Grammar Evolution is a type of evolutionary optimization where solutions are generated using a predefined set of rules, like a grammar in language. Imagine creating sentences using grammar rules, but here, the 'sentences' are computer programs or formulas. Each solution must follow these rules, ensuring they make sense. Like in genetic programming, these solutions evolve over generations, becoming better at solving a problem. It's particularly useful when solutions need a specific structure or format, allowing for complex, yet orderly, evolution.

A Genetic Algorithm is a method in evolutionary optimization that solves problems by mimicking natural evolution. Imagine a survival contest where each participant (solution) has traits (parameters). These solutions breed and mutate, creating new generations. The fittest solutions, judged by a fitness function, survive to breed again. Over time, this process 'evolves' increasingly effective solutions. It's like nature's trial-and-error but used for complex problems like route planning, where finding the best or a good-enough solution is essential.

Genetic Programming (GP) is a type of evolutionary optimization where programs themselves evolve to solve problems. Imagine a computer automatically writing and modifying its own code to get better at a task. In GP, each 'individual' is a computer program. These programs are tested for their ability to solve a problem, and the best ones are modified (mutated) or combined (crossed over) to create new programs. Over generations, this process evolves programs that become increasingly effective at the task.