## 3 Relevant Research in Wind Farm Design and Optimization
### Solution Methods
#### 3.3.3 Metaheuristic Optimization
The main advantages of local search algorithms are that they are very easy to implement and have few driving parameters. At the same time, they can be very powerful solution procedures for several problems [350,351] including the WFDO problem. The main drawback of local search is that if the search space is too complex (_i.e._, involving many local extreme points and/or many optimal solutions), the algorithm may not converge to the optimal solution. To overcome this limitation, local search metaheuristics use additional heuristics to decide which is the best neighbor solution (_i.e._, neighbor solutions with lower quality may be selected). Different local search procedures have been proposed to solve the WFDO problem. [PERSON] and [PERSON] [265] adopted VNS as a complementary local search procedure to their GRASP implementation, as previously mentioned. VNS was first introduced in 1997 [352] and is quite similar to common local search procedures such as the calculus-based multi-start procedure. VNS performs a local search from multiple neighborhoods and accepts neighbor solutions only if an improvement is made. The difference between the VNS and the multi-start algorithms is that the VNS systematically changes the neighborhoods being explored in two phases: the first phase involves a gradient decent procedure to identify local extreme points, and the second phase involves a random perturbation which allows the algorithm to explore other neighborhoods. Another successful local-search metaheuristic applied to the WFDO problem is the Simulated Annealing (SA) algorithm [327,338]. SA is based on the process of annealing of solids, which is a thermal process for obtaining low energy states in solids by exposing them to a heat bath. The annealing process consists of the following two steps [343]: (1) increase the temperature of the heat bath until the solid melts; and (2) slowly decrease the temperature of the heat bath until the particles arrange themselves in the low energy ground state of the solid. In the melt phase, the constituent particles arrange themselves randomly, and in the cooling stage the particles arrange themselves in an organized lattice. The analogy between the annealing process and the optimization process is that potential solutions of the studied problem are comparable to states of a physical system undergoing a process of annealing, and the quality of a potential solution is equivalent to the energy of a state [338]. While local search (and variable local search) generally will accept transitions between neighbor solutions only if its quality is better than the current solution, SA has the capacity of allow transitions between solutions whose qualities are worse than the current solution in the hope of avoiding getting stuck in a local extreme point. The transition to a worst solution is modeled as a probabilistic process, which relies on the Metropolis criterion [327], and depends on the actual state and the new state quality. The probability of rejection of states with lower quality increase as the search continues (_i.e._, SA behavesas a greedy algorithm), thus simulating the arrangement of particles in an organized lattice during the cooling process. The SA's ease of implementation, convergence properties, and ability to escape local extreme points have made it a popular technique during the past two decades. The SA-based metaheuristic has been implemented to solve different versions of the WFDO problem showing better or equal performance than other metaheuristics such as the genetic algorithm [154,156]. Population-based metaheuristics encompass all solution procedures that use multiple agents or individuals (_i.e._, potential solutions), which are interacted between them, to trace out for better individuals. Population-based algorithms rely on the idea in which the best characteristics of the best individuals can be combined to produce a better individual.