Lecture 15 - Population Based Algorithms Flashcards

Question

Why does the (μ, λ) Strategy work?

Answer 1

- Encourages exploration: Parents are not reused, reducing risk of local optima trapping. - Truncation ensures only high-quality parents breed. - Mutation introduces new variations in every generation.

Answer 2

λ – Population (Sampling) Size μ – Selectivity (Number of Parents) Mutate() – Variation Operator

Answer 3

"This is how many candidate solutions (children) we generate per generation." Bigger λ = more coverage of the search space (more exploration). It's similar to n in steepest ascent hill climbing (number of directions sampled). But: Bigger λ means higher computational cost. If λ → ∞, the strategy becomes just random search, since you're covering the space blindly.

Answer 4

"This controls how picky we are about who gets to be a parent." Smaller μ = more exploitation: focusing only on top performers. Larger μ = more diversity, allowing weaker candidates to contribute (more exploration). Too small a μ may cause premature convergence.

Answer 5

"This controls how much randomness we inject into the children." Mutation probability and mutation strength determine: How far the children can move from the parents. Whether we explore new areas or fine-tune current solutions. Mutation plays a critical role in avoiding local optima and encouraging discovery.

Answer 6

- Encourages diversity by not reusing parents. - Useful in early stages of search when you want to explore the space. - Reduces risk of getting stuck in local optima. - Simpler and sometimes more parallelisable, since only offspring are evaluated.

Answer 7

- Can lose good solutions because parents are thrown away. - Slower to refine near good solutions. - May need larger λ to maintain enough diversity for progress.

Answer 8

"In the (μ + λ) strategy, we start with μ parents, generate λ children, then pick the best μ from both parents and children combined to be the next parents." REFER TO SLIDES FOR CODE

Answer 9

- When you want to preserve good solutions over time (elitism) - Good if you’re close to convergence and want refinement - But beware of premature convergence if diversity is lost too early

Answer 10

- Ensures good solutions are not lost (elitism). - More exploitative — good for fine-tuning and convergence. - Fitness usually improves or stays stable over generations. - Often more efficient in late-stage optimisation.

Answer 11

- Risk of premature convergence — strong parents can dominate and reduce diversity. - Less exploratory — may not escape local optima once stuck. Needs mechanisms (like mutation or diversity control) to maintain variation.

Answer 12

REFER TO SLIDES

Answer 13

- “In the (μ + λ) strategy, the offspring compete with the parents to survive into the next generation. In (μ, λ), the parents are thrown out and only the children are considered.” ○ This key change makes (μ + λ) more conservative and focused on exploitation, while (μ, λ) is more exploratory. Exploitation vs Exploration - “Because (μ + λ) keeps the parents in the running, it’s better at preserving good solutions — but that also means it’s more likely to get stuck in a local optimum.” ○ (μ + λ): Less chance of losing good solutions → More exploitation ○ But: Also more likely to converge prematurely if diversity is lost ==== NOTE: Think of population size (μ) and offspring count (λ). When these are small, population algorithms reduce to single-state strategies. - Similar to the three hill climb examples

Answer 14

- Maintaining Diversity ○ “In population-based algorithms, it’s important to maintain diversity, especially early on. This helps the algorithm explore the space and avoid getting trapped.” - Gradual Convergence ○ “Over time, it’s normal to reduce diversity to encourage convergence — that is, to focus the search around the best regions we've found.” ○ This is called exploitation — zooming in on the best. - Premature Convergence ○ “But if diversity drops too quickly, we get premature convergence — the population becomes too similar, and we stop exploring. This can cause us to miss better solutions elsewhere in the space.” ○ This is dangerous because we can’t be sure we’ve found a globally good solution — only a local one.

Answer 15

Typical use - fixed-length vector of real-valued numbers (“chromosome”) - mutation performed using “Gaussian Convolution” (Alg. 11) - recall Gaussian mutation controlled by (or ) - called the mutation rate of ES

Answer 16

- guess? - run experiments to find a good value for the problem at hand - run a meta-optimisation! - decrease over time (cf. simulated annealing) - adaptively change based on some statistic(s) of the system…

Answer 17

REFER TO SLIDES

Answer 18

- “It’s the idea that the mutation parameters themselves (like how much to mutate or how likely) can evolve along with the individuals.” ○ In other words, instead of manually setting or adapting the mutation rate globally, we let each individual carry its own mutation settings — and those settings can mutate and evolve too.

Answer 19

* Each individual: ○ Has a solution (e.g., vector of variables). ○ Has a mutation strategy or parameter (e.g., σ — mutation step size). * When the individual reproduces: ○ It copies and mutates both: § Its solution. § Its mutation settings. * Over generations: ○ Good mutation strategies survive and propagate. ○ Bad ones are discarded with poor solutions. This is what we mean by "mutation operators themselves might mutate."

Answer 20

* Encourages dynamic, local adaptation. * Allows the algorithm to adjust automatically to different parts of the search space. * Particularly useful for complex or rugged landscapes like the one shown (Rosenbrock’s function in the image).

Answer 21

* “Imagination is the limit” — but don’t go overboard. * You must justify added complexity: * Use Occam’s Razor: keep things simple unless complexity clearly helps. * Only keep the feature if empirical results prove it’s beneficial.