=67988888

22. Simulated Annealing
• Metaphorically speaking, this is equivalent to dropping some
bouncing balls over a landscape, and as the balls bounce and lose
energy, they settle down in some local minima.
• If the balls are allowed to bounce long enough and to lose energy
slowly enough, some of the balls will eventually fall into the globally
lowest locations, hence the global minimum will be reached.
• Essentially, simulated annealing is a search along a Markov chain,
which converges under appropriate conditions.

23. Simulated Annealing
• Metaphorically speaking, this is equivalent to dropping some bouncing
balls over a landscape, and as the balls bounce and lose energy, they
settle down in some local minima.
• If the balls are allowed to bounce long enough and to lose energy slowly
enough, some of the balls will eventually fall into the globally lowest
locations, hence the global minimum will be reached.
• Essentially, simulated annealing is a search along a Markov chain, which
converges under appropriate conditions.
By Kingpin13 - Own work, CC0,
https://commons.wikimedia.org/w/index.php?curid=25010763

24. Particle Swarm Optimization
• Particle swarm optimization [1] (PSO) was developed
by Kennedy and Eberhart in 1995 [2], based on swarm
behaviour observed in nature such as fish and bird
schooling.
• Since then, PSO has generated a lot of attention, and
now forms an exciting, ever-expanding research
subject in the field of swarm intelligence.
• PSO has been applied to almost every area in
optimization, computational intelligence, and
design/scheduling applications.
» [1] Particle swarm optimization
https://en.wikipedia.org/wiki/Particle_swarm_optimization
» [2] Kennedy, J.; Eberhart, R. (1995). "Particle Swarm
Optimization". Proceedings of IEEE International Conference on
Neural Networks. IV. pp. 1942–1948.
https://pixabay.com/photos/fish-swarm-underwater-
fish-swarm-1656504/

25. Particle Swarm Optimization
• Particle swarm optimization (PSO) was
developed by Kennedy and Eberhart in 1995,
based on swarm behaviour observed in
nature such as fish and bird schooling.
• Since then, PSO has generated a lot of
attention, and now forms an exciting, ever-
expanding research subject in the field of
swarm intelligence.
• PSO has been applied to almost every area in
optimization, computational intelligence, and
design/scheduling applications.
https://pixabay.com/photos/seagulls-beach-gulls-
birds-wings-815304/

26. Particle Swarm Optimization
• PSO searches the space of an objective
function by adjusting the trajectories of
individual agents, called particles.
• Each particle traces a piecewise path
which can be modelled as a time-
dependent positionalvector. By Ephramac - Own work, CC BY-SA 4.0,
https://commons.wikimedia.org/w/index.php?curid=54975083

27. Particle Swarm Optimization
• The movement of a swarming particle
consists of two major components: a
stochastic component and a
deterministic component.
• Each particle is attracted toward the
position of the current global best and
its own best known location, while
exhibiting a tendency to move
randomly.
By Ephramac - Own work, CC BY-SA 4.0,
https://commons.wikimedia.org/w/index.php?curid=54975083

28. Example of metaheuristic algorithms applied to
engineering optimization problem
• Genetic and Ant Colony Optimization Based Communal Waste
Collection Vehicle Routing
– The problem of routing vehicles for the collection of municipal waste is
considered, which has been increasingly explored in recent years.
– A logistic model for municipal waste management has been used to
select the optimal routes of collecting and transporting municipal waste
for a realisticexample of the city of Niš in Serbia.
– Two metaheuristic methods - genetic algorithm (GA) and ant colony
optimization (ACO) – have been used to solve the problem of waste
collection vehicles routing.

29. Example of metaheuristic algorithms applied to
engineering optimization problem
Marković D., Stanković A., Petrović G., Trajanović M.,ĆojbašićŽ.,Genetic and Ant Colony Optimization Based
Communal WasteCollection VehicleRouting, Proceedings of ICIST 2019,Kopaonik,Serbia.

30. Example of metaheuristic algorithms applied to
engineering optimization problem
Marković D., Stanković A., Petrović G., Trajanović M.,ĆojbašićŽ.,Genetic and Ant Colony Optimization Based
Communal WasteCollection VehicleRouting, Proceedings of ICIST 2019,Kopaonik,Serbia.

31. Thank you for your attention.
https://pixabay.com/illustrations/thank-you-polaroid-letters-2490552/

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This project (2018-1-RS01-KA202-000411) has been funded with support from the European Commission (Erasmus+
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