The document discusses different types of nature-inspired metaheuristics used for optimization problems. It describes deterministic methods like hill-climbing that always produce the same output for a given input, and stochastic methods like genetic algorithms that can produce different outputs for the same input due to randomness. Gradient-based methods use gradients to find optimal parameters, while gradient-free methods do not. Metaheuristics employ intensification to exploit good solutions locally and diversification to explore globally. Population-based metaheuristics maintain a set of candidate solutions, while trajectory-based methods rely on a single agent. Examples of various metaheuristics are provided.

1. Nature-Inspired Metaheuristics

2. Deterministic vs Stochastic
 Deterministic
 Always give the same outcome given the same input
 Example: Hill-climbing and downhill simplex
 Stochastic
 Meaning: random, probabilistic
 Give different outcomes for the same input
 Example: Genetic algorithms and PSO

3. Gradient
 Any optimization method basically tries to find
the nearest/next best parameter(s) form the
initial parameter(s) that will optimize the given
function (done iteratively with the expectation to
get the best parameter(s) ).

4. Gradient-based vs Gradient-Free Algorithms
 Gradient-based Algorithms (Deterministic)
 The optimization method that uses gradient to get this
parameter(s)
 Example
 Newton-Raphson algorithm
 Gradient-free Algorithms (Non gradient-based)
 The optimization method that will not uses gradient to
get this parameter(s)
 Example
 Hooke-Jeeves pattern search
 Nelder-Mead downhill simplex

5. Stochastic Method
 Heuristics
 Heuristic means “to find” or “to discover by trial
and error”
 Metaheuristics
 Meta means “beyond” or “higher level”

6. Metaheuristic Algorithms:Component
 Component:
 Intensification (or exploitation )
 Diversification (or exploration)

7. Metaheuristic Algorithms:Component
 Diversification means to generate diverse solutions so as
to explore the search space on a global scale
 Algorithm searching for new solutions in new regions,
 Intensification means to focus on the search in a local
region by exploiting the information that a current good
solution is found in this region
 Use already exist solutions and make refinement to it so it's fitness
will improve

8. Metaheuristic algorithms
 Population-based
 An algorithm that maintains an entire set of candidate solutions,
each solution corresponding to a unique point in the search space
of the problem
 Use multiple agents and hence tend to perform better
 Example
 genetic algorithms
 particle swarm optimization
 firefly algorithm (FA)
 Cuckoo search
 Trajectory-based
 Rely on single-agent to search through solution space
 Example
 Simulated annealing

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