L11: Optimisation & Metaheuristics

Question 1

What is optimisation?

Answer 1

Optimizing Changing something to improve something
Changing wind farm variables to increase expected power

Optimal The best possible
Producing the maximal possible expected power

Optimization The search for the optimal

Satisfying Ensuring given requirements are met
Do not place turbines outside the site boundaries

Feasible Satisfying the given requirements
All turbine positions are within the site boundaries

Question 2

Name the optimisation terminology and what they mean

Answer 2

Optimizing Maximizing/Minimizing
Objective That which defines what ‘improving’, ‘better’, ‘best’ means
The expected power
* Usually considered as a function (e.g., denoted f )
* Also called: goal; gain, utility (max); loss, cost (min)

Variables Controllable things affecting the objective (optimization –, design –)
Turbine positions (xi
, yi), heights hi, types ti)

Solution A set of values for the optimization variables
(xi, yi) = (3.1 km, −2.6 km), hi = 140 m, ti = Haliade X
* optimal solution(s)
* feasible solutions

Constraint Requirement on the solutions
All (xi
, yi) inside set delimited by site boundaries;

Question 3

Name the categorisations of optimisation problems

Answer 3

Unconstrained vs. Constrained

Discrete vs. Continuous

Single- vs. Multi-objective

Global vs. Local

Single (global) optimum vs. Multiple (local) optima

Convex vs. Non-convex

Question 4

Describe possible optimisation techniques

Answer 4

Enumeration of all feasible solutions

Iteration (improve it step by step)

Question 5

Name some examples of metaheuristics

Answer 5

Simulated annealing

Evolutionary algorithms

Particle swarm optimisation

Question 6

Explain how simulated annealing works

Answer 6

Simulated annealing is a method for solving unconstrained and bound-constrained optimization problems. The method models the physical process of heating a material and then slowly lowering the temperature to decrease defects, thus minimizing the system energy.

At each iteration of the simulated annealing algorithm, a new point is randomly generated. The distance of the new point from the current point, or the extent of the search, is based on a probability distribution with a scale proportional to the temperature. The algorithm accepts all new points that lower the objective, but also, with a certain probability, points that raise the objective. By accepting points that raise the objective, the algorithm avoids being trapped in local minima, and is able to explore globally for more possible solutions. An annealing schedule is selected to systematically decrease the temperature as the algorithm proceeds. As the temperature decreases, the algorithm reduces the extent of its search to converge to a minimum.

Question 7

Explain how evolutionary algorithms work

Answer 7

The premise of an evolutionary algorithm (to be further known as an EA) is quite simple given that you are familiar with the process of natural selection. An EA contains four overall steps: initialization, selection, genetic operators (crossover and mutation), and termination. These steps each correspond, roughly, to a particular facet of natural selection, and provide easy ways to modularize implementations of this algorithm category. Simply put, in an EA, fitter members will survive and proliferate, while unfit members will die off and not contribute to the gene pool of further generations, much like in natural selection.

Measured against a fitness function- numerical representation of how viable solution is. Select a portion of top scoring members

Question 8

Explain how particle swarm optimisation works