Commit 13d34447 authored by Julien Lin's avatar Julien Lin
Browse files

minor fixes

parent 347a6b34
......@@ -16,7 +16,6 @@ Introduction
> Easy to evaluate = fast, but not as fast as the algorithm itself.
> Hard to solve, but not impossible.
Hard optimization
-----------------
......@@ -31,15 +30,10 @@ Usually, the set $X$ is defined intentionally and constraints on $x$ are managed
For example, using a function $g:x\mapsto \{0,1\}$:
$$\argmin_{x\in[0,1]^n} f(x),\quad\text{s.t.}\quad g(x)=0$$
[^argminmax]: In the metaheuristics literature, $\argmax$ is often assumed for evolutionary algorithms, whether $\argmin$ is often assumed for local search or simulated annealing.
Complete VS approximation VS heuristics.
Algorithmics
============
......@@ -63,7 +57,6 @@ Algorithmics
>
> The better you understand it, the better the algorithm will be.
Naive algorithms
----------------
......@@ -85,11 +78,11 @@ Naive algorithms
- When is a random walk convergent?
- Example: 2D fixed-step size random walk.
Descent Algorithms
-----------------
Generic template:
```python
x = None
p = uniform(xmin,xmax)
......@@ -100,6 +93,7 @@ for i in range(g):
```
Greedy algorithm:
```python
def select(x,p):
if better(f(x),f(p)):
......@@ -110,7 +104,6 @@ def select(x,p):
What are the conditions for which a greedy algorithm would converge?
Simulated Annealing
-------------------
......@@ -136,6 +129,7 @@ Evolutionary Algorithms
-----------------------
Generic template:
```python
P = uniform(xmin,xmax,n)
for i in range(g):
......@@ -145,6 +139,7 @@ for i in range(g):
```
More complete template:
```python
def evol(f):
opt = float('inf')
......@@ -159,6 +154,7 @@ def evol(f):
```
Evolution Strategies (ES), numerical space:
```python
def variation(parents):
P = []
......@@ -167,6 +163,7 @@ def variation(parents):
```
Genetic Algorithm (GA), boolean space:
```python
def variation(parents):
crossed = crossover(parents)
......@@ -177,7 +174,6 @@ def variation(parents):
Is ES convergent?
If $$#P=1$$, what are the differences with a random walk?
Estimation of Distribution Algorithms
-------------------------------------
......@@ -192,7 +188,6 @@ What would be an example for numerical problems?
For boolean problems?
How to ensure convergence?
Ant Colony Algorithms
---------------------
......@@ -211,14 +206,12 @@ Covariance Matrix Adaptation Evolutionary Strategies
TODO
Problem modelization
====================
> Way to assess the quality: fitness function.
> Way to model a solution: encoding.
Main models
-----------
......@@ -245,6 +238,7 @@ Constraints management
----------------------
> Main constraints management tools for operators:
>
> - penalization,
> - reparation,
> - generation.
......@@ -291,7 +285,6 @@ What is performance
>
> Golden rule: the output of a metaheuristic is a distribution, not a solution.
### Run time and target quality
One may think that the obvious objective of an optimization algorithm is to find the location of the optimum.
......@@ -304,7 +297,6 @@ and conversely, the quality of the solution which can be found in a given runtim
Of course, those two metrics tend to be contradictory: the more time is given to the search, the best the solution,
and conversely, the better the solution one want, the longer the run should be.
### Measuring time and quality
To measure the run time, a robust measure of time should be available.
......@@ -318,7 +310,6 @@ However, this may vary a lot across problem instances and be read differently if
maximization problem.
It may thus be useful to use the error against a known bound of the problem.
### Probability of attainment
For metaheuristics which are based on randomized process (which is the vast majority of them), measuring time and
......@@ -336,10 +327,8 @@ In order to have a good mental image of how to asses the performance of a solver
one should relize that we can only *estimates* the performances, considering *at least* run time, quality
*and probability* of attaining a fixed target.
### Robustness and stability
Empirical evaluation
--------------------
......@@ -399,7 +388,6 @@ Empirical Attainment Function is a generalization of an ECDF of the
value trajectories, i.e. the generic view on a stochastic solver's
performance.*
## Other tools
> Convergence curves: do not forget the golden rule and show distributions:
......@@ -408,7 +396,6 @@ performance.*
> - violin plots,
> - histograms.
Algorithm Design
================
......@@ -426,7 +413,6 @@ Algorithm Design
>
> Relationship to metric space in the continuous domain.
## Structure of problem/algorithms
> Structure of problems to exploit:
......@@ -447,7 +433,6 @@ Algorithm Design
> - taking constraints into account,
> - iterate between problem/algorithm models.
## Grammar of algorithms
> Parameter setting < tuning < control.
......@@ -478,7 +463,6 @@ Design tools:
- DEAP,
- HeuristicLab.
## Landscape-aware algorithms
> Fitness landscapes: structure of problems as seen by an algorithm.
......@@ -488,4 +472,3 @@ Design tools:
> Examples: SAT, TSP, BB.
>
> Toward automated solver design.
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