Optimization Algorithms

Optimization algorithms search for the best solution in a space of possibilities: maximise reward or minimise cost. Greedy methods (e.g. hill climbing) move toward better neighbours and stop at a local optimum — fast but can get stuck. Random restart runs hill climbing from many starts to improve the chance of finding a global optimum. Simulated annealing allows occasional downhill moves early on, then "cools" to reduce randomness and settle near a good solution. Metropolis and related MCMC methods use probabilistic acceptance to explore the space. The tradeoff: exploitation (refining the current best) vs exploration (trying new regions). Different algorithms tune that tradeoff differently.

When the landscape has many local optima, pure hill climbing can trap you. Use random restart (many independent runs) or simulated annealing (allow bad moves early, then reduce randomness). When the objective is noisy or expensive to evaluate, balance exploitation and exploration explicitly. Match the algorithm to the problem: smooth single peak → hill climbing; rugged landscape → restart or annealing.

Optimization algorithms search for best solutions: hill climbing (greedy), random restart (many runs), simulated annealing (controlled exploration then refinement). Use them when the landscape has local optima; match the algorithm to the ruggedness of the problem.