• Branch-and-Bound (B&B) becomes the central solving paradigm for discrete optimization across facility location, knapsack, and MILP problems, leveraging problem structure, duals, and pruning. Early papers demonstrate B&B's adaptability to plant location, knapsack, and mixed-integer programs. [3] [8] [9] [10] [14] [15] [18] [20]

• Cutting planes and cuts (Gomory-type, intersection, generalized) are introduced to tighten ILP relaxations, enabling more aggressive pruning and faster convergence, often integrated with branch-and-bound. [11] [12] [20]

• Transformational approaches recast discrete problems into knapsack-type or group optimization problems, enabling dynamic programming or structured decomposition to solve them. [6] [5] [4] [13] [2]

• Direct search, filter-based methods and heuristic strategies provide early practical solutions, separating easy feasibility from harder tests to rapidly solve or approximate discrete problems. [1] [7] [17] [16]

• Knapsack function theory and turnpike relations connect discrete optimization with numerical function analysis and renewal theory, yielding efficient computation and structural insights. [4] [5] [13] [2]