Local beam search

Local beam search is another optimization algorithm that is similar to hill-climbing search. The main difference is that local beam search maintains a set of k candidate solutions, or a beam, instead of just a single solution. At each iteration, the algorithm generates all possible successor solutions for each candidate solution, and selects the k best successor solutions to form the new beam. The algorithm then continues the search from these k best successor solutions.

Local beam search is useful when the search space is too large to be explored exhaustively, and hill-climbing search is likely to get stuck in a local optimum. By maintaining multiple candidate solutions, local beam search can explore multiple regions of the search space in parallel and avoid getting trapped in a local optimum. However, local beam search is still prone to getting stuck in suboptimal solutions if the search space is too large or the beam size is too small.

One disadvantage of local beam search is that it requires more memory than hill-climbing search, since it maintains a set of candidate solutions instead of just a single solution. Another disadvantage is that the search can become trapped in a plateau, where all the candidate solutions have the same objective function value and there are no better successors. To address this issue, variants of local beam search, such as stochastic beam search and beam search with restarts, have been developed to introduce randomness or periodic restarts to the search process.