Start by understanding the Max-Cut problem: it aims to partition the vertices of a graph into two sets such that the number of edges between the sets is maximized. Consider how local search can iteratively improve a solution by flipping vertices between sets.

Implement a greedy local search approach: begin with an arbitrary partition of vertices, then iteratively flip vertices that increase the cut value (number of edges crossing the partition) until no further improvement is possible. Track the best solution found during this process.

Enhance the local search with randomization: introduce techniques like simulated annealing or tabu search to escape local optima. Experiment with different neighborhood structures (e.g., flipping multiple vertices at once) and cooling schedules to balance exploration and exploitation.