Balancing a pole on a moving cart is a standard benchmark problem of control engineering. A related control problem has to be solved within the Segway personal transporter. In this exercise, we implement the most basic pole balancing problem (one single pole mounted on a cart that is only able to move in one dimension where we abstract from friction).
After implementing the pole balancing problem and getting an intuition about how difficult it is to design the linear controller for it, we will now apply fuzzy logic to create a controller that does not use all possible input measurements of the cart.
Pure Random Search (PRS) and the (1+1)EA are very simple search heuristics for discrete search spaces. Here, we consider their performance on the pseudo-boolean (i.e. dependent on bitstrings) functions ONEMAX and NEEDLE.
In the exercises on continuous optimization, we consider the (1+1)ES as well as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The following exercise sheet contains the exercises for the two lectures on February 1 and February 22.
The traveling salesperson problem is asking for a shortest Hamiltonian cycle in a given graph and obviously has several applications. In this exercise, we are going to implement a simple genetic algorithm for this problem.
We already looked at the problem of balancing a single pole on a moving cart with the help of a linear controller in a previous exercise. However, we always simulated the pole for a single (fixed) starting condition. In this exercise, we look more carefully at the problem of finding robust solutions such that the controller works for arbitrary starting conditions. To this end, we will use an artificial neural network as controller and CMA-ES to optimize its weights.
Using fitness-based partitions turned out to be a basic approach to prove upper bounds of the expected runtime of simple single-objective algorithms such as the (1+1)EA on easy pseudo-boolean functions. This approach can also be used to analyze simple evolutionary multiobjective optimizers. In this exercise, we consider the Simple Evolutionary Multiobjective Optimizer (SEMO) on the Leading Ones Trailing Zeros (LOTZ) problem.