### Summary

A Metaheuristic is a higher-level procedure used to find the best possible decision for complex problems by approximating the optimal solution. This method doesn’t guarantee an absolute optimal solution, but strives to find ‘good enough’ solutions for complex problems within a feasible time span.

### ELI5

Imagine you lost your toy in a large room full of toys. To find your toy, you wouldn’t check each toy one by one (which could take forever), but instead, you’d follow a plan: maybe start searching the room where you usually play, or checking under the bed because toys often end up there. This strategy to find your toy is like a Metaheuristic - it’s not guaranteed to find the toy fastest, but it’s a smarter way to start and saves time.

### In-depth explanation

Metaheuristics guide underlying heuristics to search efficiently through a problem’s feasible solutions space. They search from one solution to another and continually aim to improve the current solution. The majority of metaheuristics possess a set of operators that modify solutions to traverse the feasible solution space.

Some typical strategies that metaheuristics use include greedy random search, simulated annealing, or genetic algorithms.

• Greedy random search: It’s greedy because it always takes the best immediate option, and random because it sometimes makes less optimal short-term choices to explore different possibilities.

• Simulated annealing: Named after the physical annealing process of solids, this algorithm allows ‘worse’ moves to escape local minimums using a method akin to controlled random walks.

• Genetic algorithms: These employ the biological concepts of mutation and crossover to exchange valuable information between solutions and promote solution diversity.

By incrementally improving upon solutions, metaheuristics can effectively bypass the problems associated with exhaustive search methods. While this won’t always generate the ‘global best’ solution—akin to checking every toy in our ELI5 example—it often results in significantly reasonable and efficient solutions for complex problems.

Even though they don’t guarantee an optimal solution, metaheuristic approaches are beneficial for the complex, real-world problems data scientists frequently deal with—problems with multiple objectives, constraints, and uncertainties, where the best solution isn’t clear.

Optimization, Heuristic, Genetic Algorithm, Simulated Annealing, Local Search, Tabu Search, Swarm Intelligence.